Thinking Scientifically: Investigating an Hypothesis With a Difference of Means Test

As we see from the readings and from the videos from Week 3, a difference of means test is a good introduction into testing hypotheses. It’s good in that it includes many of the elements necessary in conducting scientifically-based research without introducing too much statistical complication. These elements include the writing of an hypothesis, establishing confidence in a given predicted value (that is, establishing a confidence interval around a predicted value), and learning how probability is assessed in a formal statistical test (that is, learning the logic of interpretation of Z scores and p – values / probabilities and how they are constructed statistically). Although difference of means tests are often considered to be part of a scholar’s preliminary work on a topic, they can also be the end product. This is because of the power and simplicity of the findings generated by a means test. A well thought out and executed difference of means test can reveal a lot information about a condition or a process in the social world and set the stage for a more methodologically complicated study.

Here’s what I want you to do:

1. Think about an issue in your area of study and write a null and alternative hypothesis that can be tested with a difference of means test . Remember Hoover and Donavan’s advice: keep your hypothesis simple, direct and clear. Typically, the more simple an hypothesis, the more powerful it is.
2. Use any of the class data sets and SPSS to test your hypoth esis with a difference of means test . Some SPSS operational procedures to keep in mind include:

1. Use the data selection procedures in SPSS to identify two groups of cases you would like to compare. Your two groups could be one region versus another region; one region such as Asia versus all other regions of states (the latter treated as a single group); they could be two different economically developed groups such as all developing countries versus all developed countries; or groups of states that belong to an organization such as the EU versus states that are not part of it; free versus non-free states and so forth. There are lots of ways to think about two groups that could be compared in regard to a test variable (a phenomenon) that you are interested in. And, you know how to recode variables so that you can make some unique groupings, if you think about it. (See the videos and MPM for examples of recoding.)
2. Keep in mind that if you are interested in indicators found in one of the time series cross-sectional data sets such as the Millennium data or the tscs6393 data, you need to use the data selection procedure in SPSS to select on a particular year such as 2001 or on a relatively short range of years such as from 2005 to 2007. (I can remind you how to do that easily.)
3. I discuss and illustrate two different types of means test in my videos. They are the ‘paired samples’ and the ‘independent samples’ means test. Make sure you know the difference between them before you begin. Essentially, the paired samples test assumes equal variances between two groups: males as one group and females as a second group, for example. In the Week 3 videos, I utilize this method to test the hypothesis that females tend to live longer on average than males. The male and female observations are ‘pairs’ from the same states. The sample is global.

The independent samples means test is more flexible and most likely will be the one you use. It does not assume equal variances between groups, although the variances can be equal. Nor does it assume equal sample sizes. Hence, the scholar can compare all sorts of groups such a small sample of cases versus a large sample of cases such as Latin America versus Asia. As I said, this is the method most of you will and should use, but the choice between the two means test is up to you. Make sure your choice is appropriate to your hypothesis and the conditions I mention above.

1. Generate the means table(s) in SPSS and interpret the findings . The key question is: do the finding support your alternative hypothesis? Secondly, what is the story revealed by your finding? The specific statistical findings include the difference in means, the t –test (or point estimate), the p-value (or probability value), and the confidence interval. Succinctly, integrate descriptions of how these statistics are calculated in your interpretations of the findings.

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