Critical Values of the t-Distribution
Inputs:
α = Level of Significance
df = Degrees of Freedom = sample size minus 1
Tails = one-tailed or two-tailed
Look for thecolumn heading for α and one-tailed or two-tailed.
Look for the row label for the degrees of freedom.
p-values: Area under the right tail (or under both tails)
Inputs:
t = the t value, must be positive
df = degrees of freedom
tails = 1 or 2, for one-tailed or two-tailed
Look for the column heading for the degrees of freedom
Look for the row label with the t value.
Critical Values of the t-Distribution
Inputs:
α = Level of Significance
df = Degrees of Freedom = sample size minus 1
Tails = one-tailed or two-tailed
=TINV(two-tailed α value, df)
Example: Critical value of t-distribution for α=.0.05, two tailed, df=20
TINV(0.05,20) =
2.085963
(The printed table says 2.09)
=TINV(one-tailed α value * 2, df)
Example: Critical value of t-distribution for α=.0.05,one tailed, df=20
TINV(0.05*2,20)=
1.724718
(The printed table says 1.72)
p-values: Area under the right tail (or under both tails)
Inputs:
t = the t value, must be positive
df = degrees of freedom
tails = 1 or 2, for one-tailed or two-tailed
=TDIST(t, df, tails)
Example: p-value for t = 2, df=21, one-tailed
TDIST(2,21,1)=
0.0293
(The printed table says 0.029)
Experimentation area
Critical value computation
TINV(α ,df )
α=
0.05
df =
50
tails=
1
RESULT: 1.675905
p-value computation
TDIST(t,df,tails)
t = 1.675905
df =
50
tails =
1
RESULT:
0.05
Compare to 1-NORMSINV()
Compare to NORMSDIST()
1-NORMSINV(α)=
1.644854 1-NORMSDIST(t)=
0.046878
difference =
0.031051 difference =
0.003122
2ND DISTR (on the VARS key)
Critical Values of the t-Distribution
invT(area,df)
This works differently from the Excel function!
The first argument is the cumulative area, not the α in two tails.
One-tailed α example
Example: Critical value of t-distribution for α=.0.05,one tailed, df=20
TI-84: invT(1-α, df)
Contrast with Excel:
Excel: =TINV(one-tailed α value * 2, df)
Excel: TINV(0.05*2,20)=
1.724718 (The printed table says 1.72)
Two-tailed α example
TI-84: invT(1-α/2, df)
Example: Critical value of t-distribution for α=.0.05, two tailed, df=20
Contrast with Excel:
Excel: =TINV(two-tailed α value, df)
Excel: TINV(0.05,20) =
2.085963 (The printed table says 2.09)
p-values: Area under the right tail (or under both tails)
TI-84: tcdf(lowerbound, upperbound, df)
Example: p-value for t = 2, df=21, one-tailed
Negative values and left tails work, too (Excel is restricted to positive t)
Example: area to the left of t = 2 with df = 21
Example: area to the left of t = -2 with df = 21
Note: for infinity, use 1 EE 99 (EE is 2ND COMMA)
and for minus infinity, use -1 EE 99.
For two-tailed situations, compute for one tail and then double it.
Or do 1 - the middle area.
Example: The area between t = -2 and t = 2, shown both ways.
Contrast with Excel:
Excel: =TDIST(t, df, tails)
Excel: TDIST(2,21,1)=
0.0293
(The printed table says 0.029)
The y-value of the t-distribution at some given point.
Example: Evaluate at t = 0 , t = 1, t = 2 for the curve with df = 21.
tpdf(x value, df)
This is useful if you want to graph the t distribution.
And inspect a table of values (though the table of tcdf() might be more interesting.)
Experimentation area
See the "Excel" sheet for an experimentation area if you want to compare
TI-84 results to Excel results.