Question

I have a three-group study that uses a one way ANOVA. Each group has 40 participants in it.

1. how many degrees of freedom does the omnibus F test have?

2. suppose prior to data collection I have stated two hypotheses backed by previous studies: (1) group a will score higher than group s B and C combined. and (2) group B will score higher than group C. What is my next step in the analysis?

Answer 1

1) there are three groups, therefore between treatment degree of freedom is 3-1 = 2, since the are 40 participants in each group, therefore total participants = 3*40 = 120, therefore, error degree of freedom = 120-3 = 117.

therefore, F test has {2, 117} degrees of freedom.

2) There are many ways to test these hypothesis, like t test, Tukey HSD test, etc. for t test for first part, first calculate average for A and combined average for B and C and pooled standard deviation for B and C and standard deviation for A then you can easily test, for second part it is simple to test.

if you have any doubt you can ask by comment.