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			21
Within groups (error)		36
Total	139

(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		3	21
Within groups (error)		36
Total	139

(b) Compute omega-squared

(ω²).

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

Answer 1

Source of variation	SS	DF	MSE
Between group	7	3	21
Within group (error)	132	36	3.67
Total	139	39

Let
SSB = SS(between)
SSE= SS(error)
SST = SS(total)

SSB = MSB / df(between)
SSB = 21/3 =7

SST = SSB + SSE
139 = 7 + SSE
SSE = 139 - 7 = 132

MSE = SSE/ df(error) = 132/36 = 3.67

df(total) =df(between) + df(error)
df(total) = 3 +36 = 39

Omega squared : ω2

ω2 = 7 - (3*3.67) /(139 + 3.67)
ω2 =7-11.01 / 142.67
ω2 = -4.01 / 142.67
ω2 = - 0.03

Generally ω2 is lies in 0 to 1. So the negative size can be appear & it can be considered as 0.
ω2 is a strength of association measure provides an estimate of the amount of variance in the dependent measure that can be explained by the independent measure.

Here omega is negative. Since a negative
variance has no meaning, negative values are always set to zero.