Best statistical tool to compare two groups with anxiety
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A common form of scientific experimentation is the comparison of two groups. This comparison could be of two different treatments, the comparison of a treatment to a control, or a before and after comparison. The preliminary results of experiments that are designed to compare two groups are usually summarized into a means or scores for each group. Once you’ve summarized this data, how do you decide if the observed differences between the two groups are real or just a chance difference caused by the natural variation within the measurements? A common way to approach that question is by performing a statistical analysis.
The two most widely used statistical techniques for comparing two groups, where the measurements of the groups are normally distributed, are the Independent Group t-test and the Paired t-test. What is the difference between these two tests and when should each be used?
The Independent Group t-test is designed to compare means between two groups where there are different subjects in each group. Ideally, these subjects are randomly selected from a larger population of subjects and assigned to one of two treatments. Another way to assign subjects to two groups is to randomly assign them to one of two treatments at the time they enter a study. This randomization is often performed in a double-blind fashion.
Besides the normality assumption, another requirement of the Independent Group t-test is that the variances of the two groups be equal. That is, if you were to plot the observed data from each of the two groups, the resulting bell-shaped histograms would have approximately the same shape. Before actually performing the Independent Group t-test, a statistical pre-test is often performed to verify the hypothesis that the variances are equal. Options for the unequal variance case are discussed later.
Once the data are collected and the assumptions to performing the t-test are satisfied, the means of the two groups are compared. The mathematics for the t-test may be performed by a statistical data analysis programs such as WINKS. The determination of whether there is a statistically significant difference between the two means is reported as a p-value. Typically, if the p-value is below a certain level (usually 0.05), the conclusion is that there is a difference between the two group means. The lower the p-value, the greater "evidence" that the two group means are different. It is the p-value that is usually reported in journal articles to support a researcher’s hypothesis concerning the observed outcomes for