Question

The following is an incomplete F-table summarizing the results of a study of the variance of life satisfaction scores among unemployed, retired, part-time, and full-time employees.

Source of Variation	SS	df	MS	F
Between groups			23
Within groups (error)		36
Total	153

(a) Complete the F-table. (Round your values for mean squares and F to two decimal places.)

Source of Variation	SS	df	MS	F
Between groups			23
Within groups (error)		36
Total	153

(b) Compute omega-squared

(ω²).

(Round your answer to two decimal places.)
ω² =

Answer 1

Solution:

Part 1)

Given: The following is an incomplete F-table summarizing the results of a study of the variance of life satisfaction scores among 1) unemployed, 2) retired, 3) part-time, and 4) full-time employees.

Thus k = Number of groups = 4

Source of Variation	SS	df	MS	F
Between groups			23
Within groups (error)		36
Total	153

We have to complete the F-table.

df_between = k - 1

df_between = 4 - 1

df_between = 3

MS_between = 23

thus

MS_between = SS_between / df_between

23 = SS_between / 3

SS_between = 23 X 3

SS_between = 69

We have:

SS_total = 153

thus

SS_within = SS_total - SS_between

SS_within = 153 - 69

SS_within = 84

and

df_within  = 36

thus

MS_within =SS_within / df_within  

MS_within = 84 / 36

MS_within = 2.33

and

df_total = df_between +  df_within  

df_total = 3 + 36

df_total = 39

Thus

F = MS_between / MS_within  

F = 23 / 2.33

F = 9.86

thus

Source of Variation	SS	df	MS	F
Between Groups	69	3	23.00	9.86
Within Groups	84	36	2.33
Total	153	39

Part b)

Compute omega-squared (ω²).