Runs Test (Wald-Wolfowitz-Test)
Test for randomness
● If test value |z|<1.96, then the histogram is
random with significance level 5%
● Equations for runs test (N+ is above/at median,
N- below):
●
Why do the z-values get that
extreme?
●
Problem of high bin number / runs
IntRad
Nbins = 2160
Nbins =20
0
Runs=1080
z=0
Runs=9
z=1
1
Runs=600
Z=-30.39
Runs=6
z=-0.5
Random distribution made
with normal distribution
Z-distribution for different integration radii
Int Rad in Bins
Mean
RMS
0
-0.0108
0.98
3
-30.39
0.874
15
-38.82
0.9152
30
-42.98
0.9743
90
-42.98
0.9743
135
-43.48
0.9989
Which maps form tales at the z-distribution and
are they always the same
Tale
defintion
IntRad =0
IntRad = 3
IntRad = 15
IntRad 30
IntRad = 90
mean +- 1.5
124 maps
16.78%
2.79%
0
0
Mean +- 1
307 maps
32.247%
9.44%
3.91%
2.82%
Random distribution made
with two sine distribution
Z-distributions for different phase shifts
phase shift 0
Int Rad in Bins
Mean
RMS
0
0
0.984
3
-30.42
0.9408
15
-38.79
0.9151
30
-40.94
0.9678
90
-43.1
0.9781
Phase shift pi
Int Rad in Bins
Mean
RMS
0
-41.69
0.44
3
-45.75
0.2144
15
-46.26
0.122
30
-46.36
0.058
90
-46.4
0.0054
Z-distributions for different phase shifts
Phase shift pi/2
Int Rad in Bins
mean
RMS
0
-39.77
0.5279
3
-45.49
0.2606
15
-46.18
0.1665
30
-46.32
0.093
90
-46.4
0.02
Int Rad in Bins
mean
RMS
0
-1.908
1.046
3
-33.26
0.9114
15
-42.91
0.782
30
-44.65
0.6119
90
-45.74
0.4245
Phase shift 0.1
Random distribution made
with one normal and one sine
Z-distributions for different phase shifts
phase shift 0
Int Rad in Bins
Mean
RMS
0
-36.72
0.6484
3
-45.07
0.307
15
-46.07
0.2047
30
-46.38
0.338
90
-46.4
0.016
Phase shift pi
Int Rad in Bins
Mean
RMS
0
-36.8
0.616
3
-45.1
0.3096
15
-46.08
0.1943
30
-46.39
0.036
90
-46.4
0.0202
Z-distributions for different phase shifts
Phase shift pi/2
Int Rad in Bins
mean
RMS
0
-36.79
0.656
3
-45.09
0.3076
15
-46.68
0.202
30
-46.26
0.129
90
-46.4
0.016