Psychology 320: Psychological Statistics

Professor: Howard B. Lee

Lecture Notes

Week 11: Chapter 10

ANOVA Summary Table:

source	degrees of freedom	sum of squares	mean of squares	F
between	2	16.3334	8.1667	.5334
within	21	321.5000	15.3095
Total	23	337.8334

SS within/ df within = MS within
MS between/ MS within = F

ho: u1 = u2 = u3
h1: u1 not = u2 or, u1 not = u3 or, u2 not = u3, and at least one is true.

You must find out how many group means you have by looking at the df between. This is the number of levels of IV - 1, and can be found under column "df" row "between" on the ANOVA summary table. For the above example, the number of group means = 3.

Test statistic : F = .5334
Decision rule : alpha = .05
Always treat it as a right-tailed test .
Use table E. (The top value = .05, bottom value (in bold) = alpha = .01)
df between = 2
df within = 21

Reject ho if the calculated F value is greater than or equal to the critical value found on table E.
Decision rule: Since F = .5334 < 3.47, do not reject ho.
Conclusion: (This relates back to the original problem) There is insufficient evidence of a difference between therapies.

If there are many groups:
ho : u1 = u2 = u3 = u4 = u5
h1 : at least one pair of group means are statistically different.