Applied Political Research Session 10: The Difference of Means Test - - PowerPoint PPT Presentation

College of Education School of Continuing and Distance Education

2014/2015 – 2016/2017

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

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

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• 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

• f the independent variables. If on inspection the

values of the dependent variables are

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• (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.

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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:

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Independent Variable

• Gender

Dependent Variable (Amount Contributed) GH¢ Male 10 Female 8 Female 5 Male 10 Female 10 Male 15 Male 20 Female 2 Female 5 Male 15

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• If we ignore the independent variable, we can see

that the population mean (µ) i.e. the average amount

• f 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 (δ2) using the expression given as follows:

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• 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

• riginal variation is distributed across the 2 groups as

follows

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Male Contribution Females Contribution 10 2 10 5 15 5 15 8 20 10

• Total (n) 70

Total (n) 30

• Mean

14 Mean 6

• s2

14 s2 7.6

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• 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 (s2 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

• bservations into categories that are different from

each other on the independent variable and that

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• 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 (s2 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

• f unexplained variance in the independent variable.

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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

• riginal 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.

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