Question

t is election time and voters are going to the polls to cast their vote for their favorite candidates. A researcher was interested to study whether there is a significant difference in patterns of voting turnout among three regions: Eastern, Western and Central. She randomly selected 12 voting precincts from each region and calculated the sum of squares of the rate of participation as follows: SSB= 3,342.89 SSW= 7,265.42 Write the ANOVA formula and conduct an ANOVA test of patterns for voting turnout. Write the hypotheses HO and H1, calculate F ratio and interpret the results.

Answer 1

ANOVA Table format:

As per Question:

SS(Between) = 3,342.89

SS(Error) = 7,265.42

m = No. of regions = 3

n = Total no. of observations = 12

H₀: There is a no difference in patterns of voting turnout among three regions: Eastern, Western and Central.

H₁: There is a significant difference in patterns of voting turnout among three regions: Eastern, Western and Central.

ANOVA Table:

Source	df	SS	MS	F	p-value
Factors	2	3342.89	1671.445	2.070494	0.182093
Error	9	7265.42	807.2689
Total	11	10608.31

Since p-value = 0.182093 > 0.05 i.e. we can not reject H₀ and hence we can say that there is no evidence to conclude that there is a significant difference in patterns of voting turnout among three regions: Eastern, Western and Central.

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