Question

​​​​​​​Psychology Statistics

1. You and a fellow student are comparing means for treatment and control groups, m_T=7.56 and m_C=4.78. You use a t-test, and get a statistic of t(45)=2.87, d=.856. Your colleague uses ANOVA, yielding an F statistic of F(1, 45)=8.27. It turns out that you accidentally switched which was group 1 and group 2, and your group means should have been m_T=4.78 and m_C=7.56. Does your t-statistic change? Does the F-statistic change? Does Cohen’s d change? Why or why not?

Answer 1

The value of test statistic t for (X,Y) is same as (Y,X) only the sign get changed.

t(X,Y) = - t (X,Y)

Test statistic,

Where,

Pooled variance:

F test statistic is the square of t test statistic. Hence in both the cases it remains same.

Cohen's d also remain same

d= (M1 - M2) / spooled

where M1 and M2 are means of X and Y and M1 > M2

spooled remain same in both the cases. Hence Cohen's d does not changes.