10.1 Introduction to Inference for Two Groups
Learning Objectives
By the end of this module, the student should be able to:
- Differentiate between two paired samples and two independent samples.
- Conduct and interpret hypothesis tests for two population means for independent samples.
- Conduct and interpret hypothesis tests for two population means for paired samples.
- Construct a confidence interval to estimate the population mean of paired differences.
We now extend the inference methods we have learned, so we can apply confidence intervals and hypothesis tests to differences in population means that come from two groups. Examining and understanding how groups of individuals can differ is one of the key goals in science. This understanding is particularly important when the goal is to examine whether a certain intervention is helpful. For instance, if a drug company wanted to trial a new depression medication or treatment, one group would be assigned to the treatment or intervention, and the other group would not receive the treatment.
There are two main types of statistical tests: those that look at differences Between Independent Groups and those that look at differences Within Paired Groups.
Between Independent Groups differences examine how independent groups – groups that are not the same – may differ from each other on a variable. Between Groups difference tests are useful for examining the efficacy of interventions or treatments. For example, to see if a new form of anxiety therapy is effective, the researcher would organize two groups of participants, and provide one with the new form of anxiety therapy. This group would be the treatment group. The other group would not receive the treatment, so it would be the control group. Both groups would need to receive some form of outcome measure, such as a measure of anxiety taken after the treatment. The comparison would be on the mean response for each group to see if there were any differences in mental states.
Within Paired Groups differences are similarly important. For example, if a researcher wants to examine if an exercise program is effective, the body mass index (BMI) of a group of test subjects could be measured at the start of the program and again at the end of the program. The mean BMI values would then be compared to each other. In this case, the researcher is not looking at the differences between two separate groups, but rather the differences within the same group taken at two time points.
To examine the differences between independent groups or paired groups, there are two main types of t-tests we will be focusing on, the independent samples t-test and the paired samples t-test. When examining the difference between two independent groups, use the independent samples t-test, however, if the focus is on the difference between the same group at two different time points, the paired-sample t-test is the one to use.
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