The follow data are from a research study comparing two treatment conditions. Use a two-tailed test with ? = .05 to evaluate the mean difference between treatments. For the first test, assume the data are from an independent-measures study using two separate samples. For the second test, assume the data are from a repeated-measures study using the same sample of n = 4 participant in both treatments.
treatment 1 treatment 2
5 10
10 7
4 15
5 4
M = 6 M = 9
SS = 22 SS = 66
For the repeated-measures test:
Treatments
I II D D2
5 10 5 25
10 7 - 3 9
4 15 11 121
5 4 -1 1
M = 6 M = 9 ?D = 12 ?D2 = 156
SS = 22 SS = 66
MD = 12/4 = 4 SS = 156 – 122/4 = 156 – 36 = 120 s2 = 120/3 = 40
sMD = ?40/4 = ?10 = 3.162 t = 3 – 0 / 3.162 = 3/3.162 = 0.948
critical region value = ±3.182
Fail to reject the null hypothesis. We conclude there is not a significant difference between treatments.
In this example...why is the variance and the standard error larger?