UNIVERSITY OF NORTH CAROLINA
Department of Statistics
Cilapel Hill, N. C.
TABLE OF PERCENTAGE POINTS OF
GIVEN .[f3
1
AND
f32
Su
CURVES, FOR
' EXPRESSED IN STANDARD MEASURE
by
N. L. Joimson
September 196h
Grant No. AF-84-63
Tables are provided Wid cll facilitate fitting
distribution, vhlen an inverse hyperbolic sine
transformation is approximately nor~alizing.
T.Llis research was supported by ti.le Matllematics Division of ti.le Air Force
Office of Scientific Researci.l.
Institute of Statistics
Mimeo Series No. 408
TABLE OF PERCENrAGE POINTS OF ,Su
GIVEN
J"131
CURVES,
FOR
132 , EXPRESSED IN STANDARD MEASURE l
AJ:ID
by
N. L. Johnson
===================================================================================
Description of Tables
If
z is a unit normal variable and y
is a random variable related to
z
by the equation
=
z
the distribution of
Replacing
e
y
y
'Y +
8 fey)
will be called
(y' - 1; )/A
by
Su
if
fey) - sinh
-1
y (see [1]). ( 0 > 0)
we have a four-parameter family of distributions.
The moment ratios of this family, however, depend only on
'Y
and
8
•
Explicit
formulas can be obtained, in a straightforward manner, for the moments of y (and
so also the moment. ra:tios of y
or
y') given 'Y and
8 •
In
[1]
it is shown
that
1J.2 (y}
= = i
~(y)
=
1J.4(Y}
=
JJi.(y)
sinh 0
(w - l)(W cosh 20
- t lJJ
(w -
+ 1)
1)2 (w (w+ 2)sinh 30 + 3 sinh o)
~ (w _ 1)2 (w
2{ w4 +2J3+3!.J2_3 ) cosh'
4
n ..-
+ 4w2(w+ 2) cosh 20 + 3 (2W + 1) }
where
w
=
2
exp(8- ),
0 ='Y
18 •
,[1\{y} = <- }(Y»/( 1J.2 (y})3/ 2 ana
can be written down, but it is not possible to invert
From these formulas expressions for
f3 (y) = 1J.4(y}/[ 1J.2 (y)]2
2
these formulas to give expressions for
'Y
and
It is the purpose of these tables to provide
8 in terms of
.ff31
and
132 •
2
(a)
and
(b)
Values of '1 and 8
corresponding to a number of selected val.ues of
.rf\
132 •
Standardized percentage points (that is, corresponding to a distribution with
mean zero and ntandard deviation l}for the se same values of .r13
1
Once the values of
'1 and
and
132 •
8 , as described in (a) are known, it is a very
simple matter to find the val.ues described in (b) since
Pr[z ~
Z]
=
Prey ~ sinh
(Za7 )]
Using this formula any specified percentage points can be rapidly obtained.
only necessary to find the appropriate value far
e
It is
Z from tables of percentile
points of the unit normal distribution.
It might be felt that it is unneeeenry to give the tabulated values described
in (b), since they can be so easily calculated once '1 and 8 are known. However,
comparison with
presentation in this form facilitates/similar tables [2] for Pearson Curves, and
also aids rapid approxinate fitting of
~
curves.
Comparison with Pearson Curves, and other uses of these Tables will be
described in a separate publication.
Here we will discuss only the method of calcu-
lation.
~od
of Calculation.
Use was mde of expressions for
132 obtained by Leslie [3],
13 and
1
combined with some empirical evidence on the W"d.y in which
an
with '1
and
8 ,based on/abac in [1].
In [3]
132 are obtained
the following formulas for
2
(1)
131
=
mew - 1)[4(w + 2)m + 3(w + 1)2]_
2(2m + w + 1)3
131 and
f32 vary
3
(W-l) [8( tJP+3uF-+6w +6)rrP+&y.( w4 +3ut'+.§uP+7wt-i)+uP+3uf*+6uY+10uP+9Wi:3
2(2m + w + 1)2
m = w sinh2 n •
where
~2' the corresponding value of
Given 8 and
explicit form.
order to find the pair of values
(
~1'
(
8
1
~l (
81 ,
of
can then be obtained from (1).
8 , ~2) ,of '1 corresponding to a
1
8 and the given value of
~2.
Next, the corresponding
~2) of
~l
'1 (
is caJ.culated.
From the abac in [1]
earlier, it can be seen that the lines of constant
straight lines.
When
~ (w~
is obtained from (2) in an
8 ) corresponding to given values of
'1,
~2)' we first find the value
trial value,
value,
~l
The corresponding value of
'1
~l
'1 is zero,
+ 2
To get a second approximation,
~
referred to
8 are very nearly parallel
also is zero and
where
+ 3)
8 , to
2
8, therefore, we ecpate the ratios
~ (~+
(~+
and
!
2
2
~
~
+ 3) - ~2
+ 3)
-~2
where
~2)
The process can then be repeated until
close to
is sufficiently
13 •
1
A modification of this method uses two trial values
and then 'interpolates' for the value of
=
8
1
and
8 with the formula
!(~
+
2~
+ 3) -
!(w4 + 2 fJfl + 3)
211
In
4
where
wi = exp
(5i- 2
)
and
is the interpolated value of
52
5
•
The procedures described above can be used quite conveniently with a desk
calculating machine.
For the calculation of the table, hQ'tfever, a program for the
Univac 1105 computer (Computing Center, University of North Carolina) was used.
It is a pleasure to acknowledge the very helpful assistance of Mrs. K.
Yelverton
in this work.
REFERENCES
[1]
Johnson, N. L.
"Systems of frequency curves generated by methods of transla-
tion", Biometrika, Vol.
[2]
36 (1949), pp. 149-176.
Johnson, N. L., Eric Nixon, D. E. Amos and E. S. Pearson, "Table of percentage
points of Pearson curves, ,for given
measure,"
[3]
Biometrika, Vol. 50
.[ ~l
(1963).
pp.
and.
~2' expressed in standard
459-498.
Leslie, D. C. Me, "Determination of parameters in the Johnson system of
probability distributions,"
Biometrika, Vol.
46 (1959), pp. 229-231.
5
,(f3 = 0.0
1
Probability
0.99 0.975
0.95
0.90
0.75
0.50
2.369
2.405
2.436
2.463
2.486
2.507
2.526
2.543
2.558
2.572
2.584
2.596
2.607
2.617
2.626
2.635
2.643
2.650
2.658
2.664
2.671
2.677
2.682
2.688
2.693
2.698
2.702
2.707
2.711
2.715
1.641
1.636
1.632
1.627
1.623
1.619
1.614
1.611
1.607
1.603
1.599
1.596
1.592
1.589
1.585
1.582
1.579
1.576
1.573
1.570
1.567
1.564
1.562
1.559
1.556
1'.554
1.551
1.549
1.547
1.544
1.268
1.256
1.244
1.234
1,225
1.216
1.208
1.201
1.193
1.186
1.180
1.174
1.168
1.163
1.158
1.153
1.148
1.143
1.139
1.13;
1.131
1.127
1.123
1.119
1.116
1.112
1.109
1.106
1.102
1.099
0.661
0.649
0.639
0.630
0.622
0.614
0.607
0.601
0.595
0.589
0.584
0.579
0.574
0.570
0.566
0.562
0.558
0.554
0.551
0.548
0.545
0.542
0.539
0.536
0.533
0.531
0.528
0.526
0.523
0.521
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
~ative
f32
e
3.2
3.4
3.6
3.8
·4.0
4.2
4.4
'l,i..6
4.8
5.0
5.2
5.4
5.6
5.8
6.0
6.2
6.4
6.6
6.8
7.0
7.2
7.4
7.6
7~8
8.0
8.2
8.4
8.6
8.8
9.0
0.9995 0.999 0.9975 0.995
3.491
3.668
3.826
3.968
4.097
4.216
4.325
4.426
4.520
4.608
4.690
4.768
4.841
4.910
4.976
5.038
5.098
5.154
5.209
5.261
5.311
5.359
5.405
5.449
5.492
5'.533
5.573
5.612
5.649
5.686
3.247
3.385
3.507
3.616
3.715
3.805
3.887
3.963
4.034
4.099
4.161
4.219
4.273
4.324
4.372
4.418
4.462
4.504
4.543
4.581
4.618
4.653
4.686
4.718
4.749
4.779
4.808
4.836
4.862
4.888
2.913
3.004
3.084
3.156
3.220
3.278
3.330
3.379
3.423
3.464
3.503
3.539
3.572
3.604
3.633
3.661
3.688
3.713
3.737
3.760
3.782
3.802
3.822
3.841
3.860
3.877
3.894
3.911
3.926
3.941
2.648
2.709
2.763
2.810
2.852
2.889
2.923
2.954
2.983
3'.009
3.033
3.056
3.076
3.096
3'.114
3.132
3'.148
3.163
3'.178
3.192
3'.205
3.217
3'.229
3.240
3.251
3'.262
3.272
3.281
3.290
3.299
1.972
1.982
1. 989
1.995
2.001
2.005
2.008
2.011
2.013
2.015
2.017
2.018
2.019
2.020
2.021
2.021
2.022
2.022
2.022
2.022
2.022
2.022
2.022
2.022
2.022
2.022
2.021
2.021
2.021
2.020
-----
[NOTE: For cumulative probabilities less than 0.50, the values can be ob-
tained from the relationship
-x
,&00 p(x)dx =
L
00
p(x)dx = 1 - !xP(X)dx
which holds for all symmetrical standardized distributions. ]
e
e
..._---
13
2
5 2
3.4
3.6
3.8
4.0
r
-0.3614
-0.2432
-0.1851
-0.1505
4.2
4.4
4.6
4.8
-0.1275
-0.1111
-0.0987
-0.0892
5.0 ·-0.0815
5.2
5.4
5.6
).8
-0.0752
-0.0699
-0.0654
-0.0616
6.0 -0.0582
-
....
'"-- .. _."-_. __.".
-
---'
1
~
0.1
----_._-_
..
~,~,-_.~,
o ; 0.0005 0.001 0.0025 0.005 0.01
---t4 7871-3318
3.435i -3.500
2. 872i -3.662
2.5481 -3.809
2.333\ -3.941
-0,7373
_._-...._---._._----_
J 13
e
Cumulative Probability
...•
_._-----------
-1.926
-1.938
-1.947
-1.955
-1.962
-('),016
-0.015
-0.014
-0.014
-0.013
0.653
0.642
0.632
0.623
0.615
1.278
1.265
1.254
1.243
1.233
1.667
1.662
1.656
1.651
1.645
2.016
2.023
2.029
2.034
2.038
2.436
2.469
2.498
2.523
2.545
2.733
2.791
2.842
2.887
2.927
3.016
3.104
3.182
3.251
3.313
3.375
3.510
3.629
3.736
-2.446
-2.467
-2.485
-2.502
-2.517
-1.967
-1.972
-1.976
-1.979
-1.982
-1.597
-1.594
-1.591
-1.587
-1.584
-0.013
-0.012
-0.012
-0.012
-0.011
0.607
0.600
0.594
0.588
0.583
1.224
1.216
1.208
1.200
1.193
1.640
1.635
1.631
1.626
1.622
2.041
2.043
2.045
2.047
2.048
2.564 2.963
2.5812.996
2.597 3.025
2.611 3.052
2.624 3.077
3.369
3.420
3.467
3.510
3.550
.3.9214.351
4.0014.459
4.0764.558
4.145 4.651
4.209 4.737
-2.531
-2.544
··2.556
-2.567
-2.577
··1.984
-1.986
-1.988
-1.990
-1.991
··1.581 -1.174
-1.578 -1.168
-1.574 ··1.163
-1.571 -1.157
-1.56f-l.15?
-0.590 -0.011
-0.585 -0.011
··0.580 -0.010
-0.576 -0.010
··O.57?O.OlG
0.578
0.573
0.568
0.564
0.560
1.187
1.181
1.175
1.169
1.164
1.618
1.614
1.610
1.606
1.602
2.049
2.049
2.050
2.050
2.050
2.635
2.646
2.656
2.665
2.674
3.587
3.621
3.654
3.684
3.713
4.2694.818
4.325 4.894
4.378 4.966
4.428 5.034
4.476 5.098
·-3.093
-3.241
-3.367
-3.480
-3.582
-2 295
-2.335
-2.)09
-2.398
-2.424
2.1781-4.063
2.0601-4.1'75
1.966'-4.278
1.889!-4.375
1.825\-4.465
-3.675
-3.760
-3.839
-3.912
-3.980
-3.177
-3.232
-3.283
-3.329
-3.373
-2.309
-2.846
-2.879
-2.909
-2.936
1.7701-4.549
1.7231-4.629
1.682i-4.704
1. 645/- 4.775
Lh131-4.842
-4.043
-4.103
-4.159
-4.211
-4.261
-3.413
-3.450
-3.485
-3.513
-3.549
-2.962
.-2.986
-3.008
-3.029
-3.048
e
-1.209
-1.201
-1.194
-1.187
-1.180
-0.622
-0.614
-0.608
-0.601
-0.596
0.50
..
0.10 0.25
-l.G14 ..1,258 .·0.671
-1.611 -1.21~7 -0.658
-1.608 -1.236 -0.648
-1.604 -1.226 -0.638
-1.601 -1.217 -0.629
--'
-.2.795 -2.552
-2.891 -2.618
-2.975 -2.675
-3.050 -2.725
-3.117 -2.769
0.025 0.05
_-
0.75 0.90 0.95 0.975 0·99 0.995 0.9975 0.999 0.9995
e
3.100
3.121
3.141
3.160
5.177
3.638
3.812
3.967
4.108
3~833 4.235
e
.ff3 1 = 0.1
- - -_._-. - ---,--------
i
f3
2
6.2
6.4
6.6
6.8
7.0
'Y
0
-0.0553
-0.0527
-0.0504
-0.0483
-0.0464
1.58
1.55
1.53
1.51
1.49
e
e
Cumulative Probability
0.00050.0010.00250.005
-4.906
-4.967
-5.025
-5.081
-5.134
-4.309-3.578
-4.354-3.606
-4.397-3.632
-4. 438-J.657'
-4.477-3.681
-3.067
-3.084
-3.100
-3.115
-3.130
0.01
0.025
O.O~_
-2.586
-2.595
-2.603
-2.611
-2.619
-1.992
-1.993
-1.994
-1.995
-1.995
0.75 0.90 0.95 0.9750.99 0.995 00;9975
o.'999'O.99~
-0.010
-0.010
-0.009
-0.009
0.556
0.552
0.5 49
0.546
0.542
1.158
1.154
1.149
1.144
1.140
1.599
1.595
1.592
1.589
1.585
2.050
2.050
2.050
2.050
2.049
2.682
2.689
2.696
2.702
2.708
3.193
3.209
3.223
3.237
3.250
3.740
3.765
3.790
3.813
3.835
4~2eO'5.160
4.563
4.604
4.642
4.679
5.218
5.274
5.327
5.378
0.10
0.25
0.50
-1.566
-1.563
-1.560
-1.557
-1.555
-1.147
-1.143
-1.138
-1.134
-1.130
-0.568
-0.564
-0.560
-0.557
-0.553
-O.Ole
7.2
7.4
7.6
7.8
8.0
-0.0447 1.471 -5.186 -4.514-3.704 -3.144
1.455
1.438
1.423
1.40
-5.235
-5.282
-5.327
-5.371
-4.550-3.725
-4.585-3.746
-4.618-3.766
-4.650-3.785
-2.626 -1.996
-3.157 -2.~3~·~1.996
-3.170 -2 638 -1.996
-3.182 -2.644 -1.996
-3.193 -2.650 -1.997
-1.552
-1.550
-1.547
-1.545
-1.542
-1.126
-1.122
-1.118
-1.115
-1.111
~O.550
-0.0431
-0.0417
-0.0404
-0.0391
-0.547
-0.544
-0.541
-0.538
-0.009
-0.009
-0.009
-0.009
-0.009
0.539
0.536
0.534
0.531
0.528
1.136
1.132
1.128
1.124
1.120
1.582
1.579
1.576
1.573
1.571
2.049
2.049
2.048
2.048
2.047
2.714
2.720
2.725
2.730
2.734
3.263
3.275
3.286
3.297
3.307
3.856
3.876
3.895
3.913
3.931
4.715
4.749
4.782
4.813
4.843
5.427
5.474
5.520
5.563
5.605
8.2
8.4
8.6
8.8
9·0
-0.0380
-0.0370
-0.0360
-0.0351
-0.0342
1.39J
1.383\
1.372
1.361
1.350
-5.414
-5.455
-5.494
-5.533
-5.570
-4.680-3.803
-4.710-3.821
-4.739-3.838
-4.766-3.855
-4.793-3.870
-3.2!5
-3.225
-3.235
-3.244
-2.655
-2.660
-2.665
-2.670
-2.674
-1.540
-1.538
-1.535
-1.533
-1.531
-1.108
-1.104
-1.101
-1.098
-1.095
-0.536
-0.533
-0.531
-0.528
-0.526
-0.008
-0.008
-0.008
-0.008
-0.008
0.526
0.523
0.521
0.519
0.516
1.117
1.113
1.110
1.107
1.104
1.568
1.565
1.563
1.560
1.558
2.046
2.046
2.045
2.045
2.044
2.739
2.743
2.747
2.750
2.754
3.317
3.326
3.335
3.344
3.352
3.948
3.964
3.980
3.995
4.010
4.872
4.900
4.927
4.954
4.979
5.646
5.685
5.723
5.760
5.795
0
-}~204
-1.997
-1.997
-1.997
-1.996
-1.996
I
9.2 -0.0334 1.3401-5.606 -4.819-3.886 -3.253 -2.678 -1.996 -1.529 -1.092 -0.524 -0.008 0.514 1.101 1.555 2.043 2.758 3.360 4.024 5.004 5.830
I
~
-
e
= 0.2
Cumulative Probability
.[f31
---Il---~
J
5
I 0.0005 0.001 0.0025 0.005 0.01
0.025 0.05
0.10
0.25
0.50
-1.586
-1.584
-1.583
-1.580
-1.578
-1.250
-1.239
-1.228
-1.219
-1.210
-0.681
-0.669
-0.657
-0.647
-0.638
-0.032
-0.030
-0.029
-0.028
-0.027
0.646 1.290 1.695 2.058
0.635 1.277 1.687 2.064
0.625 1.264 1.681 2.069
~616 1.253 1.674 2.072
0.608 1.243 1.668 2.074
2.498
2.530
2.557
2.580
2.600
2.809
2.866
2.916
2.959
2.998
3.106
3.194
3.270
3.338
3.398
3.483
3.617
3.736
3.842
3.938
}.'758
3.933
4.809
4.229
4.355
-1.928
-1.934
-1.939
-1.944
-1.947
-1.576
-1.573
-1.570
-1.568
-1.565
-1.202
-1.194
-1.187
-1.181
-1.174
-0.630
-0.623
-0.616
-0.609
-0.603
-0.026
-0.025
-0.024
-0.023
-0.023
0.601
0.594
0.588
0.582
0.577
1.233
1.224
1.216
1.208
1.201
1.662
1.657
1.651
1.646
1.641
2.076
2.078
2.079
2.079
2.080
2.618
2.634
2.649
2.662
2.673
3.032
3.063
3.091
3.117
3.141
3.453
3.503
3.548
3.590
3.629
4.025
4.105
4.178
.4.246
4.309
4.471
4.578
4.676
4.768
4.853
-2.474
-2.489
-2.502
-2.514
-2.525
-1.951
-1.954
-1.956
-1.958
-1.960
-1.562
-1.559
-1.557
-1.554
-1.552
-1.168
-1.163
-1.157
-1.152
-1.147
-0.598
-0.592
-0.587
-0.583
-0.578
-0.022
-0.022
-0.021
-0.021
-0.020
0.572
0.567
0.563
0.559
0.555
1.194
1.188
1.181
1.176
1.170
1.636
1.632
1.628
1.623
1.619
2.080
2.080
2.080
2.079
2.079
2.684
2.694
2.703
2.712
2.720
3.163
3.184
3.203
3.220
3.237
3.665
3.699
3.730
3.760
3.787
4.368 4.934
'4.4245.009
4.476 5.080
4.525 5.147
4.571 5.211
-2.535
-2.545
-2.554
-2.563
-2.571
-1.962
-1.964
-1.965
-1.966
-1.967
-1.549
-1.547
-1.544
-1.542
-1.539
-1.142
-1.138
-1.133
-1.129
-1.125
-0.574
-0.570
-0.566
-0.563
-0.559
-0.020
-0.019
-0.019
-0.019
-0.018
0.551
0.547
G.544
0.541
0.538
1.165
1.160
1.155
1.150
1.146
1.615
1.612
1.608
1.604
1.601
2.079
2.078
2.077
2.077
2.076
2.727
2.734
2.740
2.746
2.751
3.253
3.267
3.281
3.294
3.307
3.814
3.838
3.862
3.884
3.906
4.616 5.272
4.657 5.329
4~697 5.385
4.735 5.437
4.772 5.488
f32
-1
3.2
3.4
3.6
3.8
4.0
1.941
0.8184
0.5270
0.3928
0.3155
5.36!-3.114
3.608 -3.305
2.960 -3.474
2.604 -3.626
2.372 -3.764
-2.925
-3.075
-3.208
-3.326
-3.433
-2.659
-2.762
-2.852
-2.931
-3.002
-2.444
-2.516
-2.577
-2.631
-2.679
-2.214
-2.257
-2.295
-2.327
-2.356
-1.876
-1.891
-1,903
-1.913
-1.921
4.2
4.4
4.6
4.8
5.0
0.2651
0.2297
0.2028
0.1826
0.1664
2.201 -3.890
2.082 -4.007
1.984 -4.ll5
1.904 -4.215
1.837 -4.308
-3.530
-3.619
-3.702
-3.778
-3.849
-3.066
-3.125
-3.179
-3.228
-3.273
-2.722
-2.761
-2.797
-2.829
-2.859
-2.381
-2.403
-2.424
-2.442
-2.459
5.2
5.4
5.6
5.8
6.0
0.1532
0.1422
0.1329
0.1250
0.ll81
1.781
1.732
1.690
1.653
1.619
-4.395
-4.477
-4.555
-4.628
-4.698
-3.915
-3.977
-4.035
-4.090
-4.142
-3.315
-3.355
-3.392
-3.426
-3.459
-2.886
-2.912
-2.935
-2.957
-2.978
6.2
6.4
6.6
6.8
7.0
0.1120
0.1066
0.1019
0.0976
0·0937
1.590
1.563
1.538
1.516
1.495
-4.764
-4.827
-4.887
-4.944
-4.999
-4.191
-4.237
-4.282
-4.324
-4.365
-3.490
-3.519
-3.546
-3.572
-3.597
-2.998
-3.016
-3.034
-3.050
-3.066
~
e
e
e
e
0.75 0·90 0.95 0.975 0.99 0.995 0.9975 0.999 0.9995
.
e
e
0'1
e
,{13
1
----
e
= 0.2
Cumulative Probability
I 0.0005 0.001 0.0025 0.005 0.01
0.025 0.05
132
7.2
7.4
7.6
7.8
8.0
-y
8
0.0902
0.0870
0.0841
0.0814
0.0789
1.476
1.458
1.442
1.427
1.412
-5.052
-5.102
-5.151
-5.198
-5.243
-4.404
-4.441
-4.477
-4.511
-4.544
-3.621
-3.644
-3.666
-3.687
-3.707
-3.080
-3.094
-3.108
-3.121
-3.133
-2.579
-2.586
-2.593
-2.599
-2.606
-1.968
-1.969
-1.970
-1.970
-1.971
8.2
8.4
8.6
8.8
9.0
0.0766
0.0745
0.0725
0.0706
0.0689
1.399
1.386
1.374
1.363
1.352
-5.286
-5.328
-5.369
-5.409
-5.447
-4.576
-4.607
-4.636
-4.665
-4.692
-3.726
-3.744
-3.762
-3.779
-3.796
-3.145
-3.156
-3.167
-3.177
-3.187
-2.612
-2.617
-2.622
-2.628
-2.633
-1.971
-1.971
-1.972
-1.972
-1.972
9.2 0.0672
e
0.10
0.25
0.50
0.75 0.90 0.95 0.975 0.99 0.995 0.9975 0.999 0.9995
-1.537
-1.535
-1.533
-1.530
-1.528
-1.121
-1.117
-1.114
-1.110
-1.107
-0.556
-0.553
-0.550
-0.547
-0.544
-0.018
-0.018
-0.018
-0.017
-0.017
0.535
0.532
0.529
0.526
0.524
1.141
1.137
1.133
1.129
1.126
1.598
1.594
1.591
1.588
1.585
2.075
2.074
2.074
2.073
2.072
2.757
2.762
2.766
2.771
2.775
3.319
3.330
3.341
3.351
3.361
3.926
3.945
3.964
3.982
3.999
4.806
4.840
4.872
4.902
4.932
5.536
5.582
5.627
5.670
5.712
-1.526
-1.524
-1.522
-1.520
-1.518
-1.104
-1.100
-1.097
-1.094
-1.091
-0.541
-0.538
-0.536
-0.533
-0.531
-0.017
-0.017
-0.017
-0.016
-0.016
0.521
0.519
0.516
0.514
0.512
1.122
1.118
1.115
1.112
1.108
1.582
1.579
1.577
1.574
1.571
2.071
2.070
2.069
2.068
2.067
2.779
2.782
2.786
2.789
2.793
3.370
3.379
3.387
3.396
3.404
4.015
4.031
4.046
4.061
4.075
4.961
4.988
5.015
5.040
5.065
5.752
5.790
5.828
5.864
5.899
1.3421-5.484
-4.719 -3.812 -3.197 -2.637 -1.972 -1.516 -1.088 -0.529 -0.016 0.510 1.105 1.569 2.066 2.796 3.411 4.089 5.089 5.933
•
e
e
e
9
-.
ie
13
1
132
3.2
3.4
3.6
3.8
4.0
4.2
4.4
4.6
4.8
5.0
5.2
5.4
5.6
5.8
6.0
6.2
6.4
6.6
6.8
7.0
7.2
7.4
7.6
7.8
8.0
8.2
8.4
8.6
8.8
9.0
9.2
e
= 0.3
r
-6.407
-1.567
-0.9137
-0.6528
-0.5122
-0.4242
-0.3637
-0.3197
-0.2860
-0.2595
-0.2381
-0.2204
-0.2054
-0.1927
-0.1817
-0.1721
-0.1636
-0.1561
-0.1494
-0.1431
-0.1376
-0.1326
-0.1281
-0.1239
-0.1200
-0.1164
-0.1131
-0.1101
-0.1072
-0.1045
-0.1020
e
Cumulative Probability
I 0.0005 0.001
7.209 -2.877 -2.724
3.978 -3.080 -2.885
3.133 -3.259 -3.027
2.707 -3.420 -3.153
2.442 -3.565 -3.266
2.259 -3.698 -3.369
2.122 -3.819 -3.463
2.u!6 -3.932 -3.550
1.930 -4.036 -3.630
1.860 -4.134 -3.704
1.800 -4.225 '·3.774
1.749 -4.310 -3.839
1.705 -4.391 -3.900
1.666 -4.467 -3.957
1.631 -4.540 -4.011
1.600 -4.608 -4.063
1.572 -4.674 -4.112
1.547 -4.736 -4.158
1.524 -4.795 -4.203
1.502 -4.853 -4.246
1.483 -4.908 -4.286
1.465 -4.960 -4.325
1.448 -5.010 -4.362
1.432 -5.059 -4.398
1.418 -5.106 -4.432
1.404 -5.151 -4.465
1.391 5.194 -4.497
1.379 -5.236 -4.528
1.,67 -5.277 -4.558
1.356 -5.316 -4.586
1.346 5.355 -4.614
5
0.0025 0.005
-2.504 -2.322
-2.616 -2.401
-2.713 -2.468
-2.799 -2.527
-2.875 -2.580
-2.944 -2.627
-3.006 -2.669
-3.064 -2.707
-3.116 -2.742
-3.164 -2.774
-3.209 -2.804
-3.251 -2.831
-3.290 -2.857
-3.327 -2.881
-3.361 -2.905
-3.394 -2.924
-3.425 -2.944
-3.454 -2.963
-3.482 -2.980
-3.509 -2.997
-3.534 -3.013
-3.558 -3.028
-3.581 -3.043
-3.603 -3.057
-3.624 -3.070
-3.644 -3.082
-3.664 -3.094
-3.682 -3.106
-3.700 -3.117
-3.718 -3.128
-3.735 -3.138
0.01
-2.122
-2.171
-2.214
-2.250
-2.282
-2.310
-2.335
-2.358
-2.378
-2.397
-2.414
-2.430
-2.444
-2.457
-2.470
-2.482
-2.492
-2.503
-2.512
-2.521
-2.530
-2.538
-2.545
-2.553
-2.560
-2.566
-2.572
-2.578
-2.584
-2.589
-2.594
e
0.025
-1.821
-1.840
-1.855
-1.867
-1.877
-1.886
-1.894
-1.900
-1.906
-1.911
-1.915
-1.919
-1.923
-1.926
-1.928
-1.931
-1.933
-1.935
-1.937
-1.938
-1.940
-1.941
-1.942
-1.943
-1.944
-1.945
-1.945
-1.946
-1.947
-1.947
-1.948
0.05
-1.556
-1.557
-1.557
-1.556
-1.554
-1.553
-1.551
-1.549
-1.547
-1.545
-1.543
-1.541
-1.539
-1.537
-1.534
-1.532
-1.530
-1.528
-1.526
-1.524
-1.522
-1.520
-1.518
-1.516
-1.514
-1.512
-1.510
-1.508
-1.506
-1.505
-1.503
0.10
-1.242
-1.231
-1.221
-1.212
-1.204
-1.196
-1.188
-1.181
-1.175
-1.169
-1.163
-1.157
-1.152
-1.147
-1.142
-1.138
-1.133
-1.129
-1.125
-1.121
-1.117
-1.113
-1.110
-1.106
-1.103
-1.100
-1.096
-1.093
-1.090
-1.087
-1.085
0.25
-0.694
-0.681
-0.669
-0.658
-0.648
-0.640
-0.632
-0.624
-0.618
-0.611
-0.606
-0.600
-0.~95
-0.590
-0.585
-O.~81
-0.577
-0.573
-0.569
-0.566
-0.562
-0.559
-0.553
-0.550
-0.547
-o.~
-0.542
-0.539
-0."7
-0.5~
-0.532
0.50 0.75 0.90 0.95
-0.049 0.641 1.304 1.723
-0,046 0.629 1.289 1.714
-0.044 0.620 1.276 1.706
-0.042 0.611 1.264 1.698
-0.040 0.603 1.253 1.691
-0.039 0.596 1.243 1.685
-0.038 0.589 1.234 1.678
-0.036 0.583 1.225 1.672
-0.035 0.577 1.217 1.667
-0.034 0.572 1.209 1.661
-0.031~ 0.567 1.202 1.656
-0.033 0.562 1.195 1.651
-0.032 0.558 1.189 1.646
-0.031 0.554 1.183 1.641
-0.031 0.550 1.177 1.637
-0.030 0.546 1.172 1.633
-0.029 0.543 1.166 1.628
-0.029 0.539 1.161 1.624
-0.028 0.536 1.157 1.621
-0.028 0.533 1.152 1.617
-0.027 0.530 1.147 1.613
-0.027 0.527 1.143 1.610
-0.027 0.524 1.139 1.606
-0.026 0.522 1.135 1.603
-0.026 0.520 1.131 1.600
-0.025 0.517 1.127 1.597
-0.025 0.514 1.124 1.594
-0.025 0.512 1.120 1.591
-0.024 0.510 1.117 1.588
-0.024 0.508 1.114 1.585
-0.024 0.506 1.110 1.582
e
0.975
2.100
2.104
2.107
2.109
2.111
2.111
2.112
2.112
2.112
2.112
2.111
2.110
2.110
2.109
2.108
2.107
2.106
2.105
2.104
2.103
2.101
2.100
2.099
0.99
2.555
2.586
2.612
2.634
2.653
2.670
2.685
2.699
2.711
2.722
2.732
2.741
2.749
2.757
2.764
2.771
2.777
2.783
2.788
2.793
2.798
2.802
2.807
0.995
2.877
2.933
2.982
3.025
3.063
3.096
3.127
3.154
2.179
3.202
3.224
3.243
3.262
3.279
3.295
3.310
3.324
3.337
3.350
3.361
3.372
3.383
3.393
2.097
2.096
2.094
2.093
2.092
2.091
2.090
2.814
2.818
2.821
2.825
2.828
2.830
2.833
3.412
3.421
3.430
3,438
3.446
3.454
3.461
2~c98 7.811 3.~
0.9975 0.999 0.9995
3.184 3.571 3.853
3.271 '.707 4.031
3.348 3.827 4.189
3.415 3.934 4.330
3.475 4.030 4.458
3.529 4.117 4.575
3.579 4.197 4.682
3.624 .4.270 4.781
2.665 ~4~·}38 4.e73
3.703 4.4014.958
3.738 4.459 5.038
3.771 4.514 5.114
3.802 4.566 5.185
3.831 4.615 5.252
3.858 ~.~661 5.315
3.884 4.704 5.375
3.908 4.746 5.433
3.931 4.785 5.487
3.953 4.823 5.540
3.973 4.858 5.589
3.993 4.892 5.637
4.012 4.925 5.683
4.0304.957 5.727
4.01~tl 4.987 5.7'(0
4.064 5.016 $.S1I
4.080 5.044 5.851
4.095 5.071 5.889
4.110 5.097 5.926
4.124 5.123 5.962
4.138 5.147 5.996
It.151 5~171 6.030
-
e
'.[(31
= 0.4
Cumulative Probability
~
(32
3.4
3.6
3.8
4.0
4.2
4.4
4.6
4.8
5.0
5.2
5.4
5.6
5.8
6.0
6.2
6.4
6.6
6.8
7.0
7.2
7.4
7.6
7.8
8.0
8.2
8.4
8.6
8.8
9.0
9.2
e
e
"1
5
-3.4724
-1.5654
-1.0281
-0.7733
-0.6244
-0.5265
-0.4571
-0.4054
-0.3653
-0.3332
-0.3070
-0.2851
4.809
3.448
2.882
2.557
2.340
2.184
2.065
1.970
1.893
1.829
1.774
1.726
1.685
1.648
1.616
1.586
1.560
1.535
1.513
1.493
1.474
1.457
1.440
1.425
1.411
1.398
1.385
1.373
1.362
1.352
-0.2666
-0.2507
-0.2369
-0.2248
-0.2141
-0.2045
-0.1959
-0.1882
-0.1811
-0.1747
-0.1689
-0.1635
-0.1585
-0.1538
-0.1495
-0.1455
-0.1418
-0.1383
0.0005 0.001
-2.821 -2.667
-3.013 -2.821
-3.185 -2.957
-3.340 -3.079
-3.481 -3.189
-3.610 -3.290
-3.729 -3.382
-3.840 -3.467
-3.942 -3.546
-4.038 -3.620
-4.128 -3.689
-4.213 -3.753
-4.293 -3.814
-4.369 -3.871
-4.440 -3.925
-4.509 -3.977
-4.574 -4.026
-4.636 -4.072
-4.695 -4.117
-4.752 -4.159
-4.807 -4.200
-4.859 -4.239
-4.910 -4.276
-4.958 -4.3~2
-5.005 -4.347
-5.050 -4.380
-5.094 -4.4~2
-5.136 -4.443
-5.177 -4.473
-5.217 -4.502
0.0025 0.005
-2.449 -2.269
-2.556 -2.345
-2.650 -2.411
-2.733 -2.469
-2.808 -2.521
-2.876 -2.568
-2.937 -2.610
-2.994 -2.648
-3.046 -2.683
-3.094 -2.715
-3.139 -2.745
-3.181 -2.773
-3.221 -2.799
-3.257 -2.823
-3.292 -2.846
-3.325 -2.867
-3.356 -2.888
-3.386 -2.907
-3.414 -2.925
-3.440 -2.942
-3.466 -2.958
-3.490 -2.974
-3.514 -2.989
-3.536 -3.003
-3.557 -3.016
-3.578 -3.029
-3.598 -3.042
-3.617 -3.054
-3.635 -3.065
-3.653 -3.076
e
0.01
-2.074
-2.122
-2.164
-2.200
-2.232
-2.261
-2.286
-2.309
-2.~30
-2.349
-2.367
-2.383
-2.398
-2.412
-2.425
-2.437
-2.448
-2.459
-2.469
-2.478
-2.487
-2.495
-2.503
-2.511
-2.518
-2.525
-2.532
-2.538
-2.544
-2.550
0.025
-1.783
-1.801
-1.817
-1.830
-1.841
-1.851
-1.859
-1.866
-1.872
-1.878
-1.883
-1.887
-1.891
-1.895
-1.898
-1.901
-1.904
-1.906
-1.908
-1.910
-1.912
-1.913
-1.915
-1.916
-1.917
-1.919
-1.920
-1.921
-1.921
-1.922
0.05
-1.526
-1.528
-1.529
-1.529
-1.529
-1.528
-1.527
-1.526
-1.525
-1.523
-1.522
-1.520
-1.518
-1.517
-1.515
-1.513
-1.511
-1.510
-1.508
-1.506
-1.504
-1.503
-1.501
-1.499
-1.498
-1.496
-1-494
-1.493
-1.491
-1.489
0.10
-1.224
-1.214
-1.205
-1.197
-1.190
-1.183
-1.176
-1.170
-1.164
-1.158
-1.153
-1.147
-1.142
-1.138
-1.133
-1.129
-1.125
-1.121
-1.117
-1.113
-1.109
-1.106
-1.102
-1.099
-1.096
-1.093
-1.090
-1.087
-1.084
-1.081
0.25
-0.694
-0.681
-0.670
-0.660
-0.650
-0.642
-0.634
-0.627
-0.620
-0.614
-0.609
-0.603
-0.598
-0.593
-0.589
-0.584
-0.580
-0.576
-0.573
-0.569
-0.566
-0.562
-0.559
-0.556
-0.553
-0.550
-0.548
-0.545
-0.542
-0.540
0.50
-0.063
-0.060
-0.057
-0.055
-0.053
-0.051
-0.049
-0.048
-0.047
-0.045
-0.044
-0.043
-0.042
-0.041
-0.040
-0.040
-0.039
-0.038
-0.038
-0.037
-0.036
-0.036
-0.035
-0.035
-0.034
-0.034
-0.033
-0.033
-0.033
-0.032
0.75 0·90 0·95 0.975
,0.625 1.304 1.742 2.144
0.615 1.290 1.733 2.146
0.606 1.277 1.724 2.147
0.598 1.265 1.716 2.147
0.591 1.254 1.708 2.147
0.584 1.244 1.701 2.146
0.578 1.235 1.694 2.146
0.572 1.227 1.688 2.145
0.567 1.219 1.682 2.144
0.562 1.~ 1.676 2.142
0.558 1.204 1.670 2.141
0.553 1.197 1.665 2.140
0.549 1.191 1.660 2.138
0.545 1.185 1.655 2.137
0.542 1.179 1.650 2.135
0.538 1.174 1.646 2.134
0.535 1.169 1.642 2.132
0.532 1.164 1.637 2.131
0.529 1.159 1.633 2.139
0.526 1.154 1.629 2.128
0.523 1.150 1.626 2.126
0.520 1.145 1.022 2.125
0.518 1.141 1.618 2.123
0.515 1.137 1.615 2.122
0.513 1.133 1.612 2.120
0.510 1.130 1.608 2.119
0.508 1.126 1.605 2.117
0.506 1.122 1.602 2.116
0.504 1.119 1.599 2.114
0.502 1.116 1.596 2.113
e
0.99
2.639
2.664
2.685
2.704
2.720
2.734
2.747
2.758
2.769
2.778
2.787
2.794
2.802
2.808
2.814
2.820
2.825
2.830
2.835
2.539
2.843
2.847
2.850
2.854
2.857
2.860
2.863
2.865
2.868
2.870
0.995
2.994
3.043
3.085
3.123
3.156
3.186
3.213
3.238
3.260
3.281
3.300
3.318
3.334
3.350
3.364
3.378
3.391
3.403
3.414
3.425
3.435
3.445
3.454
3.463
3.472
3.480
3.488
3.495
3.502
3.509
0.9975
3.338
3.415
3.484
3.544
3.599
3.648
3.693
3.734
3.772
3.807
3.839
3.870
3.898
3.925
3.950
3.974
3.997
4.018
4.038
4.058
4.076
4.094
4.111
4.127
4.143
4.158
4.172
4.186
4.199
4.212
0·999
3.778
3.902
4.011
4.108
4.197
4.278
4.351
4.420
4.483
4.542
4.597
4.648
4.697
4.743
4.786
4.828
4.867
4.904
4.940
4.974
5.006
5.037
'5.067
5.096
5.124
5.151
5.177
5.202
5.226
5.249
0.9995
4.104
4.267
4.412
4.543
4.662
4.771
4.871
4.964
5.050
5.131
5.207
5.278
5.345
5.409
5.469
5.527
5.582
5.634
5.684
5.732
5.777
5.822
5.864
5.905
5.944
5.982
6.019
6.055
6.089
6.122
e
e
e
J~l = 0.5
Cumulative Probability
(\J
r-I
~2
3.6
3.8
4.0
4.2
4.4
4.6
4.8
5.0
5.2
5.4
5.6
5.8
6.0
6.2
6.4
6.6
6.8
7.0
7.2
7.4
7.6
7.8
8.0
8.2
8.4
8.6
8.8
9.0
9·2
9.4
e
'Y
-3.1569
-1.6868
-1.1692
-0.9031
-0.7407
-0.6311
-0.5520
-0.4922
-0.4453
-0.4076
-0.3765
-0.3504
-0.3283
-0.3091
-0.2925
-0.2778
-0.2648
-0.2532
-0.2428
-0.2333
-0.2248
-0.2169
-0.2097
-0.2031
-0.1970
-0.1913
-0.1860
-0.1811
-0.1765
-0.1722
5
; 0.0005 0.001 0.0025 0.005
4.088
3.184
2.739
2.465
2.276
2.136
2.028
1.941
1.869
1.808
1.756
1.711
1.672
1.637
1.605
1.577
1.551
1.528
1.506
1.487
1.468
1.451
1.435
1.421
1.407
~.394
1.381
1.370
1.359
1.349
-2.731
-2.918
-3.085
-3.237
-3.376
-3.504
-3.621
-3.731
-3.833
-3.928
-4.018
-4.102
-4.182
-4.258
-4.330
-4.398
-4.463
-4.526
-4.586
-4.643
-4.698
-4.750
-4.801
-4.850
-4.897
-4.943
-4.987
-5.030
5.071
5.111
-2.584
-2.733
-2.867
-2.987
-3.096
-3.195
-3.287
-3.372
-3.451
-3.524
-3.593
-3.658
-3.719
-3.776
-3.831
-3.882
-3.932
-3.979
-4.023
-4.066
-4.107
-4.147
-4.185
-4.221
-4.256
-4.290
-4.322
-4.354
-4.384
-4.414
-2.375
-2.480
-2.573
-2.656
-2.730
-2.798
-2.859
-2.916
-2.969
-3.017
-3.063
-3.105
-3.144
-3.182
-3.217
-3.251
-3.282
-3.312
-3.341
-3.368
-3.394
-3.419
-3.443
-3.466
-3.487
-3.509
-3.529
-3.548
-3.567
-3.585
-2.205
-2.279
-2.345
-2.403
-2.4,5
-2.502
-2.544
-2.583
-2.619
-2.652
-2.682
-2.711
-2.737
-2.762
-2.785
-2.807
-2.828
-2.848
-2.866
-2.884
-2.901
-2.917
-2.932
-2.947
-2.961
-2.974
-2.987
-2.999
-'.011
-3.023
0.01
-2.019
-2.067
-2.109
-2.146
-2.118
-2.208
-2.234
-2.257
-2.279
-2.299
-2.317
-2.334
-2.349
-2.364
-2.377
-2.390
-2.402
-2.413
-2.423
-2.433
-2.443
-2.452
-2.460
-2.468
-2.476
-2.483
-2.490
-2.497
-2.503
-2.509
e
0.025 0.05
-1.741
-1.761
-1.777
-1.791
-1.805
-1.814
-1.823
-1.831
-1.838
-1.844
-1.850
-1.855
-1.859
-1.864
-1.867
-1.871
-1.874
-1.877
-1.879
-1.882
-1.884
-1.886
-1.888
-1.889
-1.891
-1.892
-1.894
-1.895
-1.896
-1.897
-1.497
-1.500
-1.502
-1.503
-1.504
-1.504
-1.504
-1.503
-1.~
-1.502
-1.501
-1.499
-1.498
-1.497
-1.496
-1.494
-1.493
-1.492
-1.490
-1.489
-1.487
-1.486
-1.484
-1.483
-1.482
-1.480
-1.479
-1.477
-1.476
-1.474
0.10
0.25
0.50
-1.207
-1.199
-1.191
-1.184
-0.696
-0.684
-0.672
-0.662
-0.653
-0.645
-0.638
-0.630
-0.624
-0.618
-0.612
-0.607
-0.602
-0.597
-0.592
-0.588
-0.584
-0.580
-0.576
-0.573
-0.569
-0.566
-0.563
-0.560
-0.557
-0.554
-0.551
-0.549
-0.546
-0.544
-0.078
-0.074
-0.071
-0.068
-0.065
-0.063
-0.061
-0.059
-0.058
-0.056
-0.055
-0.054
-0.052
-0.051
-0.050
-0.049
-0.048
-0.048
-0.047
-0.046
-0.045
-0.045
-0.044
-0.043
-0.043
-0.042
-0.042
-0.041
-0.041
-0.040
-~.171
-1.171
-1.164
-1.159
-1.153
-1.148
-1.143
-1.138
-1.133
-1.129
-1.125
-1.121
-1.117
-1.113
-1.109
-1.105
-1.102
-1.099
-1.095
-1.092
-1.089
-1.086
-1.083
-1.081
-1.078
-1.075
0.75 0.90 0.95 0.975 0.99 0.995 0.9975 0.999 0.9995
0.611 1.305 1.761
0.602 1.291 1.751
0.594 1.278 1.742
0.586 1.267 1.733
0.580 1.256 1.725
0.574 1.246 1.717
0.568 1.237 1.710
0.563 1.229 1.703
0.558 1.221 1.697
0.553 1.213 1.691
0.549 1.206 1.685
0.545 1.200 1.679
0.5411.194 1.674
0.537 1.1881.669
0.534 1.182 1.664
0.531 1.176 1.659
0.527 1.171 1.655
0.524 1.166 1.650
0.522 1.161 1.646
0.519 1.157 1.642
0.516 1.152 1.638
0.513 1.148 1.634
0.511 1.144 1.630
0.509 1.140 1.627
0.506 1.136 1.623
0.504 1.132 1.620
0.502 1.129 1.617
0.500 1.125 1.613
0.498 1.122 1.610
0.496 1.118 1.607
e
2.185
2.185
2.184
2.183
2.181
2.179
2.178
2.176
2.174
2.172
2.170
2.168
2.166
2.164
2.162
2.160
2.158
2.156
2.154
2.153
2.151
2.149
2.147
2.145
2.143
2.142
2.140
2.138
2.136
2.135
2.713
2.735
2.753
2.768
2.782
2.794
2.805
2.815
2.823
2.831
2.838
2.845
2.851
2.857
2.862
2.867
2.871
2.875
2.879
2.883
2.886
2.889
2.892
2.895
2.898
2.900
2.903
2.905
2.907
2.909
3.098
3.141
3.179
3.212
3.242
3.269
3.293
3.315
3.336
3.354
3.372
3.388
3.403
3.417
3.430
3.443
3.454
3.465
3.476
3.486
3.495
3.504
3.513
3.521
3.529
3.536
3.543
3.550
3.557
3.563
3.473
3.543
3.605
3.661
3.711
3.756
3.797
3.835
3.870
3.903
3.933
3.962
3.988
4.013
4.037
4.059
4.080
4.100
4.119
4.138
4.155
4.172
4.187
4.203
4.217
4.231
4.245
4.258
4.271
4.283
3.960 4.323
4.073 4.474
·4.174 4.610
4.265 4.733
4.347 4.~~
4.423 4.947
4.492 5.042
4.556 5.130
4.616 5.212
4.672 5.289
4.724 5.361
4.773 5.429
4.8:L95.494
4.862 5.555
4.903 5.613
4.943 5.668
4.980 5.720
5.016 5.770
5.049 5.818
5.082 5.864
5.113 5.908
5.143 5.951
5.172 50992
5.199 6.031
5.226 6.069
5.251 6.106
5.276 6.141
5.300 6.176
5.323 6.209
5.346 6.241
e
e
e
.[f31 = 0.6
~
Cumulative Probability
f32
3.8
4.0
4.2
4.4
4.6
4.8
5.0
5.2
5.4
5.6
5.8
6.0
6.2
6.4
6.6
6.8
7.0
7.2
7.4
7.6
7.8
8.0
8.2
8.4
8.6
8.8
9.0
9.2
9.4
9.6
e
r
-3.3684
-1.9060
-1. 3492
-1.0540
-0.8705
-0.7451
-0.6539
-0.5845
-0.5298
-0.4856
-0.4491
-0.4184
-0.3923
-0.3697
-0.3500
-0.3326
-0.3172
-0.3034
-0.2910
-0.2797
-0.2695
-0.2602
-0.2516
-0.2437
-0.2364
-0.2296
-0.2233
-0.2174
-0.2119
-0.2067
5
3.772
3.049
2.662
2.414
2.240
2.109
2.007
1.924
1.855
1.796
1.746
1.703
1.664
1.630
1.599
1.572
1.547
1.524
1.503
1.483
1.465
1.448
1.433
1.418
1.405
1.392
1.380
1.368
1.357
1.347
i 0.0005 0.001 0.0025 0.005 0.01
-2.612
-2.795
-2.961
-3.113
-3.251
-3.378
-3.496
-3.605
-3.708
-3.803
-3.894
-3.979
-4.059
-4.135
-4.208
-4.277
-4.343
-4.406
-4.466
-4.524
-4.579
-4.633
-4.684
-4.734
-4.781
-4.828
-4.872
-4.916
-4.957
-4.998
-2.477
-2.624
-2.757
-2.877
-2.986
-3.086
-3.178
-3.264
-3.343
-3.417
-3.487
-3.552
-3.614
-3.672
-3.727
-3.780
-3.830
-3.877
-3.923
-3.966
-4.008
-4.048
-4.087
-4.124
-4.159
-4.194
-4.227
-4.259
-4.290
-4.320
-2.286
-2.390
-2.483
-2.566
-2.641
-2.710
-2.772
-2.830
-2.883
-2.933
-2.979
-'.022
-3.063
-3.101
-3.137
-3.171
-3.203
-3.234
-3.263
-3.291
-3.318
-3.343
-3.368
-3.391
-3.414
-3.435
-3.456
-3.476
-3.496
-3.514
-2.129
-2.203
-2.270
-2.329
-2.382
-2.430
-2.473
-2.513
-2.5 49
-2.583
-2.614
-2.644
-2.671
-2.697
-2.721
-2.743
-2.765
-2.785
-2.804
-2.823
-2.840
-2.857
-2.873
-2.888
-2.902
-2.916
-2.930
-2.943
-2.955
-2.967
-
-1.956
-2.005
-2.048
-2.086
-2.120
-2.150
-2.177
-2.202
-2.224
-2.245
-2.264
-2.282
-2.298
-2.313
-2.328
-2.341
-2.353
-2.365
-2.376
-2.387
-2.397
-2.406
-2.415
-2.424
-2.432
-2.440
-2.447
-2.454
-2.461
-2.467
0.025
-1.697
-1.718
-1.736
-1.751
-1.764
-1.775
-1.785
-1.794
-1.802
-1.809
-1.816
-1.821
-1.827
-1.831
-1.836
-1.840
-1.843
-1.846
-1.850
-1.852
-1.855
-1.857
-1.860
-1.862
-1.864
-1.865
-1.867
-1.869
-1.870
-1.871
0.05
-1.467
-1.472
-1.475
-1.477
-1.478
-1.479
-1.480
-1.480
-1.480
-1.480
-1.479
-].. 479
-1.478
-1.477
-1.476
-1.475
-1.474
-1.473
-1.472
-1.471
-1.470
-1.469
-1.468
-1.467
-1.465
-1.464
-1.463
-1.462
-1.461
-1.460
0.10
-1.192
-1.185
-1.178
-1.171
-1.165
-1.159
-1.154
-1.148
-1.143
-1.138
-1.133
-1.129
-1.125
-1.121
-1.116
-1.113
-1.109
-1.105
-1.102
-1.098
-1.095
-1.092
-1.089
-1.086
-1.083
-1.080
-1.077
-1.075
-1.072
-1.069
0.25
-0.699
-0.687
-0.676
-0.666
.0.658
-0.649
-0.642
-0.635
-0.628
-0.622
-0.616
-0.611
-0.606
-0.601
-0.597
-0.592
-0.588
-0.584
-0.580
-0.577
-0.573
-0.570
-0.567
-0.564
-0.561
-0.558
-0.555
0.50
-0.092
-0.088
-0.084
-0.081
-0.078
-0.075
-0.073
-0.071
-0.069
-0.067
-0.066
-0.064
-0.063
-0.061
-0.060
-0.059
-0.058
-0.057
-0.056
-0.055
-0.054
-0.053
-0.053
-0.052
-0.051
-0.050
-0.050
~0.553 -0.049
-0.550 -0.049
-0.548 -0.048
0.75
0.598
0.590
0.582
0.576
0.570
0.564
0.559
0.554
0.5 49
0.545
0.541
0.537
0.533
0.530
0.527
0.524
0.520
0.518
0.515
0.512
0.510
0.507
0.505
0.503
0.500
0.498
0.496
0.494
0.492
0.490
0.90
1.308
1.294
1.281
1.270
1.259
1.249
1.240
1.232
1.224
1.217
1.210
1.203
1.197
1.191
1.185
1.179
1.174
1.169
1.164
1.160
1.155
1.151
1.147
1.143
1.139
1.135
1.131
1.128
1.124
1.121
e
0.95
1.780
1.770
1.760
1.750
1.742
1.734
1.726
1.719
1.712
1.706
1.700
1.694
1.688
1.683
1.678
1.673
1.668
1.663
1.659
1.655
1.651
1.647
1.643
1.639
1.635
1.632
1.628
1.625
1.622
1.619
0.975
2.224
2.222
2.219
2.217
2.214
2.212
2.209
2.207
2.204
2.201
2.199
2.196
2.194
2.191
2.189
2.186
2.184
2.182
2.179
2.177
2.175
2.173
2.170
2.168
2.166
2.164
2.162
2.160
2.158
2.156
0.99
2.782
2.800
2.815
2.829
2.840
2.850
2.860
2.868
2.875
2.882
2.888
2.894
2.899
2.904
2.908
2.912
2.916
2.919
2.922
2.925
2.928
2.931
2.933
2.936
2.938
2.940
2.942
2.944
2.945
2.947
0.995 0.9975
3.191 3.594
3.230 3.658
3.264 3.716
3.294 3.767
3.321 3.813
3.346 3.855
3.368 3.894
3.388 3.929
3.407 3.962
3.424 3.993
3.4404.021
3.454 4.048
3.468 4.073
3.481 4.096
3.493 4.118
3.504 4.139
3.515 4.159
3.525 4.178
3.535 4.196
3.544 4.213
3.553 4.230
3.561 4.246
3.569 4.261
3.576 4.275
3.583 4.289
3.590 4,302
3.597 4.315
3.603 4.327
3.609 4.339
3.615 4.351
0.9990.9995
4.119 4.513
4.225 4.656
4.320 4.785
4.406 4.902
4.484 5.008
4.555 5.106
4.621 5.197
4.682 5.282
4.738 5.560
4.791 5,434
4.841 5.504
4.888 5.569
4.932 5.631
4.974 5.690
5.013 5.745
5.051 5,799
5.086 5.849
5.120 5.898
5.153 5.944
5.184 5.989
5.214 6.031
5.243 6.073
5.270 6.112
5.297 6.150
5.322 6.187
5.347 6.223
5 371 6.257
5 394 6.291
5416 6.323
5.438 6.354
e
e
"{f31
~
= 0.7
Cumulative Probability
f3
2
4.0
4.2
4.4
4.6
4.8
5.0
5.2
5.4
5.6
5.8
6.0
6.2
6.4
6.6
6.8
7.0
7.2
7.4
7.6
7.8
8.0
8.2
8.4
8.6
8.8
9.0
9.2
9.4
9.6'
9.8
e
e
1
B
-4.0942 3.657
-2.2542 2.996
-1.5896 2.631
-1.2403 2.395
-1.0238 2.226
-0.8761 2.099
-0.7687 1.999
-0.6870 1.918
-0.6226 1.850
-0.5706 1.793
-0.5276 1.743
-0.4915 1.700
-0.4607 1.662
-0.4;41.1.628
-0.4109 1.598
-0.3905 1.571
-0.3723 1.546
-0.3561 1.523
-0.3415 1.502
-0.3283 1.483
-0.3162 1.465
-0.3053 1.448
-0.2952 1.433
-0.2859 1.418
-0.2773 1.404
-0.2693 1.392
-0.2619 1.380
-0.2550 1. 368
-0.2485 1.357
-0.2424 1.347
0.0005 0.001 0.0025 0.005 0.01
-2.461
-2.646
-2.813
-2.965
-3.105
-3.233
-3.352
-3.463
-3.566
-3.664
-3.755
-3.841
-3.923
-4.000
-4.074
-4.144
-4.211
-4.275
-4.336
-4.395
-4.451
-4.506
-4.558
-4.608
-4.657
-4.704
-4.750
-4.794
-4.836
-4.873
-2.345
-2.494
-2.628
-2.750
-2.860
-2.962
-3.055
-3.142
-3.223
-3.298
-3.369
-3.436
-3.499
-3.558
-3.614
-3.668
-3.719
-3.768
-3.814
-3.859
-3.901
-3.942
-3.982
-4.020
-4.056
-4.091
-4.125
-4.158
-4.190
-4.221
-2.179
-2.285
-2.379
-2.464
-2.541
-2.611
-2.675
-2.734
-2.789
-2.840
-2.887
-2.932
-2.974
-3.013
-3.050
-3.085
-3.118
-3.150
-3.180
-3.209
-3.237
-3.263
-3.288
-3.312
-3.336
-3.358
-3.379
-3.400
-3.420
-3.440
-2.039
-2.116
-2.185
-2.245
-2.300
-2.349
-2.394
-2.436
-2.474
-2.509
-2.541
-2.572
-2.600
-2.627
-2.652
-2.676
-2.698
-2.719
-2.739
-2.758
-2.776
-2.794
-2.810
-2.826
-2.841
-2.856
-2.870
-2.883
-2.896
-2.909
e
-1.885
-1.936
-1.981
-2.021
-2.056
-2.088
-2.116
-2.142
-2.166
-2.188
-2.208
-2.227
-2.244
-2.260
-2.275
-2.289
-2.303
-2.315
-2.327
-2.338
-2.3 49
-2.359
-2.368
-2.377
-2.386
-2.394
-2.402
-2.410
-2.417
-2.424
0.025 0.05
-1.649
-1.672
-1.691
-1.708
-1.722
-1.735
-1.746
-1.756
-1.765
-1.773
-1.780
-1.787
-1.793
-1.798
-1.803
-1.807
-1.812
-1.815
-1.819
-1.822
-1.825
-1.828
-1.831
-1.833
-1.836
-1.838
-1.840
-1.842
-1.843
-1.845
-1.436
-1.442
-1.446
-1.450
-1.452
-1.454
-1.456
-1.457
-1.457
-1.458
-1.458
-1.458
-1.458
-1.457
-1.457
-1.456
-1.456
-1.455
-1.454
-1.454
-1.453
-1.452
-1.451
-1.450
-1.449
-1.448
-1.447
-1. 41~6
-1.445
-1.444
0.10
0.25
0.50
-1.177
-1.171
-1.165
-1.159
-1.154
-1.148
-1.143
-1.138
-1.133
-1.129
-1.125
-1.120
-1.116
-1.112
-1.109
-1.105
-1.102
-1.098
-1.095
-1.092
-1.088
-1.085
-1.082
-1.080
-1.077
-1.074
-1.071
-1.069
-1.066
-1.064
-0.704
-0.692
-0.681
-0.672
-0.663
-0.654
-0.647
-0.640
-0.633
-0.627
-0.621
-0.616
-0.611
-0.606
-0.601
-0.597
-0.593
-0.589
-0.585
-0.581
-0.578
-0.575
-0.571
-0.568
-0.565
-0.562
-0.560
-0.557
-0.554
-0.552
-0.107
-0.102
-0.098
-0.094
-0.091
-0.088
-0.085
-0.083
-0.080
-0.078
-0.076
-0.075
-0.073
-0.072
-0.070
-0.069
-0.068
-0.066
-0.065
-0.064
-0.063
-0.062
-0.061
-0.061
-0.060
-0.059
-0.058
-0.057
-0.057
-0.056
0.75 0.90 0.95 0.975 0.99 0.995 0.9975 0.999 0.9995
0.586
0.579
0.572
0.566
0.560
0.555
0.550
0.545
0.541
0.537
0.533
0.530
0.526
0.523
0.520
0.517
0.514
0.511
0.508
0.506
0.503
0.501
0.499
0.497
0.495
0.492
0.490
0.489
0.487
0.484
1.3l2 1.800
1.298 1.789
1.285 1.778
1.274 1.768
1.2631.759
1.253 1.751
1.244 1.743
1.236 1.735
1.228 1.728
1.220 1.721
1.213 1.715
1.207 1.709
1.200 1.703
1.194 1.697
1.188 1.692
1.183 1.687
1.178 1.682
1.173 1.677
1.168 1.672
1.163 1.668
1.159 1.664
1.154 1.659
1.150 1.655
1.146 1.651
1.142 1.648
1.138 1.644
1.135 1.640
1.131 1. 637
1.127 1.634
1.124 1.630
e
2.261
2.258
2.254
2.251
2.247
2.243
2.240
2.237
2.233
2.230
2.227
2.224
2.221
2.218
2.215
2.212
2.209
2.207
2.204
2.201
2.199
2.196
2.194
2.192
2.189
2.187
2.185
2.182
2.180
2.178
2.846
2.861
2.874
2.886
2.896
2.904
2.912
2.919
2.925
2.931
2.936
2.941
2.945
2.949
2.953
2.956
2.959
2.962
2.964
2.967
2.969
2.971
2.973
2.975
2.977
2.978
2.980
2.981
2.983
2.984
3.277
3.313
3.344
3.371
3.396
3.418
3.438
3.457
3.474
3.490
3.504
3.518
3.531
3.542
3.553
3.564
3.574
3.583
3.592
3.600
3.608
3.616
3.623
3.630
3.637
3.643
3.649
3.655
3.660
3.666
3.702
3.763
3.816
3.865
3.908
3.948
3.984
4.017
4.048
4.077
4.104
4.129
4.153
4.175
4.196
4.216
4.235
4.253
4.270
4.286
4.302
4.317
4.331
4.344
4.358
4.370
4.382
4.394
4.406
4.416
. ~.259
4.360
4.451
4.533
4.797
4.852
4.902
4.950
4.995
5.038
5.078
5.116
5.152
5.186
5.219
5.251
5.281
4.679
4.816
4.940
5.053
5.155
5.250
5.338
5.419
5.496
5.567
5.634
5.698
5,758
5.815
5.869
5.921
5.970
6.017
6.062
6.106
5.337
5.364
5.390
5.414
5.438
5.461
5 483
5.505
5.526
6.187
6.226
6.263
6.299
6.333'
6.367
6.399
6.431
6.461
!~.607
4.676
4.7~
5:310~6.147
e
e
,r~l
e
= 0.8
l!"\
r-I
e
Cumulative Probability
~2
'1
8
4.6
4.8
5.0
5.2
5.4
5.6
5.8
6.0
6.2
6.4
6.6
6.8
7.0
7.2
7.4
7.6
7.8
8.0
8.2
8.4
8.6
8.8
9.0
9.2
9.4
9.6
9.8
10.0
10.2
10.4
-1.9324
-1.4850
-1.2154
-1..0343
-0.9040
-0.8055
-0.7284
-0.6663
-0.6152
-0.5724
-0.5360
-0.5045
-0.4772
-0.4531
-0.4318
-0.4127
-0.3956
-0.3801
-0.3660
-0.3531
-0.3413
-0.3305
-0.3204
-0.3111
-0.3025
-0.2944
-0.2868
-0.2798
-0.2731
-0.2669
2.642
2.403
2.234
2.105
2.005
1.923
1.855
1.797
1.747
1.704
1.666
1.632
1.601
1.573
1.548
1.525
1.504
1.485
1.467
1.450
1.435
1.420
1.406
1. 393
1.381
1.370
1.359
1.349
1.339
1.329
I
0.0005 0.001
-2.639 -2.479
-2.795 -2.604
-2.937 -2.717
-3.068 -2.821
-3.190 -2.918
-3.303 -3.007
-3.409 -3.090
-3.508 -3.167
-3.601 -3.240
-3.689 -3.308
-3.773 -3.373
-3.852 -3.434
-3.927 -3.492
-3.999 -3.547
-4.067 -3.599
-4.132 -3.649
-4.195 -3.697
-4.255 -3.743
-4.313 -3.787
-4.369 -3.829
-4.422 -3.869
-4.474 -3.908
-4.524 -3.946
-4.572 -3.982
-4.618 -4.017
-4.663 -4.051
-4.707 -4.084
-4.749 -4.115
-4.790 -4.146
..4.830 -4.176
0.0025 0.005
-2.261 -2.089
-2.349 -2.152
-2.429 -2.209
-2.501 -2.261
-2.568 -2.308
-2.629 -2.352
-2.686 -2.391
-2.739 -2.428
-2.788 -2.462
-2.834 -2.494
-2.877 -2.524
-2.918 -2.552
-2.956 -2.578
-2.993 -2.603
-3.028 -2.626
-3.060 -2.649
-3.092 -2.670
-3.122 -2.690
-3.150 -2.709
-3.177 -2.727
-3.204 -2.744
-3.229 -2.761
-3.253 -2.777
-3.276 -2.792
-3.298 -2.807
-3.320 -2.821
-3.341 -2.835
-3.361 -2.848
-3.380 -2.860
-3.399 -2.873
e
0.01
-1.906
-1.949
-1.986
-2.020
-2.050
-2.078
-2.103
-2.126
-2.148
-2.168
-2.186
-2.203
-2.220
-2.235
-2.249
-2.262
-2.275
-2.287
-2.298
-2.309
-2.319
-2.329
-2.338
-2.347
-2.356
-2.364
-2.372
-2.379
-2.386
-2.393
0.025
-1.643
-1.662
-1.678
-1.692
-1.704
-1.716
-1.726
-1.735
-1.743
-1.750
-1.757
-1.763
-1.769
-1.774
-1.779
-1.783
-1.787
-1.791
-1.795
-1.798
-1.801
-1.804
-1.807
-1. 809
-1.812
-1.814
-1.816
-1.818
-1.820
-1.822
0.05
-1.417
-1.422
-1.425
-1.428
-1.431
-1.432
-1.434
-1.435
-1.436
-1.436
-1.437
-1.437
-1.437
-1.437
-1.437
-1.436
-1.436
-1.435
-1.435
-~.435
-1.434
-1.433
-1.433
-1. 432
-1.431
-1.431
-1.430
-1.429
-1.428
-1.428
0.10
-1.152
-1.147
-1.142
-1.138
-1.133
-1.128
-1.124
-1.120
-1.116
-1.112
-1.108
-1.105
-1.101
-1.098
-1.094
-1.091
-1.088
-1.085
-1.082
-1.079
-1.076
-1.074
-1.071
-1. 068
-1.066
-1.063
-1.061
-1.058
-1.056
-1.054
0.25
-0.688
-0.678
-0.669
-0.660
-0.653
-0.646
-0.639
-0.633
-0.627
-0.621
-0.616
-0.611
-0.607
-0.602
-0.598
-0.594
-0.590
-0.586
-0.583
-0.580
-0.576
-0.573
-0.570
-0.567
-0.564
-0.562
-0.559
-0.556
-0.554
-0.551
0.50
-0.112
-0.108
-0.104
-0.101
-0.098
-0.095
-0.092
-0.090
-0.088
-0.086
-0.084
-0.082
-0.080
-0.079
-0.078
-0.076
-0.075
-0.074
-0.073
-0.071
-0.070
-0.069
-0.068
-0.068
-0.067
-0.066
-0.065
-0.064
-0.064
-0.063
o. 75
0~'90
0.562 1.290
0.557 1.279
0.551 1.268
0.546 1.258
0.542 1.249
0.537 1.241
0.533 1.233
0.530 1.225
0.526 1.218
0.522 1.211
0.519 1.205
0.516 1.198
0.513 1.193
0.510 1.187
0.507 1.182
0.505 1.177
0.502 1.172
0.500 1.167
0.498 1.162
0.495 1.158
0.493 1.154
0.491 1.150
0.489 1.146
0.487 1.142
0.485 1.138
0.483 1.134
0.481 1.131
0.480.1.128
0.478 1.124
0.476 1.121
e
0.95
1.797
1.787
1.777
1.768
1.760
1.752
1.744
1.737
1.730
1.724
1.718
1.712
1.706
1.701
1.696
1.691
1.686
1.681
1.677
1.673
1.668
1.664
1.660
1.656
1.653
1.649
1.646
1.642
1.639
1.636
0.915
2.289
2.284
2.280
2.275
2.271
2.267
2.263
2.259
2.255
2.252
2.248
2.245
2.241
2.238
2.235
2.232
2.229
2.226
2.223
2.220
2.217
2.215
2.212
2.210
2.207
2.205
2.202
2.200
2.198
2.195
0.99 . 0.995'0',9915
2.931 3.418 3.909
2.941 3.443 3.955
2.949 3.466 3.996
2.956 3.487 4.034
2.963 3.505 4.068
2.969 3.523 4.100
2.974 3.538 4.129
2.9793.553 4.157
2.983 3.566 4.182
2.987 3.579 4.206
2.990 3.591 4.229
2.993 3.602 4.250
2.996 3.612 4.270
2.999 3.6214.289
3~001 3.631 4.307
3.004 3.639 4.324
3.006 3.647 4.340
3.008 3.655 4.356
3.010 3.662 4.371
3.011 3.669 4.385
3.013 3.676 4.398
3.014 3.682 4.411
3.015 3.688 4.424
3.017 3.694 4.436
3.018 3.700 4.448
3.019 3.705 4.459
3.020 3.710 4.470
3.021 3.715 4.480
3.022 3.720 4.490
3.022 3.724 4.500
o. 99~' 0.9995
4.569
4.648
4.720
4.786
4.847
4.904
4.956
5.006
5.052
5.095
5.137
5.175
5.212
5.247
5.281
5.313
5.343
5.372
5.400
5.427
5.453
5.478
5.502
5.525
5,548
5.569
5.590
5.610
5.630
5.649
5.078
5.187
5.288
5.380
5.466
5.545
5.620
5.689
5.755
5.817
5.876
5,931
5.984
6.035
6.083
6.129
6.173
6.215
6.256
6.295
6.333
6.369
6.404
6.438
6.471
6.503
6.533
6.563
6.592
6.620
e
e
e
'{f31 = 0.9
Cumulative Probability
~
f3 2
4.6
4.8
5.0
5.2
5.4
5.6
5.8
6.0
6.2
6.4
6.6
6.8
7.0
7.2
7.4
7.6
7.8
8.0
8.2
8.4
8.6
8.8
9.0
9·2
9.4
9.6
9.8
10.0
10.2
10.4
"Y
-4.0271
-2.4735
-1.8320
-1.4703
-1. 2360
-1.0711
-0.9486
-0.8537
-0.7780
-0.7161
-0.6646
-0.6209
-0.5835
-0.5510
-0.5224
-0.4972
-0.4747
-0.4546
-0.4364
-0.4199
-0.4048
-0.3910
-0.3783
-0.3666
-0.3558
-0.3457
-0.3363
-0.3276
-0.3193
-0.3116
5
.
3.093
2.695
2.441
2.262
2.128
2.023
1.939
1.868
1.809
1.758
1.713
1.674
1.639
1.608
1.580
1.555
1.531
1.510
1.490
1.472
1.455
1.439
1.424
1.410
1.397
1.385
1.373
1.362
1.352
1.342
0.0005 0.001
-2.264 -2.166
-2.439 -2.308
-2.599 -2.438
-2.746 -2.556
-2.882 -2.664
-3.007 -2.763
-3.124 -2.856
-3.233 -2.942
-3.335 -3.022
-3.431 -3.098
-3.522 -3.169
-3.608 -3.235
-3.689 -3.299
-3.767 -3.359
-3.841 -3.416
-3.911 -3.470
-3.979 -3.522
-4.043 -3.571
-4.105 -3.619
-4.164 -3.664
-4.221 -3.707
-4.277 -3.749
-4.330 -3.790
-4.381 -3.828
-4.430 -3.866
-4.478 -3.902
-4.524 -3.937
-4.569 -3.971
-4.613 -4.003
-4.655 -4.035
0.0025 0.005
-2.024 -1.905
-2.127 -1.981
-2.219 -2.048
-2.303 -2.109
-2.379 -2.164
-2.449 -2.214
-2.513 -2.259
-2.572 -2.301
-2.627 -2.340
-2.679 -2.377
-2.727 -2.410
-2.773 -2.442
-2.815 -2.471
-2.855 -2.499
-2.894 -2.525
-2.930 -2.550
-2.964 -2.574
-2.997 -2.596
-3.028 -2.617
-3.058 -2.637
-3.086 -2.656
-3.114 -2.675
-3.140 -2.692
-3.165 -2.709
-3.189 -2.725
-3.213 -2.741
-3.235 -2.756
-3.257 -2.770
-3.278 -2.784
-3.298 -2.797
0.01
-1.772
-1.823
-1.869
-1.909
-1.945
-1.978
-2.008
-2.035
-2.060
-2.083
-2.105
-2.125
-2.143
-2.160
-2.177
-2.192
-2.206
-2.220
-2.233
-2.245
-2.257
-2.268
-2.278
-2.288
-2.298
-2.307
-2.315
-2.324
-2.332
-2.340
0.025
-1.566
-1.590
-1.611
~1.629
-1.645
-1.660
-1.672
-1.684
-1.694
-1.703
-1.712
-1.719
-1.726
-1.733
-1.739
-1.744
-1.749
-1.754
-1.759
-1.763
-1.767
-1.770
-1.774
-1.777
-1.780
-1.783
-1.785
-1.788
-1.790
-1.793
0.05
-1.377
-1.385
-1.391
-1.397
-1.401
-1.404
-1.407
-1.409
-1.411
-1.413
-1.414
-1.415
-1.416
-1.416
-1.417
-1.417
-1.417
-1.417
-1.417
-1.417
-1.417
-1.417
-1.416
-1.416
-1.415
-1.415
-1.415
-1.414
-1.413
-1.413
0.10
-1.144
-1.140
-1.135
-1.131
-1.127
-1.123
-1.119
-1.115
-1.111
-1.107
-1.104
-1.100
-1.097
-1.094
-1.090
-1.087
-1.084
-1.081
-1.078
-1.076
-1.073
-1.070
-1.068
-1.065
-1.063
-1.060
-1.058
-1.055
-1.053
-1.051
0.25
-0.706
-0.695
-0.685
-0.676
-0.667
-0.659
-0.652
-0.645
-0.639
-0.633
-0.628
-0.622
-0.617
-0.613
-0.608
-0.604
-0.600
-0.596
-0.592
-0.588
-0.585
-0.582
-0.578
-0.575
-0.572
-0.569
-0.567
-0.564
-0.561
-0.559
0.50
-0.133
-0.127
-0.123
-0.li8
-0.114
-0.111
-0.107
-0.105
-0.102
-0.099
-0.097
-0.095
-0.093
-0.091
-0.089
-0.088
-0.086
-0.085
-0.083
-0.082
-0.081
-0.080
-0.079
-0.077
-0.076
-0.075
-0.074
-0.074
-0.073
-0.072
0.75
0.559
0.553
0.548
0.543
0.538
0.534
0.530
0.526
0.522
0.519
0.515
0.512
0.509
0.507
0.504
0.501
0.499
0.496
0.494
0.492
0.490
0.487
0.485
0.483
0.482
0.480
0.478
0.476
0.475
0.473
0.90
1.310
1.297
1.285
1.274
1.264
1.255
1.246
1.238
1.230
1.223
1.216
1.210
1.203
1.197
1.192
1.186
1.181
1.176
1.171
1.167
1.162
1.158
1.154
1.150
1.146
1.142
1.138
1.135
1.131
1.128
0.95
1.830
1.818
1.806
1.796
1.787
1.778
1.769
1.761
1.754
1.747
1.740
1.733
1.727
1.721
1.716
1.710
1.705
1.700
1.695
1.691
1.686
1.682
1.677
1.673
1.669
1.665
1.662
1.658
1.654
1.651
0.975 0.99
2.330 2.977
2.324 2.986
2.318 2.994
2.313 3.001
2.307 3.007
2.302 3.013
2.297 3.017
2.293 3.022
2.288 3.025
2.284 3.029
2.280 3.032
2.275 3.035
2.272 3.037
2.268 3.039
2.264 3.041
2.2613.043
2.257 3.045
2.254 3.046
2.250 3.048
2.247 3.049
2.244 3.051
2.241 3.052
2.238 3.053
2.235 3.054
2.232 3.054
2.230 3.055
2.227 3.056
2.224 3.056
2.222 3.057
2.219 3.058
0.995 0.9975
3.461 3.946
3.488 3.995
3.512 4.038
3.533 4.078
3.552 4.114
3.570 4.147
3.586 4.178
3.600 4.206
3.614 4.232
3.626 4.257
3.638 4.280
3.649 4.301
3.659 4.322
3.668 4.341
3.677 4.359
3.686 4.376
3.694 4.393
3.7014.408
3.708 4.423
3.715 4.437
3.721 4.451
3.728 4.464
3.733 4.476
3.739 4.488
3.744 4.500
3.749 4.511
3.754 4.522
3.759 4.532
3.764 4.542
3.768 4.551
0.999 0.9995
4.589 5.081
4.675 5,200
4.752 5.307
4.823 5.406
4.887 5.497
4.947 5.581
5.002 5.660
5.054 5.733
5.102 5.801
5.147 5,866
5.1895927
5.229 5.985
5.267 6.039
5.303 6.091
5.338 6.141
5.370 6.188
5,401 6.236
5,431 6.277
5.459 6.318
5.487 6.358
5.513 6.397
5.538 6.434
5.562 6.470
5.586 6.504
5.608 6537
5 630 6.570
5.651 6.601
5.672 6.631
5.691 6.660
5 710 6.689
e
.
'[13 1
-
-
e
= 1.0
Cumulative Probability
132
5.0
5.2
5.4
5.6
5.8
6.0
6.2
6.4
6.6
6.8
7.0
7.2
7.4
7.6
7.8
8.0
8.2
8.4
8.6
8.8
9.0
9.2
9.4
9.6
9.8
10.0
10.2
10.4
10.6
10.8
r
-3.5425
-2.3862
-1.8390
-1. 5105
-1.2894
-1.1296
-1.0085
-0.9133
-0.8365
-0.7731
-0.7198
-0.6744
-0.6352
-0.6010
-0.5709
-0.5442
-0.5203
-0.4988
-0.4793
-0.4616
-0.4454
-0.4305
-0.4169
-0.4042
-0.3925
-0.3816
-0.3714
-0.3619
-0.3529
-0.3445
5
2.800
2.512
2.315
2.170
2.057
1. 967
1.892
1.830
1.776
1.730
1.689
1.653
1.620
1.591
1.565
1.541
1.519
1.498
1.479
1. 462
1.446
1.431
1.416
1.403
1.390
1.379
1.367
1.357
1.347
1.337
0.0005 0.001
-2.209 -2.113
-2.377 -2.249
-2.530 -2.373
-2.672 -2.487
-2.802 -2.591
-2.924 -2.688
-3.037 -2.778
-3.144 -2.862
-3.244 -2.941
-3.338 -3.015
-3.427 -3.085
-3.512 -3.151
-3.592 -3.214
-3.669 -3.273
-3.742 -3.330
-3.811 -3.384
-3.878 -3.435
-3.942 -3.484
-4.004 -3.532
-4.063 -3.577
-4.120 ~3.620
-4.175 -3.662
-4.227 -3.703
-4.279 -3.742
-4.328 -3.779
-4.376 -3.815
-4.422 -3.850
-4.467 -3.884
-4.510 -3.917
-4.553 -3.949
0.0025 0.005
-1.974 -1.858
-2.072 -1.931
-2.161 -1.996
-2.242 -2.055
-2.316 -2.109
-2.384 -2.158
-2.447 -2.203
-2.506 -2.245
-2.560 -2.283
-2.611 -2.319
-2.659 -2.353
-2.704 -2.384
-2.746 -2.414
-2.786 -2.442
-2.824 -2.468
-2.860 -2.493
-2.895 -2.517
-2.928 -2.539
-2.959 -2.561
-2.989 -2.581
-3.018 -2.601
-3.045 -2.619
-3.072 -2.637
-3.097 -2.654
-3.121 -2.671
-3.145 -2.686
-3.168 -2.702
-3.190 -2.716
-3.211 -2.730
-3.231 -2.744
0.01
-1.729
-1.779
-1.824
-1.863
-1.899
-1. 931
-1.961
-1.988
-2.013
-2.037
-2.058
-2.078
-2.097
-2.115
-2.131
-2.147
-2.161
-2.175
-2.189
-2.201
-2.213
-2.224
-2.235
-2.245
-2.255
-2.265
-2.274
-2.282
-2.291
-2.299
0.025
-1.532
-1.556
-1.576
-1.595
-1.611
-1. 625
-1.638
-1.650
-1.661
-1.670
-1.679
-1.687
-1.695
-1.702
-1.708
-1.714
-1.719
-1.725
-1.729
-1. 734
-1.738
-1.742
-1.746
-1.749
-1.752
-1.756
-1.758
-1.761
-1.764
-1.766
0.05
-1.351
-1.359
-1.366
-1.371
-1.376
-1. 380
-1.383
-1.386
-1.388
-1.390
-1.392
-1.394
-1.395
-1.396
-1.396
-1.397
-1.398
-1.398
-1.398
-1. 398
-1.398
-1.398
-1.398
-1.398
-1.398
-1.398
-1.398
-1.397
-1.397
-1.397
0.10
-1.126
-1.123
-1.119
-1.116
-1.112
-1.109
-1.105
-1.102
-1.099
-1.095
-1.092
-1.089
-1.086
-1.083
-1.080
-1.077
-1.075
-~.072
-1.069
-1.067
-1.064
-1.062
-1.059
-1.057
-1.054
-1.052
-1.050
-1.048
-1.046
-1.044
0.25
-0.704
-0.694
-0.684
-0.675
-0.667
-0.660
-0.653
-0.646
-0.640
-0.634
-0.629
-0.624
-0.619
-0.614
-0.610
-0.606
-0.602
-0.598
-0.594
-0.591
-0.587
-0.584
-0.581
-0.578
-0.575
-0.572
-0.569
-0.566
-0.564
-0.561
0.50
-0.144
-0.138
-0.133
-0.129
-0.125
-0.121
-0.118
-0.114
-0.112
-0.109
-0.107
-0.104
-0.102
-0.100
-0.098
-0.097
-0.095
-0.093
-0.092
-0.091
-0.089
-0.088
-0.087
-0.086
-0.084
-0.083
-0.082
-0.081
-0.080
-0.079
0.75
0.544
0.539
0.534
0.530
0.526
0.522
0.518
0.515
0.512
0.509
0.506
0.503
0.500
0.498
0.495
0.493
0.490
0.488
0.486
0.484
0.482
0.480
0.478
0.476
0.475
0.473
0.471
0.469
0.468
0.466
0.90
1.304
1.292
1.281
1.271
1.261
1.252
1.244
1.236
1.229
1.222
1.215
1.209
1.203
1.197
1.191
1.186
1.181
1.176
1.171
1.167
1.163
1.158
1.154
1.150
1.146
1.143
1.139
1.136
1.132
1.129
0.95
1.839
1.827
1.816
1.806
1.797
1.788
1.779
1.771
1.764
1.757
1.750
1.743
1.737
1.731
1.726
1.720
1.715
1.710
1.705
1.700
1.696
1.691
1.687
1.683
1.679
1.675
1.671
1.667
1.664
1.660
0.975
2.360
2.353
2.346
2.340
2.334
2.328
2.323
2.318
2.313
2.308
2.303
2.299
2.295
2.291
2.287
2.283
2.279
2.275
2.272
2.268
2.265
2.262
2.259
2.256
2.253
2.250
2.247
2.244
2.241
2.239
0.99
3.040
3.046
3.052
3.057
3.062
3.065
3.069
3.072
3.074
3.077
3.079
3.080
3.082
3.084
3.085
3.086
3.087
3.088
3.089
3.090
3.090
3.091
3.091
3.092
3.092
3.093
3.093
3.093
3.093
3.094
0.995
3.555
3.577
3.597
3.615
3.632
3.647
3.660
3.673
3.684
3.695
3.705
3.715
3.724
3.732
3.740
3.747
3.754
3.760
3.767
3.773
3.778
3.784
3.789
3.794
3.798
3.803
3.807
3.811
3.815
3.819
0.9975
4.074
4.117
4.155
4.190
4.222
4.252
4.279
4.304
4.328
4.350
4.371
4.391
4.409
4.426
4.443
4.459
4.474
4.488
4.502
4.515
4.527
4.539
4.551
4.562
4.572
1~.583
4.592
4.602
4.611
4.620
0.999
4.770
4.846
4.916
4.980
5.038
5.093
5.144
5.191
5.235
5.277
5.317
5.354
5.389
5.423
5.455
5.485
5.514
5.542
5.569
5.595
5.619
5.643
5.666
5.688
5.709
5.730
5.750
5.769
5.788
5.806
0.9995
5.305
5.413
5.511
5.602
5.685
5.763
5.836
5.904
5.968
6.028
6.085
6.139
6.191
6.240
6.287
6.331
6.374
6.415
6.455
6.493
6.529
6.565
6.599
6.632
6.663
6.694
6.724
6.753
6.781
6.808
e
e
e
'[131
= 1.1
Cumulative Probability
r-i
132
5.4
5.6
5.8
6.0
6.2
6.4
6.6
6.8
7.0
7.2
7.4
7.6
7.8
8.0
8.2
8.4
8.6
8.8
9.0
9.2
9.4
9.6
9.8
10.0
10.2
10.4
10.6
10.8
11.0
11.2
'Y
-3.. 5312
-2.4517
-1.9216
-1. 5959
-1.3729
-1.2097
-1.oB48
-0.. 9858
-0.9054
-0.8387
-0.7824
-0.7342
-0.6925
-0.6560
-0.6237
-0.5950
-0.5693
-0.5462
-0.5252
-0.5060
-0.4885
-0.4724
-0.4576
-0.4439
-0.4311
-0.4192
-0.4oB2
-0.3978
-0.3881
-0.3789
e
I
2.631
2.400
2.235
2.109
2.009
1.928
1.860
1.803
1.753
1.710
1.671
1.637
1.607
1.579
1.,54
1.531
1.510
1.490
1.472
1.455
1.440
1.425
1.411
1.398
1.386
1.374
1.363
1.353
1.343
1.334
0.0005 0.001
-2.124 -2.034
-2.286 -2.166
-2.435 -2.287
-2.573 -2.398
-2.701 -2.501
-2.820 -2.596
-2.932 -2.685
-'.036 -2.769
-3.135 -2.847
-3.229 -2.920
-3.317 -2.990
-3.401 -3.056
-3.481 -3.118
-3.557 -3.177
-3.630 -3.234
-3.700 -3.288
-3.766 -3.340
-3.830 -3.389
-3.892 -3.437
-3.951 -3.482
-4.008 -3.526
-4.063 -3.568
-4.116 -3.609
-4.167 -3.648
-4.217 -3.686
-4.265 -3.722
-4.311 -3.757
-4.356 -3.792
-4.400 -3.825
-4.443 -3.857
0.0025 0.005
-1..906 -1.798
-2.002 -1.870
-2.oB9 -1.934
~2.168 -1.992
-2.241 -2.045
-2.309 -2.094
-2.371 -2.139
-2.429 -2.181
-2.483 -2.220
-~S34 -2.256
-2.582 -2.290
-2.627 -2.322
-2.670 -2.352
-2.710 -2.380
-2.749 -2.407
-2.785 -2.432
-2.820 -2.456
-2.853 -2.479
-2.885 -2.501
-2.915 -2.521
-2.944 -2.541
-2.972 -2.560
-2.999 -2.579
-3.024 -2.596
-3.049 -2.613
-3.073 -2.629
-3.096 -2.645
-3.119 -2.660
-3.140 -2.674
-3.161 -2.688
0.01
-1.679
-1.728
-1.772
-1.811
-1.847
-1.880
-1.910
-1.937
-1.963
-1.986
-2.ooB
-2.0~
-2.048
-2.066
-2.083
-2.099
-2.11~
-2.128
-2.142
-2.155
-2.167
-2.179
-2.190
-2.201
-2.211
-2.221
-2.230
-2.239
-2.248
-2.256
0.025
-1.493
-1.517
-1.539
-1.557
-1.574
-1.589
-1.603
-1.615
-1.626
-1.636
-1.645
-1.654
-1.662
-1.669
-1.676
-1.682
-1.688
-1.694
-1.699
-1.704
-1.708
-1.713
-1.717
-1.721
-1.724
-1.728
-1.731
-1.734
-1.737
-1.740
0.05
-1.323
-1.332
-1.339
-1.345
-1.351
-1.355
-1.359
-1.362
-1.365
-1.368
-1.370
-1.372
-1.373
-1.375
-1.376
-1..377
-1.378
-1.379
-1.379
-1.380
-1.380
-1.380
-1.381
-1.381
-1.381
-1.381
-1.381
-1.381
-1.381
-1.380
0.10
-1.110
-1.107
-1.104
-1.101
-1.099
-1.096
-1.093
-1.090
-1.087
-1.084
-1.081
-1.078
-1.076
-1.073
-1.970
-1.068
-1.065
-1.063
-~.060
-1.058
-1.056
-1.053
-1.051
-1.049
-1.047
-1.045
-1.043
-1.041
-1.039
-1.037
0.25
-0.703
-0.694
-0.684
-q.676
-0.668
-0.661
-0.654
-0.648
-0.642
-0.637
-0.631
-0.626
-0.621
-0.617
-0.613
-0.608
-0.604
-0.601
-0.597
-0.593
-0.590
-0.587
-0.584
-0.581
-0.578
-0.575
-0.572
-0.569
-0.567
-0.564
0.50
-0.155
-0.150
-0.144
-0.140
-0.135
-0.131
-0.128
-0.125
-0.122
-0.119
-0.116
-0.114
-0.112
-0.110
-o.loB
-0.106
-0.104
-0.102
-0.101
-0.099
-0.098
-0.096
-0.095
-0.094
-0.093
-0.091
-0.090
-0.089
-0.088
-0.087
0.75 0.90
0.530 1.301
0.526 1.289
0.522 1.279
0.518 1.269
0.514 1.260
0.511 1.251
0.508 1.243
0.505 1.235
0.502 1.228
0.499 1.221
0.496 1.215
0.494 1.209
0.491 1.203
0.489 1.197
0.487 1.192
0.485 1.187
0.482 1.182
0.480 1.177
0.478 1.172
0.4761.168
0.475 1.163
0.473 1.159
0.471 1.155
0.469 1.151
0.468 1.147
0.466 1.144
0.465 1.140
0.463 1.137
0.461 1.133
0.460 1.130
0.95
1.850
1.838
1.827
1.817
1.807
1.798
1.790
1.782
1.774
1.767
1.760
1.754
1.747
1.741
1.736
1.730
1.725
1.720
1.715
1.710
1.705
1.701
1.696
1.692
1.688
1.684
1.680
1.676
1.673
1.669
0.975
2.388
2.381
1.373
2.367
2.360
2.354
2.348
2.343
2.337
2.332
2.327
2.322
2.318
2.313
2.309
2.305
2.301
2.297
2.293
2.290
2.286
2..283
2.279
2.276
2.273
2.270
2.267
2.26h
2.261
2.258
0.99
3.099
}.103
3.107
3.110
3.113
3.116
3.118
3.120
3.121
3.123
3.124
3.125
3.126
3.126
3.127
3.128
3.128
3.128
3.129
3.129
3.129
3.129
3.129
3.129
3.129
3.129
3.129
3.129
3.129
3.129
0.995
3.641
3.659
3.677
~.0692
3.706
3.719
3.730
3.741
3.751
3.761
3.770
3.778
3.785
3.793
3.800
3.806
3.812
3.818
3.823
3.828
3.833
3.838
3".842
}.0847
3.851
3.855
3.858
3.862
3.866
3.869
0.9975
4.190
4.228
4.262
4.293
4.322
4.349
4.373
4.396
4.418
4.438
4.457
4.475
4.492
4.508
4.523
4.537
4.551
4.564
4.577
4.589
4.600
4.611
4.622
4.632
4.642
4.65.2
4.661
4.670
4.678
4.686
0.999 0.9995
4~9il 5.505
5.000 5.603
5.064 5.694
5.123 5.778
5.177 5.856
5.227 5.929
5.274 5.997
5.318 6.061
5.359 6.121
5.398 6.178
5.435 6.232
5.470 6.283
5.502 6.332
5.535 6.379
5.565 6.423
5.594 6.466
5.621 6.506
5.647 6.546
5.673 6.583
5.697 6.620
5.720 6.654
5.743 6.688
5.765 6.721
5.786 6.752
5.806 6.783
5.825 6.812
5.844 6.841
5.863 6.869
5.880 6.895
5.898 6.922
e
-
e
.[~1
},
r-I
= 1.2
Cumulative Probability
~2
5.8
6.0
6.2
6.4
6.6
6.8
7.0
7.2
7.4
7.6
7.8
8.0
8.2
8.4
8.6
8.8
9.0
9.2
9.4
9.6
9.8
10.0
10.2
10.4
10.6
10.8
11.0
11.2
11.4
11.6
'1
B
I
-3.8946
-2.6550
-2.0793
-1. 7292
-1.4899
-1.3148
-1.1805
-1.0740
-0.9872
-0.9152
-0.8543
-0.8021
-0.7569
-0.7172
-0.6822
-0.6510
-0.6230
-0.5978
-0.5749
-0.5541
-0.5350
-0.5174
-0.5012
-0.4862
-0.4723
-0.4593
-0.4472
-0.4359
-0.4252
-0.4152
2.531
2.332
2.184
2.070
1.979
1.903
1.840
1.785
1.738
1.697
1.660
1.628
1.598
1.572
1.547
1.525
1.504
1.485
1.468
1.451
1.436
1.421
1.408
1.395
1.383
1.372
1.361
1.351
1.341
1.332
0.0005 0.001
-2.008 -1.932
-2.168 -2.062
-2.315 -2.182
-2.451 -2.292
-2.578 -2.394
-2.696 -2.489
-2.807 -2.578
-2.912 -2.661
-3.010 -2.739
-3.103 -2.813
-3.192 -2.883
-3.276 -2.949
-3.356 -3.012
-3.432 -3.071
-3.505 -3.128
-3.575 -3.183
-3.642 -3.235
-3.707 -3.285
-3.769 -3.333
-3.828 -3.379
-3.886 -3.423
-3.941 -3.466
-3.995 -3.507
-4.046 -3.547
-4.096 -3.585
-4.145 -3.622
-4.192 -3.658
-4.238 -3.693
-4.282 -3.736
-4.325 -3.759
0.0025 0.005
-1.821 -1.726
-1.916 -1.797
-2.002 -1.861
-2.081 -1.920
-2.154 ~~.913
-2.222 -2.023
-2.285 -2.068
-2.343 -2.110
-2.398 -2.150
-2.449 -2.187
-2.498 -2.221
-2.543 -2.253
-2.586 -2.284
-2.627 -2.'13
-2.666 -2.340
-2.703 -2.366
-2.738 -2.391
-2.772 -2.414
-2.804 -2.437
-2.835 -2.458
-2.865 -2.478
-2.893 -2.498
-2.921 -2.517
-2.947 -2.535
-2.972 -2.552
-2.997 -2.569
-3.020 -2.585
-3.043 -2.600
-3.065 -2.615
-3.086 -2.630
0.01
-1.619
-1.668
-1.713
-1.753
-1.789
-1.822
-1.853
-1.881
-1.907
-1.932
-1.954
-1.975
-1.995
-2.014
-2.031
-2.048
-2.064
-2.079
-2.093
-2.106
-2.119
-2.131
-2.143
-2.154
-2.165
-2.175
-2.185
-2.194
-2.203
-2.212
0.025
-1.451
-1.476
-1.498
-1.517
-1.535
-1.550
-1.564
-1.577
-1.589
-1.600
-1.610
-1.619
-1.628
-1.635
-1.643
-1.650
-1.656
-1.662
-1.668
-1.673
-1.678
-1.683
-1.687
-1.691
-1.695
-1.699
-1.702
-1.706
-1.709
-1.712
0.05'0.10
-1.293 -1.093
-1.303 -1.091
-1.311 -1.089
-1.318 -1.087
-1.324 -1.085
-1.330 -1.083
-1.334 -1.080
-1.338 -1.078
-1.342 -1.075
-1.345 -1.073
-1.347 -1.070
-1.350 -1.068
-1.352 -1.065
-1.354 -1.063
-1.355 -1.061
-1.356 -1.058
-1.358 -1.056
-1.359 -1.054
-1.360 -1.052
-1.361 -1.049
-1.361 -1.047
-1.362 -1.045
-1.362 -1.043
-1.363 -1.041
-1.363 -1.039
-1.363 -1.037
-1.364 -1.035
-1.364 -1.033
-1.364 -1.031
-1.)64 -1.030
0.25
-0.704
-0.695
-0.686
-0.678
-0.670
-0.663
-0.657
-0.651
-0.645
-0.639
-0.634
-0.629
-0.624
-0.620
-0.616
-0.611
-0.608
-0.604
-0.600
-0.597
-0.593
-0.590
-0.587
-0.584
-0.581
-0.578
-0.575
-0.573
-0.570
-0.568
0.50
-0.168
-0.161
-0.156
-0.151
-0.147
-0.142
-0.139
-0.135
-0.132
-0.129
-0.126
-0.124
-0.121
-0.119
-0.117
-0.115
-0.113
-O.lll
-0.110
-0.108
-0.106
-0.105
-0.104
-0.102
-0.101
-0.100
-0.098
-0.097
-0.096
-0.095
0.75
0.517
0.513
0.510
0.507
0.504
0.501
0.498
0.495
0.492
0.490
0.488
0.485
0.483
0.481
0.479
0.477
0.475
0.473
0.471
0.469
0.468
0.466
0.464
0.463
0.461
0.460
0.458
0.457
0.455
0.454
0.90
1.299
1.288
1.278
1.268
1.259
1.251
1.243
1.236
1.229
1.222
1.215
~.209
1.204
1.198
1.193
1.187
1.183
1.178
1.173
1.169
1.164
1.160
1.156
1.152
1.149
1.145
1.141
1.138
1.134
1.131
0.95
1.861
1.849
1.838
1.828
1.819
1.810
1.801
1.793
1.785
1.778
1.771
1.765
1.758
1.752
1.746
1.741
1.735
1.730
1.725
1.720
1.715
1.711
1.706
1.702
1.698
1.694
1.690
1.686
1.682
1.679
0.975
2.417
2.409
2.401
2.393
2.386
2.380
2.373
2.367
2.362
2.356
2.351
2.346
2.341
2.336
2.332
2.327
2.323
2.319
2.315
2.311
2.307
2.303
2.300
2.296
2.293
2.290
2.286
2.283
2.280
2.277
0.99
3.154
3.157
3.159
3.161
3.163
3.164
3.165
3.166
3.167
3.167
3.168
3.168
3.168
3.168
3.168
3.168
3.168
3.168
3.168
3.168
3.167
3.167
3.167
3.166
3.166
3.166
3.165
3.165
3.164
3.164
0.995
3.720
3.736
3.751
3.764
3.776
3.787
3.797
3.807
3.815
3.824
3.831
3.838
3.8!~5
3.851
3.857
3.863
3.868
3.873
3.878
3.882
3.886
3.891
3.895
3.898
3.902
3.905
3.909
3.912
3.915
3.918
0.9975
4.296
4.330
4.361
4.389
4.415
4.439
4.462
4.483
4.502
4.521
4.538
4.555
4.570
4.585
4.599
4.612
4.625
4.637
4.649
4.660
4.671
4.681
4.691
4.700
4.710
4.718
4.727
4.735
4.743
4.751
0.999
5.076
5.140
5.199
5.254
5.304
5.351
5.395
5.436
5.475
5.512
5.546
5.579
5.611
5.640
5.669
5.696
5.722
5.747
5.771
5.794
5.817
5.838
5.859
5.879
5.898
5.917
5.935
5.952
5.969
5.986
0.9995
5.682
5.775
5.860
5.939
0.012
6.081
6.145
6.206
6.263
6.317
6.369
6.417
6.464
6.508
6.551
6.592
6.631
6.668
6.704
6.739
6.773
6.805
6.837
6.867
6.896
6.925
6.952
6.979
1.005
7.030
e
e
tit
,[t31 = 1.3
:>
Cumulative Probability
\l
t32
6.2
6.4
6.6
6.8
7.0
7.2
7.4
7.6
7.8
8.0
8.2
8.4
8.6
8.8
9.0
9.2
9.4
9.6
9.8
10.0
10.2
10.4
10.6
10.8
11.0
11.2
11.4
11.6
11.8
12.0
"I
-5.1251
-3.0563
-2.3365
-1.9248
-1.6505
-1.4523
-1.3015
-1.1825
-1.0859
-1.0058
-0.9383
-0.8806
-0.8305
-0.7867
-0.7480
-0.7136
-0.6828
-0.6550
-0.6297
-0.6068
-0.5857
-0.5664
-0.5486
-0.5321
-0.5167
-0.5025
-0.4891
-0.4767
-0.4650
-0.4540
o I 0.0005 0.001 0.0025 0.005 0.01
2.477
2.294
2.157
2.049
1.962
1.890
1.829
1.776
1.731
1.691
1.655
1.623
1.594
1.568
1.544
1.522
1.502
1.483
1.466
1.450
1.434
1.420
1.407
1.394
1.382
1.371
1.360
1.350
1.340
1.331
-1.865
-2.023
-2.170
-2.306
-2.433
-2.552
-2.664
-2.769
-2.868
-2.962
-3.051
-3.136
-3.217
-3.294
-3.368
-3.439
-3.506
-3.572
-3.634
-3.695
-3.753
-3.809
-3.863
-3.910
-3.967
-4.016
-4.064
-4.110
-4.155
-4.199
-1.807
-1.936
-2.056
-2.167
-2.270
-2.365
-2.455
-2.539
-2.618
-2.693
-2.763
-2.830
-2.894
-2.955
-3.013
-3.068
-3.121
-3.172
-3.220
-3.267
-3.312
-3.356
-3.396
-3.438
-3.477
-3.515
-3.551
-3.587
-3.621
-3.654
-1.719
-1.814
-1.901
-1.981
-2.055
-2.124
-2.188
-2.247
-2.303
-2.355
-2.404
-2.451
-2.495
-2.537
-2.576
-2.614
-2.650
-2.685
-2.718
-2.750
-2.780
-2.809
-2.837
-2.864
-2.890
-2.915
-2.940
-2.963
-2.986
-3.008
-1.641
-1.713
-1.778
-1.838
-1.892
-1.943
-1.989
-2.032
-2.073
-2.111
-2.146
-2.179
-2.211
-2.241
-2.269
-2.295
-2.321
-2.345
-2.368
-2.390
-2.411
-2.432
-2.451
-2.470
-2.488
-2.505
-2.521
-2.538
-2.553
-2.568
-1.551
-1.601
-1.646
-1.688
-1.725
-1.760
-1.791
-1.820
-1.847
-1.e73
-1.896
-1.918
-1.939
-1.958
-1.977
-1.994
-2.010
-2.026
-2.041
-2.055
-2.068
-2.081
-2.093
-2.105
-2.116
-2.127
-2.137
-2.147
-2.157
-2.166
0.025 0.05
-1.404
-1.430
-1.453
-1.473
-1.492
-1.509
-1.524
-1.537
-1.550
-~.562
-1.572
-1.582
-1.591
-1.600
-1.608
-1.615
-1.622
-1.629
-1.635
-1.641
-1.646
-1.651
-1.656
-1.651
-1.665
-1.669
-1.673
-1.677
-1.680
-1.684
-1.262
-1.273
-1.282
-1.290
-1.297
-1.303
-1.308
-1.313
-1.317
-1.321
-1.324
-1.327
-1.329
-1.332
-1.334
-1.335
-1.337
-1.338
-1.340
-1.341
-1.342
-1.343
-1.~
-1.344
-1.345
-1.346
-1.346
-1.346
-1.347
-1.347
0.10
0.25
0.50
-1.077
-1.076
-1.075
-1.073
-1.072
-1.070
-1.068
-1.066
-1.064
-1.062
-1.060
-1.057
-1.055
-1.053
-1.051
-1.049
-1.047
-1.045
-1.043
-1.041
-1.039
-1.037
-1.035
-1.033
-1.032
-1.030
-1.028
-1.026
-1.025
-1.023
-0.707
-0.697
-0.689
-0.681
-0.673
-0.667
-0.660
-0.654
-0.648
-0.643
-0.638
-0.633
-0.628
-0.623
-0.619
-0.615
-0.611
-0.607
-0.604
-0.600
-0.597
-0.594
-0.591
-0.587
-0.585
-0.582
-0.579
-0.576
-0.574
-0.571
-0.181
-0.174
-0.168
-0.163
-0.158
-0.154
-0.150
-0.146
-0.143
-0.140
-0.137
-0.134
-0.132
-0.129
-0.127
-0.125
-0.123
-0.121
-0.119
-0.117
-0.115
-0.114
-0.112
-O.lll
-0.109
-0.108
-0.107
-0.106
-0.104
-0.103
0.75 0.90 0.95 0.975 0.99 0.995 0.9975 0.9990.9995
0.504
0.501
0.498
0.496
0.493
0.490
0.488
0.486
J.483
0.481
0.479
0.477
0.475
0.473
0.471
0.469
0.467
o.46j
0.464
0.462
0.461
0.459
0.457
0.456
0.455
0.453
0.452
0.450
0.449
0.448
1.298
1.287
1.278
1.268
1.260
1.251
1.244
1.236
1.229
1.223
1.217
1.211
1.205
1.199
1.194
1.189
1.184
1.179
1.175
1.170
1.166
1.162
1.158
1.154
1.150
1.147
1.143
1.140
1.136
1.133
1.874 2.445 3.208
1.862 2.437 3.209
1.B51 2.428 3.210
1.841 2.420 3.211
1.831 2.413 3.211
1.822 2.406 3.211
1.813 2.399 3.211
1.805 2.392 3.211
1.797 2.386 3.211
1.790 2.380 3.211
1.783 2.375 3.211
1.776 2.369 3.210
1.770 2.364 3.210
1.763 2.359 3.209
1.757 2.354 3.209
1.752 2.350 3.208
1.746 2.345 3.208
1.741 2.341 3.207
1.736 2.336 3.206
1.731 2.332 3.206
1.726 2.328 3.205
1.721 2.324 3.204
1.717 2.321 3.204
1.713 2.317 3.203
1.708 2.313 3.202
1.704 2.310 3.201
1.700 2.306 3.201
1.696 2.303 3.200
1.692 2.300 3.199
1.689 2.297 3.198
3.795
3.809
3.821
3.833
3.843
3.853
3.861
3.869
3.877
3.884
3.891
3.897
3.903
3.908
3.913
3.918
3.923
3.927
3.931
3.935
3.939
3.942
3.~5
3.949
3.952
3.955
3.958
3.960
3.963
3.965
4.394
4.425
4.453
4.479
4.502
4.525
4.546
4.565
4.583
4.600
4.616
4.631
4.646
4.659
4.672
4.685
4.697
4.708
4.719
4.729
4.739
4.748
4.758
4.706
4.775
4.783
4.791
4.799
4.806
4.813
5.208
5.268
5.324
5.375
5.422
5.466
5.508
5.547
5.584
5.618
5.651
5.683
5.712
5.741
5.768
5.794
5.819
5.842
5.865
5.887
5.909
5.929
5.949
5.96CS
5.986
6.004
6.022
6.038
6.055
6.071
5.843
5.930
6.011
6.086
6.156
6.221
6.282
6.340
6.395
6.447
6.496
6.543
6.588
6.630
6.671
6.710
6.748
6.784
6.819
6.853
6.885
6.916
6.947
6.976
7.004
7.032
7.058
7.084
7.110
7.134
e
.[f31
= 1. 1+
Cumulative Probability
r-I
C\J
--
e
f3 2
"I
8
0.0005 0:001 0.0025 0.005 0.01
0.025 0.05
0.10
0.25
0.50
0.75 0.90
0.95 0.975 0.99 0.995 0.9975 0.9990.9995
6.8
7.0
7.2
7.4
7.6
7.8
8.0
-3.9507
-2.7700
-2.2184
-1.8754
-1.6361
-1.4577
-1.3189
2.282
2.148
2.043
1.958
1.887
1.827
1. 775
-1.852 -1.789 -1.696
-2.001 -1.911 -1.785
-2~139 -2.023 -1;867
~2.a67 ~2.128 -1.943
-2.388 -2.225 ...2.014
-2.501 -2.317 -2.079
-2.608 -2.402 -2.140
-1.616 -1.525 -1.379
-1.683 -1.572 -1.404
~1.745 -1.615 -1.426
.~801 -1.654 -1.446
-1.853 -1.690 -1.464
-1.902 -1.723 -1.480
-1.946 -1.754 -1.495
-1.240
-1.251
-1.260
-1.268
-1.275
-1.281
-1.286
-1.060
-1.060
-1.059
-1.058
-1.057
-1.055
-1.054
-0.701
-0.693
-0.685
-0.677
-0.671
-0.664
-0.658
-0.188
-0.182
-0.176
-0.171
-0.166
-0.162
-0~158
0.489 1.288 1.875
0.487 1.278 1.864
0.485~1.269 1.854
0.483 1.261 1.844
0.480 1.253 1.835
0.478 1.245 1.826
0.476 1.238 1.8~8
8.2
8.4
8.6
8.8
9.0
-1.2074
-1.1156
-1.0386
-0.9730
-0.9164
1.730
1.690
1.655
1.623
1.595
-2.708
-2.804
-2.895
-2.981
-3.063
-2.483
-2.559
-2.631
-2.700
-2.765
-2.197
-2.251
-2.302
-2.350
-2.395
-1.988
-2.027
-2.064
-2.099
-2.131
-1.782
-1.809
-1.833
-1.857
-1.878
-1.508
-1.521
-1..532
-1.543
-1.553
-1.291
-1.295
-1.299
-1.303
-1.306
-1.052
-1.050
-1.049
-1.047
-1.045
-0.652
-0.647
-0.642
-0.637
-0.632
-0.154
-0.151
-0.148
-0.145
-0.142
0.474
0.472
0.470
0.468
0.467
1.231
1.225
1.218
1.212
1.207
9.2
9.4
9.6
9.8
10.0
-0.8670
-0.8235
-0.'7649
-0.7503
-0.7192
1. 568
1.545
1. 523
1.503
1. 484
-3.141
-3.217
-3.289
-3.358
-3.424
-2.886
-2.942
-2.997
-3.049
-2.8~7
-2.438
-2.479
-2.518
-2.555
-2.591
-2.16?
-2.192
-2.219
-2.246
-2.271
-1.899
-1.918
-1.936
-1.953
-1.970
-1.562
-1.571
-1. 579
-1.587
-1.594
-1~~09 -~043 -0.628 -0.140 0.465
-1.311 -1.042 -0.623 -0.137 Q.463
.... Lft4 ",J:...400 ""M19 -0.135 0.461
-1.316 -1.038 -0.615 -0.133 0.460
-1.317 -1.036 -0.611 -0.130 0.458
10.2
10.4
10,,6
10'.8
11.0
-0.6911
-0.6654
-0.6420
-0.6205
-0.6007
1.467
1.450
1.435
1. 421
1.408
-3.488
-3.559
-3.609
-3.666
-3.721
-3'.098
-3.146
-3.192
-3.237
-3.280
-2.625
-2.658
-2.689
-2.719
-2.748
-2.295
-2.318
-2.340
-2.361
-2.381
-1.985
-2.000
-2.014
-2.028
-2.041
-1.600
-1.607
-1.613
-1.618
-1.624
-1.319
-1.321
-1.322
-1.323
-1.324
11.2
11.4
11.6
11.8
12.0
-0.5824
-0.5654
-0.5495
-0.5348
-0.5210
1.395
1.383
1.372
1.361
1. 351
-3.775
-3.827
-3.877
-3.926
-3.973
-3'.321
-3'.361
-3.400
-3.437
-3.474
-2.776
-2.803
-2.829
-2.854
-2.878
-2.401
-2.419
-2.437
-2.454
-2.471
-2.053
-2.065
-2.076
-2.087
-2.098
-1.629 -1.325 -1.026 -0.592
-1.633 -1.326 -1.024 -0.589
-1.638 -1.327 -1.022 -0.586
-1.6~2 -1.328 -1.021 -0.583
-1.646 -1.329 -1.019 -0.580
3.260
3.259
3.259
3.258
3'.258
3.257
3.256
3.878
3.889
3.899
3.908
3.916
3.923
3.930
4.515
4.540
4.564
4.586
4.607
4.626
4.644
5.387
5.439
5.487
5.532
1.810
1.802
1.795
1.788
1.782
2.411 3.255
2.405 3.254
2.399 3'.253
2.393 3.252
2.3884.351
3.937
3.943
3.949
3.954
3.959
4.660
4.676
4.691
4.705
4.718
5.686
5.719
5.751
5.780
5.809
6.518
6.568
6.615
6.661.
6.704
1.201
1.196
1.191
1.186
1.181
1.775
1.769
1. 763
1.758
1.752
2.382
2.377
2.372
2.368
2.363
3.250
3.249
3.248
3.247
3.246
3.964
3.968
3.972
3.976
3.980
4.731
4.743
4.755
4.766
4.776
5.836
5.862
5.887
5.911
5.933
6.745
6.785
6.823
6.859
6.894
1.177
1.172
1.168
1.164
1.160
1.747
1.742
1.737
1.732
1.728
2.358
2.354
2.350
2.346
2.342
3'.245 3'.983 4.786
3.244 3.987 4.796
~.24~ 3.990 4.805
3'.2413.993 4.81.4
3.240 3.996 4.822
5.955
5.977
5.997
6.017
6.036
6.928
6.961
6.992
7.022
7.052
0.449 1.156
o.!~ 1.153
0.447 1.149
0.446 1.145
0.444 1.142
1.723
1.719
1.715
1.711
1.707
2.338
2.334
2.330
2.327
2.323
3.239
3.238
3.237
3.236
3.235
6.054
6.072
6.089
6.106
6.122
7.080
7.108
7.134
7.160
7.185
u
-1.034 -0.608 -0.128
-1.033 -0.604 -0.127
-1.031 -0.601 -0.125
-1.029 -0.598 -0.123
-1.027 -0.595 -0.121
-0.120
-0.118
-0.117
-0.115
-0.114
0.457
0.455
0.u;4
0...452
0.451
2.465
2.456
2.448
2.440
2.432
2.425
2.418
3.998 4.831
4.001 4.839
4.003 4.846
4.0064.854
4.008 4.861
6.072
6.149
6.221
6.288
5.57!~ 6.350
5.614 6.410
5.651 6.465
12.2 -0.5080 1. 342 -4.019 -3.509 -2.901 -2.487 -2.108 -1.650 -1.329 -1.018 -0.578 -0.113 0.443 1.139 1.703 2.320 3.234 4.010 4.868 6.137 7.210
12.4 -0.4958 1.332 -4.063 -3.543 -2.924 -2.503 -2.117 -1.654 -1.330 -1.016 -0.575 -O.lll 0.442 1. 135 1.699 2.316 3.233 ~.~12 4~874 6.153 7.234
12.6 -0.4844 1.324 -4.107 -3.576 -2.946 -2.518 -2.127 -1.658 -1.330 -1.014 -0.573 -0.110 0.441 1.132 1.695 2.313 3.232 1~.014 4.881 6.167 7.257
e
It
e
.ff31=1. 5
~
f3 2
r
0
1~0005
Cumulative Proba.bility
0.001 0.0025 0.005 0.01
0.025 0.05
0.10
0.25
0.50
0.75 0.90 0.95 0.975 0.99 0.995 0.9975 0.999 0.9995
-0.697
-0.689
-0.682
-0.675
7.4
7.6
7.8
8.0
-3.6890
-2.7066
-2.2118
-1.8941
2.158
2.052
1.966
1.894
-1.805
-1.946
-2.078
-2.201
-1.743
-1.859
-1.967
-2.067
-1.653
-1.738
-1.817
-1.890
-1.576
-1.641
-1.700
-1.754
-1.489
-1.534
-1.576
-1.614
-1.349
-1.373
-1.395
-1.414
-1.216
-1.227
-1.236
-1.244
-1.044
-1.044
-1.044
-1.043
-0.196
-0.190
-0.184
-0.179
0.476
0.474
0.472
0.470
1.280
1.271
1.263
1.255
1.879
1.868
1.858
1.848
2.485
2.476
2.467
2.459
3.309
3.307
3.305
3.304
3.955
3.963
3.971
3.978
4.624 5.546 6.275
4.646 5.592 6.345
4.6665.605 6.410
4.685 5.676 6.470
8.2
8.4
8.6
8.8
9.0
-1. 6678
-1.4965
-1.3616
-1. 2521
-1.1613
1. 833
1.781
1. 736
1. 696
1.660
-2.317
-2.427
-2.530
-2.628
-2.721
-2.161 -1.958
-2.249- -2.021
-2.332 -2.081
-2.411 -2.137
-2.485 -2.189
=1.805
-1.852
-1.895
-1.936
-1.975
=1.6!~9
-1.681
-1.711
-1.739
-1.765
-1.432
-1.448
-1.463
-1.477
-1.489
-1.251
-1.258
-1.264
-1.269
-1.273
-1.042 -0.669 -0.175
-1.041 -0.663 -0.171
~l.~ ~.6~7 -0.167
-1.039 -0.652 -0.163
-1.038 -0.646 -0.159
0.468
0·.4(;;7
0.465
0.463
0.462
1.247
1.240
1.233
1.227
1.221
1.840
1.831
1.823
1.815
1.808
2.451
2.444
2.437
2.430
2.424
3·.302
3.301
3.299
Y.297
3.296
3.984
3.990
3.996
4.001
4.006
4.703
4.719
4.735
4.749
4.763
5.714
5.749
5.783
5.815
5.845
6.528
6.582
6.65'
6.681
6.728
9.2
9.4
9. 6
9.8
10.0
-1.0846
..1. 0188
-0.9618
-0.9118
-0.8676
1.628
1. 599
1.573
1. 549
1.527
-2.809
-2.893
-2.974
-3.051
-3.125
-2.556
-2.623
-2.687
-2.747
-2.806
-2.239
-2.286
-2.331
-2.373
-2.414
-2.011 -1.790
-1.813
-2.0;2 -1.834
-2.108 -1.855
-2.137 -1.874
-1.501
-1.512
-1.522
-1.532
-1.540
-1.277 -1.0oG -0.641 -0.156
-1.281 -1.035 -0.637 -0.153
-1.285 -1.033 -0.632 -0.150
-1.a88 -1.032 -0.628 -O.~~
-1.291 -1.030 -0.£24 -0.145
0.460 1.215
0.458· 1.209
0.1~57 1.204
0.455 1.198
0.454 1.19~
1.801
1.794
1.788
1.782
10776
2.418
2.412
2.406
2.401
2.396
3.294
3.292
3.291
3.289
3.288
4.014
4.018
4.022
4.025
4.o~
4.116
4.789
4.801
4.812
4.823
5.874
5.901
5.927
5.952
5.976
6.772
6.813
6.854
6.892
6.929
10.2
10.4
10.6
10.8
11.0
11.2
11.4
11.6
11.8
12.0
12.2
12.4
12.6
12.8
13.0
-0.8281
-0.7928
-0.7606
-0.7318
-0.7054
-0.6812
-0.6589
-0.6383
-0.6192
-0.6015
-0. 5850
-0.5696
-0.5552
-0.5416
-0. 5288
1. 506
1. 488
1.470
1. 454
1.439
1. 424
1. 411
1.398
1.386
1.375
1. 364
1. 354
1.344
1. 335
1. 326
-3.195
-3.264
-3.329
-3.392
-3.453
-3.512
-3.568
-Y.623
-3.676
-3.728
-3.778
-3·.826
-3.873
-3.919
-3.963
-2.861
-2.915
-2.966
-3.016
-3.063
-3.109
-3.153
-3.196
-3.237
-3.277
-3.315
-3.353
-3.389
-3.424
-3.458
-2.453 -2.165
-2.490 -2.191
-2.525 -2.216
-2.559 -2.240
-2.591 -2.263
-2.623 -2.285
-2.653 -2.307
-2.682 -2.327
-2.709 -2.346
-2.736 -2.365
-2.762 -2.383
-2.787 -2.401
-2.812-2.418
-2.835 -2.434
-2.858 -2.450
-1.549
-1.557
-1.564
-1.571
-1.577
-1.584
-1.590
-1.595
-1.600
-1.605
-1.610
-1.615
-1.619
-1.623
-1.627
-1.293
-1.295
-1.298
-1.300
-1.301
-1.303
-1.304
-1.306
-l.307
-1.308
-1.309
-1.310
-1.311
-1.312
-1.313
0.452 1.188 1.770 2.391 3.286
0.451 1.184 1.764 2.386 3.285
0.449 1.179 1.759 2.381 3.283
a.448 1.175 1.754 2.376 3.281
0.447 1.171 1.749 2.372 3.280
0.445 1.167 1.744 2.367 3.278
0~444 1.i63 1.7;9 2.363 3.277
0.443 1.159 1.735 2.359 3.276
0.44? 1.155 1.730 2.355 3.274
0.440 1.151 1.726 ,2.351 3.273
0.439 1.148 1.722 2.347 3.271
0.438 1.144 1.717 2.344 3.210
0.4371.1411.713 2.3403.2 5.1
0.436 1.138 1.710 2.337 3.267
0.435 1.135 1.706 2.333 3.266
-2.ol~5
-1.892
-1.910
-1.926
-1.942
-1.957
-1.971
-1.985
-1.998
-2.011
-2.023
-2.034
-2.045
-2.056
-2.066
-2.079
-1.029
-1.027
-1.026
-1.024
-1.023
-1.021
-1.020
-1.018
-1.017
-1.015
-1.014
-1.012
-1.011
-1.009
-1.008
-0.620
-0.616
-0.612
-0.609
-0.605
-0.602
-0.599
-0.596
-0.593
-0.590
-0.587
-0.585
-0.582
-0.579
-0.577
-0.143
-0.141
-0.138
-0.136
-0.134
-0.133
-0.131
-0.129
-0.127
-0.126
-0.124
-0.123
-0.121
-0.120
-0.119
4.029 4.833
4.032 4.843
4.035 4.852
4.037 4.861
4.040 4.870
4.043 4.878
4.045 4.886
4.047 4.894
4.050 4.901
4.052 4.908
4.054 4.915
4.055 4.922
4.0574.928
4.059 4.954
4.061 4.940
5.999 6.964
6.021 6.999
6.042 7.031
6.062 7.063
6.082 7.094
6.101 7.123
6.119 7.152
6.137 7.180
6.154 7.206
6.171 7.232
6.187 7.258
6.202 7.282
6.2177.306
6.232 7.329
6.246 7.352
13.2 -0. 5168 1. 318 -4.007 -3.491 -2.880 -2.465 -2.086 -1.631 -1.313 -1.006 -0.574 -0.117 0.434 1.131 1.702 2.330 3.265 4.062 4.946 ,6.2607.374
e
e
e
.[~1 = 1.6
,
Cumulative Probability
(\J
8
10.0005 0.001 0.0025 0.005 0.01 0.025 0.05 0.:0
r
132
8.0 -3.8382 2.075 -1.727 -1.673 -1.593 -1.523 -1.444 -1.315 -1.191 -1.028
8.2 -2.7971 1.986 -1.863 -1.785 -1.675 -1.586 -1.488 -1.339 -1.202 -1.029
8.4 -2.2923 1.911 -1.991 -1.889 -1.752 -1.644 -1.529 -1.360 -1.211 -1.029
8.6 -1.9702 1.849 -2.111 -1.987 -1.823 -1.697 -1.566 -1.380 -1.220 -1.029
8.8 -1. 7406 1.795 -2.224 -2.079 -1.890 -1.747 -1.601 -1.398 -1.227 -1.028
9·0 -1.5664 1.748 -2.331 -2.165 -1.952 -1.793 +1.6,3 -1.414 -1.234 -1.028
0.25
-0.695
-0.688
-0.681
-0.674
-0.668
-0.663
0.50
-0.205
-0.199
-0.194
-0.189
-0.184
-0.180
0.75
0.463
0.461
0.460
0.459
0.457
0.456
0.9::>
1.274
1.265
1.257
1.250
1.24}
1.236
0.95"
1.883
1.873
1.863
1.854
1.845
1.837
0.975
2.505
2.496
2.487
2.479
2.471
2.463
0.99
3.355
3.353
3.350
3.348
3.345
3.343
0.995
4.026
4.033
4.038
4.044
4.049
4.053
0.9975
4.724
4.743
4.761
4.777
4.793
4.807
0.999
5.691
5.733
5".772
5.808
5.842
5.875
0.9995
6.459
6.522
6.582
6.638
6.691
6.740
9.2
9.4
9.6
9.8
10.0
-1.4288
-1.3167
-1.2235
-1.1444
-1.0766
1.707
1.670
1.637
1.608
1.581
-2.432
-2.528
-2.620
-2.707
-2.790
-2.247
-2.324
-2.397
-2.467
-2.533
-2.011
-2.066
-2.118
-2.167
-2.214
-1.836
-1.877
-1.915
-1.951
-1.985
-1.663
-1.691
-1.717
-1.742
-1.765
-1.429
-1.443
-1.456
-1.468
-1.479
-1.240
-1.245
-1.250
-1.255
-1.259
-1.027
-1.026
-1.025
-1.024
-1.023
-0.657
-0.652
-0.647
-0.642
-0.638
-0.176
-0.172
-0.168
-0.165
-0.162
0.454
0.453
0.451
0.450
0.449
1.230
1.224
1.218
1.212
1.206
1.829
1.822
1.814
1.808
1.801
2.456
2.450
2.443
2.437
2.431
3.340
3.338
3.336
3.334
3.332
4.058
4.062
4.065
4.069
4.072
4.821
4.834
4.846
4.857
4.868
5.906
5.935
5.962
5.989
6.014
6.788
6.833
6.876
6.917
6.956
10.2
10.4
10.6
10.8
11.0
-1.0175
-0.9656
-0.9197
-0.8786
-0.8417
1.557
1.534
1.513
1.494
1.476
-2.869
-2.945
-3.019
-3.089
-3.156
-2.596
-2.657
-2.714
-2.770
-2.823
-2.258
-2.301
-2.341
-2.380
-2.417
-2.018
-2.048
-2.078
-2.105
-2.132
-1.787
-1.807
-1.827
-1.845
-1.863
-1.490
-1.499
-1.508
-1.517
-1.525
-1.263
-1.266
-1.269
-1.272
-1.275
-1.022
-1.021
-1.019
-1.018
-1.017
-0.633
-0.629
-0.625
-0.621
-0.617
-0.159
-0.156
-0.154
-0.151
-0.149
0.447
0.446
0.445
0.444
0.442
1.201
1.196
1.191
1.187
1.182
1.794
1.788
1.782
1.777
1.771
2.425
2.419
2.414
2.409
2.404
3.329
3.327
3.325
3.323
3.321
4.075
4.078
4.081
4.083
4.086
4.879
4.889
4.899
4.908
4.916
6.038
6.061
6.083
6.105
6.125
6.994
7.030
7.064
7.098
7.130
11.2
11.4
11.6
11.8
12.0
-0.8084
-0.7780
-0.7503
-0.7249
-0.7015
1.460
1.444
1.430
1.416
1.403
-3.221
-3.284
-3.345
-3.403
-3.460
-2.874 -2.452 -2.157
-2.181
-2.971 -2.519 -2.205
-3.017 -2.550 -2.227
-3.061 -2.580 -2.248
-1.880
-1.896
-1.911
-1.926
-1.940
-1.533
-1.540
-1.547
-1.553
-1.560
-1.277
-1.280
-1.282
-1.284
-1.285
-1.Q15
-1.014
-1.013
-1.011
-1.010
-0.614
-0.610
-0.607
-0.604
-0.601
-0.147
-0.145
-0.143
-0.141
-0.139
0.441
0.440
0.439
0.437
0.436
1.178
1.174
1.169
1.165
1.162
1.766
1.761
1.756
1.751
1.746
2.399
2.394
2.390
2.385
2.381
3.319
3.318
3.316
3.314
3.312
4.088
4.090
4.092
4.094
4.096
4.925
4.933
4.941
4.948
4.955
6.145
6.164
6.182
6.200
6.217
7.161
7.191
7.220
7.248
7.275
12.2
12.4
12.6
12.8
13.0
-0.6799
-0.6598
-0.6412
-0.6237
-0.6075
1.391
1.379
1.369
1.358
1.348
-3.514
-3.567
-3".619
-3.669
-3.717
-3.103
-3.145
-3.185
-3.223
-3.261
-2.609
-2.637
-2.665
-2.691
-2.716
-2.269
-2.289
-2.308
-2.326
-2.344
-1.953
-1.966
-1.978
-1.990
-2.001
-1.565
-1.571
-1.576
-1.581
-1.586
-1.287
-1.288
-1.290
-1.291
-1.292
-1.009
-1.007
-1.006
-1.005
-1.003
-0.598
-0.595
-0.592
-0.589
-0.587
-0.137
-0.135
-0.134
-0.132
-0.130
0.435
0.434
0.433
0.432
0.431
1.158
1.154
1.151
1.147
1.144
1.742
1.737
1.733
1.729
1.725
2.377 3.310
2.373 3.308
2.369 3.307
2.365 "3.;05
2.361 3.303
4.098
4.099
4.101
4.102
4.104
4.962 6.234 7.301
4.969 6.250 7.326
4.975 6.265 7.351
4.981~ 6.280 7.375
4.987 6.295 7.398
13.2
13.4
13.6
13.8
-0.5922
-0.5779
-0.5644
-0.5517
1.339
1.330
1.321
1.313
-3.764
-3.810
-3.854
-3.898
-3.297
-3.333
-3.367
-3.L~
-2.741
-2.764
-2.787
-2.810
-2.361
-2.378
-2.394
-2.409
-2.012
-2.023
-2.033
-2.043
-1.591
-1.595
-1.600
-1.604
-1.293
-1.294
-1.295
-1.296
-1.002
-1.001
-1.000
-0.998
-0.584
-0.581
-0.579
-0.577
-0.129
-0.128
-0.126
-0.125
0.430
0.429
0.428
0.427
1.141
1.137
1.134
1.131
1.721
1.717
1.713
1.709
2.357
2.353
2.350
2.346
4.105
4.107
4.108
4.109
4.993
4.999
5.004
5.010
-2.9~~ -2~486
3.302
3.300
3.298
3.297
6.309
6.323
6.336
6.349
7.421
7.443
7.4C5
7.486
e
-
e
"[f31 = 1. 7
Cumulative Probability
....:j-
C\I
f32
"1
8.6 .4.6621
8.8 -3.0649
9.0 -2.4688
8
0.0005 0.001 0.0025 0.005 0.01 0.025 0.05
0.10
0.25
0.50
0.75 0.90 0.95 0.975 0.99 0.995 0.9975 0.999 0.9995
-L621 -1.579 -1.515 -1.458 -1.390 -1.276 -1.164 -1.012 -0.694 -0.215 0.450 1.269 1.889 2.525 3.400 4.094 4.817 5.824 6.627
-1.755 -1.689 -1.596 -1.519 -1.434 -1.300 -1.175 -1.013 -0.687 -0.209 0.449 1.261 1.879 2.516 3.397 4.099 4.834 5.862 6.685
-1.880 -1.792 -1.672 -1.577 -1.475 -1.322 -1.185 -1.014 -0.681 -0.203 0.448 1.253 1.870 2.507 3.394 1~.103 4.850 5.898 6.740
9.2
9.4
9.6
9.8
10.0
-2.1093
-1.8588
-1.6709
-1.5234
-1.4037
-1.998
-2.110
-2.215
-2.315
-2.411
-1.889
-1.979
-2.065
-2.146
-2.222
-1.743
-1.809
-1.871
-1.929
-1.984
-1.630
-1.680
-1.726
-1.769
-1.810
-1.512
-1.547
-1.579
-1.610
-1.638
-1.342
-1.360
-1.377
-1.392
-1.407
-1.194
-1.202
-1.209
-1.215
-1.221
-1.014
-1.014
-1.014
-1.014
-1.013
-0.675
-0.669
-0.663
-0.658
-0.653
-0.198
-0.194
-0.189
-0.185
-0.181
0.447
0.446
0.445
0.444
0.443
1.246
1.239
1.233
1.227
1.221
1.861
1.852
1.844
1.836
1.829
2.499
2.491
2.483
2.476
2.469
3.390
3.387
3.384
3.381
3.378
4.107
4.111
4.114
4.117
4.120
4.878
4.890
4.902
4.914
~.864
5.931
5.963
5.992
6.021
6.048
6.792
6.841
6.888
6.932
6.974
10.2
10.4
10.6
10.8
11.0
-1.3043
-1.2203
-1.11J.81
-1.0853
-1.0302
-2.501
-2.588
-2.670
-2.750
-2.826
-2.295
-2.365
-2.431
-2.494
-2.554
-2.037
-2.086
-2.133
-2.178
-2.220
-1.848
-1.885
-1.919
-1.952
-1.983
-1.664
-1.689
-1.713
-1.735
-1.756
-1.420
-1.432
-1.444
-1.455
-1.465
-1.227
-1.232
-1.236
-1.240
-1.244
-1.013
-1.012
-1.011
.l.010
-1.009
-0.648
-0.643
-0.639
-0.635
-0.631
-0.178
-0.174
-0.171
-0.168
-0.165
0.442
0.440
0.439
0.4;8
0.437
1.215
1.210
1.205
1.200
1.195
1.822
1.815
1.808
1.802
1.796
2.462
2.456
2.450
2.444
2.438
3.375
3.373
3.370
3.367
3.365
4.123' 4.925
4.126 4.935
1~.128 4.945
4.130 4.954
4.133 4.963
6.073
6.098
6.121
6.144
6.165
7.015
7.053
7.090
7.125
7.160
11.2
114
,
11.6
11.8
12.0
-0.9813
-0.9377
-0.8984
-0.8629
-0.8307
-2.898
-2.969
-3.036
-3.101
-3.164
-2.612
-2.668
-2.721
-2.772
-2.822
-2.261
-2.300
-2.337
-2.373
-2.407
-2.012
-2.040
-2.067
-2.093
-2.118
-1.776
-1.795
-1.813
-1.830
-1.846
-1.475
-1.484
-1.492
-1.500
-1.508
-1.247
-1.251
-1.254
-1.256
-1.259
-1.008
-1.007
-1.006
-1.005
-1.004
-0.627
-0.623
-0.619
-0.616
-0.612
-0.163
-0.160
-0.158
-0.155
-0.153
0.436
0.435
0.434
0.433
0.432
1.190
1.185
1.181
1.177
1.173
1.790
1.784
1.779
1.774
1.768
2.433
2.427
2.422
2.417
2.412
3.363
3.3eo
3.358
3.355
3.353
4.135
4.136
4.138
4.140
4.141
4.972
4.980
4.987
4.995
5.002
6.186
6.206
6.225
6.243
6.261
7.192
7.224
7.254
7.284
7.312
12.2
12.4
12.6
12.8
13.0
-0.8012
-0.7741
-0.7492
-0.7262
-0.7048
-3.224
-3.283
-3.340
-3.395
-3.448
-2.869
-2.915
-2.960
-3.003
-3.044
-2.440
-2.472
-2.502
-2.532
-2.560
-2.141
-2.164
-2.186
-2.207
-2.227
-1.862
-1.877
-1.891
-1.905
-1.918
-1.515
-1.522
-1.528
-1.535
-1.541
..1.261
-1.264
-1.266
-1.267
-1.269
-1.003
-1.002
-1.001
-1.000
-0.998
-0.609
-0.606
-0.603
-0.600
-0.597
-0.151
-0.149
-0.147
-0.145
-0.143
0.4311.1691.763
0.430 1.165 1.759
0.429 1.161 1.754
0.428 1.157 1.749
0.427 1.154 1.745
2.408
2.403
2.399
2.394
2.390
3.3514.143
3.349 4.144
3.347 4.146
3.345 4.1~·7
3.342 4.148
5.009
5.016
5.022
5.028
5.034
6.278
6.295
6.311
6.326
6.341
7.339
7.366
7.392
7.417
7.441
13.2
13.4
13.6
13.8
14.0
-0.6849
-0.6664
-0.6490
-0.6327
-0.6175
-3.500
-3.550
-3.598
-3.646
-3.692
-3.085
-3.124
-3.161
-3.198
-3.234
-2.588
-2.614
-2.640
-2.665
-2.689
-2.246
-2.265
-2.283
-2.301
-2.318
-1.931
-1.943
-1.955
-1.966
-1.977
-1.546
-1.552
-1.557
-1.562
-1.566
-1.271
-1.272
-1.274
-1.275
-1.276
-0.997
-0.996
-0.995
-0.994
-0.993
-0.594
-0.592
-0.589
-0.586
-0.584
-0.142
-0.140
-0.138
-0.137
-0.135
0.426
0.425
0.424
0.423
0.422
2.386
2.382
2.378
2.374
2.371
3.340
3.338
3.337
3.335
3.333
5.040
5.046
5.051
5.057
5.062
6.356
6.370
6.;84
6.397
6.410
7.464
7.487
7.510
7.531
7.552
14.2 -0.6031
14.4 -0.5895
1.150
1.147
1.144
1.140
1.137
1.741
1.736
1.732
1.728
1.724
4.149
4.150
4.151
4.152
4.153
-3.737 -3.268 -2.712 -2.334 -1.988 -1.571 -1.278 -0.991 -0.581 -0.l34 0.421 1.134 1.721 2.367 3.331 4.154 5.067 6.423 7.573
-3.780 -3.302 -2.735 -2.350 -1.998 -1.575 -1.279 -0.990 -0.579 -0.133 0.420 1.131 1.717 2.363 3.329 4.155 5.071 6.435 7.593
e
e
,rf31 --
t32
r
--
1. 8
Cumulative Probability
5
~.0005
0.001 0.0025 0.005
o.o~
0.025 0.05
0.10
0.25
0.50
0.75 0.90 0.95 0.975 0.99 0.995 0.9975 0.9990.9995
9. 4
9.6
9.8
10.0
-3.7199 1'9~-1.620 -1.572
-2.7956 1.849 -1.745 -1.675
-2.3366 1.796 -1.863 -1.772
-2.0374 1.750 -1.974 -1.863
-1.502
-1.578
-1. 649
-1.716
-1.441
-1.499
-1.553
-1.603
-1.371
-1.413
-1.451
-1.486
-1.257
-1.280
-1.300
-1.319
-1.146
-1.156
-1.166
-1.174
-0.997
-0.999
-0.999
-1.000
-0.688
-0.682
-0.676
-0.670
-0.220
-0.214
-0.209
-0.204
0.437
0.436
0.436
0.435
10.2
10.4
10.6
10.8
11.0
-1.8202
-1.6529
-1.5190
-1.4087
-1.3159
1.7091-2.079
1.673 -2.180
1.640 -2.275
1.611 -2.365
1.584 -2.452
-1.948
-2.029
-2.106
-2.179
-2.249
-1.778
-1.837
-1.893
-1.945
-1.995
-1.650
-1.694
-1.735
-1.774
-1.811
-1.519
-1.550
-1.579
-1.606
-1.632
-1.337
-1.353
-1.368
-1.382
-1.395
-1.182
-1.189
-1.196
-1.202
-1.207
-1.000
-1.000
-1.000
-1.000
-1.000
-0.665
-0.659
-0.655
-0.650
-0.645
-0.199
-0.195
-0.191
-0.188
-0.184
0.434 1.231
0.433 1.225
0.433 1.219
0.432 1. 214
0.4311.208
1.852 2.504 3.425 4.173
1.844 2.496 3.421 4.175
1.837 2.489 3.418 4.178
1~8302.482 3".415-4.179
1.823 2.476 3.411 4.181
4.970
4.981
4.991
5.000
5.010
6.103
6.130
6.155
6.179
6.201
7.025
7.067
7.107
7.145
7.181
11.2
11.4
11.6
11.8
12.0
-1.2366
-1.1680
-1.1078
-1.0546
-1.0072
1.560
1.538
1.517
1.498
1.480
-2.535
-2.615
-2.691
-2.764
-2.835
-2.316
-2.379
-2.440
-2.499
-2.555
-2.043
-2.088
-2.131
-2.172
-2.212
-1.846
-1.880
-1.911
-1.941
-1.970
-1.656
-1.679
-1.700
-1.721
-1.740
-1.407
-1.418
-1.429
-1.439
-1.448
-1.212
-1.217
-1.221
-1.225
-1.228
-0.999
-0.999
-0.998
-0.997
-0.997
-0.641
-0.637
-0.633
-0.629
-0.625
-0.181
-0.178
-0.175
-0.172
-0.169
0.430
0.429
0.428
0.427
0.426
1.203
1.198
1.194
1.189
1.185
1.816 2.470
1.810 2.463
1.804 2.458
1.79 8 2.45~
1.792 2.446
3.408
3.405
3.402
3.399
~.396
4.183
4.184
4.186
4.187
4.189
5.018
5.027
5.035
5.042
5.049
6.223
6.244
6.266
6.284
6.302
7.216
7.250
7.282
7.313
7.343
12.2
12.4
12.6
12.8
13.0
-0.9646
-0.9261
-0.8912
-0.8593
-0.8300
1.463
1.448
1.433
1.420
1.407
-2.903
-2.968
-3.031
-3.092
-3.151
-2.609
-2.660
-2.710
-2.758
-2.805
-2.250
-2.286
-2.321
-2.354
-2.387
-1.997
-2.024
-2.049
-2.073
-2.096
-1.759
-1.777
-1.793
-1.810
-1.825
-1.457
-1.466
-1.474
-1.481
-1.489
-1.232
-1.235
-1.238
-1.240
-1.243
-0.996
-0.995
-0.994
-0.993
-0.992
-0.622
-0.618
-0.615
-0.612
-0.609
-0.167
-0.164
-0.162
-0.160
-0.158
0.425
0.425
0.424
0.423
0.422
1.180
1.176
1.172
1.168
1.164
1.787
1.782
1. 776
1. 771
1.767
2.441
2.436
2.431
2.426
2.422
3.394
3.391
3.389
3.386
3.384
4.190
4.191
4.192
4.193
4.194
5.056
5.063
4.070
5.076
5.082
6.320
6.337
6.354
6.370
6.386
7.372
7.400
7.427
7.454
7.479
13.2
13.4
13.6
13.8
14.0
-0.8031
-0.7782
-0.7551
-0.7337
-0.7137
1.394
1.383
1.372
1.362
1.352
-3.209
-3.264
-3.318
-3.370
-3.421
-2.850
-2.893
-2.936
-2.976
-3.016
-2.418
-2.448
-2.477
-2.505
-2.532
-2.119
-2.140
-2.161
-2.181
-2.200
.1.840
-1.854
-1.868
-1.881
-1.894
-1.496
-1.502
-1.508
-1.514
-1.520
-1.245
-1.247
-1.249
-1.251
-1.253
-0.991
-0.990
-0.989
-0.988
-0.987
-0.606
-0.603
-0.600
-0.597
-0.594
-0.156
-0.154
-0.152
-0.150
-0.148
0.421
0.420
0.419
0.418
0.418
1.161
1.157
1.154
1.150
1.147
1.762
1.757
1.753
1.749
1.744
2.417
2.412
2.408
2.404
2.400
3.381
3.379
3.376
3.374
3.372
4.195
4.195
4.196
4.197
4.197
5.088
5.093
5.099
5.104
5.109
6.401
6.416
6.430
6.444
6.457
7.503
7.527
7.551
7.573
7.595
14.2
14.4
14.6
14.8
15.0
-0.6950
-0.6775
-0.6610
-0.6455
-0.6309
1.342
1.333
1.325
1.316
1.308
-3.470
-3.518
-3.564
-3.609
-3.654
-3.054
-3.091
-3.128
-3.163
-3.197
-2.558
-2.583
-2.608
-2.632
-2.655
-2.219
-2.237
-2.254
-2.271
-2.287
-1.906
-1.918
-1.929
-1.940
-1.950
-1.526
-1.531
-1.536
-1.541
-1.545
-1.255
-1.256
-1.258
-1.259
-1.261
1.257
1.250
1.243
1.237
1.886
1.877
1.868
1.860
2.537 3.440 4.162 4.921 5.9836.835
2.528 3.1~36 4.165 4.934 6.016 6.887
2.519 3.432 4.168 4.947 6.046 6.935
2.511 3.429 4.171 4.959 6.076 6.982
-0.986 -0.592 -0.147 0.417 1.144 1.740 2.396 3.370 4.198 5.114 6.470 7.616
-0.985 -0.589 -0.145 0.416 1.140 1.736 2.392 3'.367 4.199 5.118 6.483 7.637
-0.984 -0.587 -0.143 0.415 1.137 1.732 2.388 3.365 4.199 5.123 6.495 7.657
-0.983 -0.584 -0.142 0.414 1.134 1.729 2.384 3.363 4.200 5.127 6.507 7.677
-0.982 -0.582 -0.140 0.414 1.131 1.725 2.381 3.361 4.200 5.132 6.519 7.696
15.2 -0.6171 1.3011-3.697 -3.230 -2.678 -2.303 -1.961 -1.550 -1.262 -0.981 -0.580 -0.139 0.413 1.129 1.721 2.377 3.359 4.201 5.136 6.530 7.715
-
-
e
'[f31 = 1.9
C\l
f32
'1
8
1~0005
10.2
10.4
10.6
10.8
11.0
-3.5112
-2.7292
-2.3145
-2.0372
-1.8328
1.83
1.78
1.74
1.70
1.66
11.2
11.4
11.6
11.8
12.0
-1.6736
-1.5 44 9
-1.4381
-1.3477
-1.2700
-2.120
-2.212
-2.299
1.55 -2.383
1.534 -2.464
12.2
12.4
12.6
12.8
13.0
-1.2024
-1.1429
-1.0900
-1.0428
-1.0002
1.514
1.495
1.477
1.461
1.446
13.2
13.4
13.6
13.8
14.0
-0.9616
-0.9264
-0.8942
-0.8647
-0.8374
14.2
14.4
14.6
14.8
15.0
-0. B122
15.2
15.4
15.6
15.8
16.0
Cumulative Probability
0.001 0.0025 0.005 0.01
-1.536
-1.705
-1.817
-1.923
-1.539
-1.636
-1.728
-1.815
-2.~24 -1.897
0.025 0.05
0.10
0.25
0.50
0.75 0.90 0.95 0.975 0.99 0.995 0.9975 0.999 0.9995
-0.226
-0.220
-0.215
-0.211
-0.206
0.425
0.424
0.424
0.424
0.423
-1.470
-1.542
-1.610
-1.673
-1.733
-1.411
-1.466
-1.517
-1.565
-1.610
-1.343
-1.382
-1.419
-1.453
-1.485
-1.233
-1.254
-1.274
-1.293
-1.310
-1.125
-1.136
-1.145
-1.154
-1.16.2
-0.983
-0.984
-0.985
-0.986
-0.987
-0.684
-0.678
-0.672
-0.667
-0.662
1.248
1.241
1.235
1.229
1.223
1.885
1.877
1.868
1.860
1.853
2.550
2.541
2.533
2.525
2.517
3.479
3.474
3.470
3.465
3.461
4.226
4.228
4.229
4.231
4.232
5.015
5.026
5.037
5.047
5.056
6.127
6.156
6.183
6.209
6.233
7.024
7.070
7.113
7.155
7.194
-1.975
-2.049
-2.120
-2.187
-2.252
-1.790
-1.843
-1.894
-1.. 943
-1.989
-1.652
-1.692
-1.730
-1. 766
-1.800
-1.514
-1.543
-1.569
-1. 594
-1.618
-1.325
-1.340
-1.354
-1. 361'
-1.379
-1.169
-1.175
-1.181
-1.187
-1.192
-0.987
-0.987
-0.967
-0.. 981
-0.987
-0.657 -0.202 0.423 1.218
-0.652 -0.198 0.422 1.213
-0.648 -0.194 0.421 1.207
-O.~ -0.191- 0.. 421 1.203
-0.640 -0.188 0.420 1.198
1.845
1.838
1.831
1.825
1.819
2.510
2.503
2.496
2.490
2.483
3.457
3.454
3.450
3.446
3.443
4.233
4.235
4.236
4.237
4.238
5.065
5.074
5.082
5.090
5.097
6.257
6.279
6.300
6.321
6.340
7.232
7.268
7.303
7.336
7.368
-2.541
-2.615
-2.686
-2.755
-2.822
-2.314
-2.373
-2.430
-2.485
-2.538
-2.033
-2.075
-2.116
-2.154
-2.192
-1.833
-1.864
-1.893
-1.922
-1.949
-1.640
-1.661
-1.682
-1.701
-1.719
-1.390
-1.401
-1.411
-1.420
-1.429
-1.196
-1.201
-1.205
-1.209
-1.212
-0.986
-0.986
-0.986
-0.985
-0.985
-0.636
-0.632
-0.628
-0.625
-0.621
-0.185
-0.182
-0.179
-0.176
-0.174
1.193 1.813
1.189 1.807
1.184 1.801
1.180 1.796
0.416 1.1761;790
2.477
2.472
2.466
2.461
2.~ 455
3.439
3.436
3.433
3. L30
3.427
4.238
4.239
4.240
4.240
4.241
5.104
5.111
5.117
5.124
5.130
6.359
6.378
6.395
6.412
6.428
7.399
7.429
7.457
7.485
7.512
1.432
1.418
1.405
1.393
1.382
-2.886
-2.948
-3.008
-3.066
-3.122
-2.588
-2.638
-2.685
-2.731
-2.775
-2.227
-2.262
-2.295
-2.327
-2.357
-1.975
-2.000
-2.024
-2.047
-2.069
-1.737
-1.754
-1.770
-1.785
-1.800
-1.438
-1.446
-1.454
-1.461
-1.468
-1.215
-1.218
-1.221
-1.224
-1.227
-0.984
-0.983
-0.983
-0.982
-0.981
-0.618
-0.615
-0.612
-0.609
-0.606
-0.171
-0.169
-0.167
-0.165
-0.162
0.416
0.415
0.414
0.413
0.413
1.172
1.168
1.165
1.161
1.157
1.785
1.780
1.775
1.770
1.766
2.450
2.445
2.440
2.436
2.431
3.424
3.421
3.418
3.416
3.413
4.242
4.a42
4.242
4.243
4.243
5.135
5.141
5.146
5.151
5.156
6.444
6.459
6.474
6.488
6.502
7.538
7.563
7.587
7.611
7.634
-0.7887
-0.7668
-0.7464
-0.7273
1.371
1.361
1.351
1.342
1.333
-3.176
-3.229
-3.281
-3.331
-3.379
-2.818
-2.859
-2.900
-2.939
-2.977
-2.387
-2.416
-2.444
-2.471
-2.497
-2.090
-2.111
-2.131
-2.150
-2.168
-1.814
-1.828
-1.841
-1.854
-1.866
-1.475
-1.481
-1.487
-1.493
-1.499
-1.229
-1.231
-1.233
-1.235
-1.237
-0.980
-0.979
-0.979
-0.978
-0.977
-0.603
-0.600
-0.597
-0.595
-0.592
-0.161
-0.159
-0.157
-0.155
-0.153
0.412
0.411
0.410
0.410
0.409
1.154
1.151
1.l47
1.144
1.141
1.761
1.757
1.158
1.749
1.745
2.427 3.410 4.244
2.422 3.408 4.244
2.4~8 '.405 4.244
2.414 3.403 4.244
2.410 3.400 4.244
5.161
5.166
5.170
5.175
5.179
6.516
6.529
6.541
6.554
6.566
7.656
7.677
7.698
7.719
7.739
-0.7094
-0.6925
-0.6766
-0.6616
-0.6474
1.324
1.316
1.308
1.301
1.293
-3.427
-3.473
-3.518
-3.561
-3.604
-3.014
-3.050
-3.084
-3.118
-3.152
-2.522
-2.546
-2.570
-2.593
-2.616
-2.186
-2.204
-2.221
-2.237
-2.253
-1.878
-1.889
-1.900
-1.911
-1.922
-1.504
-1.509
-1.514
-1.519
-1.524
-1.239 -0.976
-1.240 -0.975
-1.242 -0.974
-+.243 -0.973
-1.245 -0.972
-0.590
-0.587
-0.585
-0.583
-0.580
-0.152
-0.150
-0.149
-0.147
-0.146
0.408
0.408
0.401
0.406
0.405
1.138
1.135
1.132
1.129
1.126
1.741
1.737
1.733
1.729
1.726
2.406
2.402
2.398
2.394
2.391
3.398
3.396
3.393
3.391
3.389
5.183
5.187
5.191
5.195
5.198
6.577
6.589
6.600
6.611
6.621
7.758
7.777
7. 79f)
7.814
7.832
0.419
0.419
0.418
0.417
4.245
4.245
4.245
4.245
4.245
--
e
.rt31
tI
= 2.0
Cumulative Probability
\l
t3,
'Y
1')-
8
~0005
0.001 0.0025 0.005 0.01
0.025 0.05
0.10
0.25
0.50
0.75 0.90 0.95 0.975 0.99 0.995 0.9975 0.9990.9995
""
11.0
11.2
11.4
11.6
11.8
12.0
-3.6561
-2..8072
-2..3793
-2.0972
-1.8902
-1. 7291
-1.523
-1.637
-1.745
-1.848
-1.946
-2.039
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-1.748
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-1.904
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-1.412
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-1.473
-1.204
-1.225
-1.244
-1.262
-1.279
-1.295
-1.103
-].1l4
-1.123
-1.132
-1.139
-1.147
-0.968
-0.970
-0.971
-0.972
-0.973
-0.974
-0.680
-0.675
-0.670
-0.665
-0.660
-0.655
-0.233
-0.227
-0.222
-0.a18
-0.213
-0.209
0.413
0.413
0.413
0.412
0.412
0.412
1.240
1.234
1.228
1.222
1.217
1.212
1.886
1.877
1.870
1.862
1.855
1.848
2.563
2.554
2.546
2.539
2.531
2.524
3.516
3.511
3.506
3.501
3.497
3.493
4.286
4.287
4.288
4.288
4.289
4.289
5.103
5.113
5.121
5.130
5.138
5.145
6.260
6.285
6.309
6.332
6.354
6.375
7.196
7.237
7.277
7.314
7.350
7.385
12.2
12.4
12.6
12.8
13.0
-1.5989
-1.4908
-1.3991
-1.3202
-1.2514
-2.129
-2.214
-2.296
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-2.450
-1.976
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-1.747
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-0.192
0.411
0.411
0.411
0.410
0.410
1.207
1.202
1.197
1.193
1.189
1.841
1.834
1.828
1.822
1.816
2.517
2.510
2.504
2.498
2.492
3.489
3.484
3.481
3.477
3.473
4.289
4.290
4.290
4.290
4.290
5.152 6.395
4.159 6.414
5.166 6.433
5.172-6.451
5.178 6.468
7.418
7.450
7.481
7.510
7.539
13.2
13.4
13.6
13.8
14.0
-1.1907
-1.1368
-1.0884
-1.0448
-1.0052
-2.523
-2.593
-2.661
-2.726
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-1.895
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-1.676
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-1.390
-1.399
-1.408
-1.180
-1.184
-1.188
-1.192
-0.974
-0.974
-0.974
-0.973
·ojo.L1l95 ...0.973
-0.631 -0.189
-0.628 -0.186
-0.625 -0.184
-0.621 -0.181
..0,"618· ...0.1~9
0.409 1.184
0.409 1.180
0.408 1.176
0.407 1.172
0.. 407.1..169
1.810
1.805
1.799
1.794
1.789
2.486 3.470
~.480 ).466
2.475 3.463
2.470 3.459
2.465 3.456
4.291
4.291
4.291
4.291
4.291
5.184
5.189
5.195
5.200
5.205
6.485 7.566
6.501 7.593
6.516 7.618
,6.5}17.643
6.545 7.667
14.2
14.4
14.6
14.8
15.0
-0.9691
-0.9361
-0.9056
-0.8775
-0.8515
1.40
1.394
1.383
1.372
1.362
-2.851
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-3.023
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-2.554
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-2.733
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-1.742
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-0.971
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-0.606
0.406
0.406
0.405
0.404
1.784
1.780
1.775
1.770
4.291 5.210
4.291 5.214
4.291 5.219
4.291 5.223
4.2915.227
6.559 7.691
6.573 7.714
6.586 7.736
6.599 7.757
6.6117.778
15.2
15.4
15.6
15.8
16.0
-0.8273
-0.8047
-0.7836
-0.7638
-0.7452
1.352
1.343
1.334
1.325
1.317
-3.130
-3.181
-3.230
-3.279
-3.326
-2.774
-2.815
-2.853
-2.891
.2.928
-2.349
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-2.056
-2.076
-2.096
-2.114
-2.132
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-1.812
-1.824
-1.836
-1.453
-1.459
-1.465
-1.471
-1.476
-1.212
-1.215
-1.217
-1.219
-1.221
-0.970
-0.969
-0.968
-0.968
-0.967
-0.601
-0.598
-0.596
-0.593
-0.591
2.436
2.432
2.425
2.424
2.420
3.439 4.290 5.252
3.436 4.290 5.235
J.4" 4.290 5.239
3.431 4.290 5.242
3.428 4.290 5.246
6.6a37.798
6.635 7.818
6.646 7.837
6.657 7.856
6.668 7.874
16.2
16.4
16.6
16.8
-0.7277
-0.7112
-0.6956
-0.6808
1.309
1.302
1.294
1.287
-3.371
-3.416
-3.460
-3.502
-2.964
-2.999
-3.033
-3.066
-2.480
-2.504
-2.527
-2.549
-2.150
-2.167
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-2.199
-1.848
-1.859
-1.870
-1.880
-1.482
-1.487
-1.492
-1.497
-1.222 -0.966 -0.588
2.416
2.412
2.409
2.405
3.425
3.423
3.421
3.418
6.679
6.689
6.699
6.709
\1
-0.176
-0.174
-0.172
-0.170
-0.603 -0.168,
1.165
1.161
1.158
1.155
2.460 3.453
2.455 3.450
2.450 3.447
2.445 3.444
0.~04-1.1:51·L766 2-.!"!U'3.;441
-0.166 0.403 1.148 1.762
-0.164 0.403 1.145 1.758
-0.162 0.402 1.142 1.153
-0.160 0.401 1.139 1.749
-0.159 0.401 1.136 1.746
-0~157
.1~2@4·-o.965 ~o.586 ~0.155
0.400
0.400
-1.226 -O.~ ·o.~84 -0.154 0.399
-1.227 -0.964 -0.582 -0.152 0.398
1.133
1.130
1.127
1.125
1.742
1.738
1.734
1.731
4.290
4.290
4.289
4.289
5.249
5.253
5.256
5.259
7.892
7.910
7.927
7.943