An investigator used ANOVA to compare four groups of students on numerical ability on the basis of a test. After analysis of raw scores, the following results were obtained:

Source of variation	df	Sum of Squares
Between Groups	3	625.00
Within Groups	36	2128.00

 

The value of F-ratio would be approximate:

ANOVA is a test used to detect differences between continuous variables when there are more than two groups, so it would be ideal to use an ANOVA to compare four groups of students on numerical ability on the basis of a test. As part of performing an ANOVA on this data, we need to calculate an F-ratio.

The F-ratio is defined as the ratio of the between-group variance (MSB) to the within-group variance (MSW).

⇒F = \(\frac{between\ group\ variance}{within\ group\ variance}\) = \(\frac{MSB}{MSW}\)

The calculated F-ratio can be compared to a table of critical F-ratios to determine if there are actually any differences between groups or not.

MSB = Sum of Squares (between)/ degree of freedom(df_between) 

MSB = 625/3 = 208.333

MSW = Sum of Squares (within)/ degree of freedom(dfwithin) 

MSW = 2128/36 = 59.111

F = \(\frac{between\ group\ variance}{within\ group\ variance}\) = \(\frac{MSB}{MSW}\)

F = 208.333/59.111 = 3.52