POLI 443 Applied Political Research Session 10: The Difference of Means Test Lecturer: Prof. A. Essuman-Johnson , Dept. of Political Science Contact Information: aessuman-johnson@ug.edu.gh College of Education School of Continuing and Distance Education 2014/2015 – 2016/2017
Difference of Means Test • Introduction • One of the tests for the influence of an independent variable on what is happening with the dependent variable is provided by the difference of means test. • Crosstab data analysis is appropriate when both variables are nominal or ordinal level measures. When the independent variable is nominal or ordinal and the dependent variable is interval or ratio, a crosstab data analysis would have far too many columns or rows to permit a straightforward and Slide 2
• meaningful analysis. Two similar analysis techniques, namely the difference of means test and analysis of variance (ANOVA) are used. Both techniques help the researcher’s hypothesis that the dependent variable (which is at interval or ratio level) is related to the independent variable. To start the analysis, first the cases are divided into categories based on the values of the independent variables. If on inspection the values of the dependent variables are Slide 3
• (1) less varied within each category of the independent variable than they were before and (2) quite different in general for different values of the independent variable then a relationship exists between the two variables. Slide 4
Illustration • A researcher hypothesizes that there is a relationship between Gender and the amount of monies contributed by people to political election campaigns. A sample of 10 people was selected and asked of the amount of monies they contributed to a particular election campaign. The data collected is as follows: Slide 5
Independent Variable Dependent Variable (Amount - Gender Contributed) GH¢ Male 10 Female 8 Female 5 Male 10 Female 10 Male 15 Male 20 Female 2 Female 5 Male 15 Slide 6
• If we ignore the independent variable, we can see that the population mean (µ) i.e. the average amount of money contributed by all the 10 people is $10 (000) and the variation around the (µ) i.e. the population variance is 26.8. (Compute the population variance (δ 2 ) using the expression given as follows: Slide 7
2 = ∑(X – µ) 2 /N • • It is this variation (variance) that we are trying to explain. The issue is: how does the independent variable (Gender) help the researcher to account for this variation. The independent variable is clearly a nominal level measure. If we divide the cases into 2 groups based on gender we would notice that the original variation is distributed across the 2 groups as follows Slide 8
Male Contribution Females Contribution 10 2 10 5 15 5 15 8 20 10 • Total (n) 70 Total (n) 30 • Mean 14 Mean 6 • s 2 s 2 14 7.6 Slide 9
• Analysis • The average amount of money contributed by the two groups is quite different (14 for the males and 6 for the females), and the variation in the amount contributed is much less within both groups than it was originally (s 2 for males is 14 and 7.6 for females compared to 26.8). This means that the independent variable (Gender) has been helpful in grouping the observations into categories that are different from each other on the independent variable and that Slide 10
• contain observations that are similar to each other. The analysis has revealed a pattern in the data that males and females contribute differently towards election campaigns (males contribute much more than females). The disaggregated data has also reduced the amount of unexplained variation in the data (s 2 for males is 14 and 7.6 for females compared to 26.8). • This is the basic logic of the difference of means test analysis technique. We begin with a certain amount of unexplained variance in the independent variable. Slide 11
We use the measurement of the independent variable to divide the cases into analysis groups and determine if the groups created are dissimilar from each other and are more homogeneous than the original data. The difference of means test involves comparing the means of the two groups created with the independent variable to see if the difference is statistically significant. Slide 12
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