STATZIKI

Paired T-Test Calculator

Input






Summary

Mean Diff -6.1111
STD Diff 7.7046
Sum diff -55
Sum diff^2 811
n 9
t-value -2.3795
p-value oneside 0.0223
p-value twoside 0.0446

Formulas and Output

\[S_d = \left[\frac{\sum d_j^2 - \frac{1}{n}(\sum d_j)^2}{n-1} \right] = \left[\frac{ 811 - \frac{1}{ 9 }( -55 )^2}{ 9 -1} \right]^{0.5} = 7.7046\] \[dmean = \frac{1}{n} \sum d_j = \frac{1}{ 9 } -55 = -6.1111 \] \[t = \frac{diffmean }{S_d/\sqrt{n}} = \frac{ -6.1111 }{ 7.7046 /\sqrt{ 9 }} = -2.3795\] \[H_0: \mu_d = 0\] \[H_1: \mu_d \neq 0\]

When should you use a paired t-test?

A paired mean test is used to deternmine whether the mean difference between two sets of observations is zero. This method is commonly used compare the same dataset at different time points to see if there is any differences between the dataset from time point 1 and time point 2.

The paired t-test assumes the variances are unkown, commonly when n < 50.

Example, professor Bob have two learning methods and he wants to test which method is the best. During time period 1 he uses method X and during time period 2 he used method Y on the same students, he then measure the average exam score on each student and compare the score from period 1 and 2. The data he collected can be seen in the lists below.

Method X average score = [70 68 66 98 77 66 55 3 98]
Method Y average score = [73 69 78 99 88 68 78 4 99]