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Differentiate between independent samples and paired samples.
Two-sample t tests compare the mean of one sample (e.g., an experimental group) to the mean of another sample (e.g., a control group) in order to conclude whether the population means differ. There are two types of two-sample t tests: independent-samples t tests and paired-samples t tests. With an independent-samples t test, how the cases are selected for one sample has no impact on case selection for the other sample. With paired samples, the selection of cases for one sample influences or determines case selection for the other sample.
Conduct the steps for an independent-samples t test.
To conduct an independent-samples t test, the assumptions must be checked, the hypotheses generated, and the decision rule formulated. To find t, the difference between the sample means is divided by the standard error of the difference.
Interpret an independent-samples t test.
The decision rule is applied to decide if the null hypothesis is rejected. If it is rejected, the researcher concludes that the difference between sample means probably represents a difference between population means. Next, Cohen’s d and r2 are used to calculate effect size and categorize it as small, medium, or large. If the effect size is meaningful and the null hypothesis was not rejected, the researcher should consider the possibility of Type II error. Finally, the researcher should calculate the confidence interval for the difference and interpret it based on whether (1) it captures zero, (2) how close to zero it comes, and (3) how wide it is.
Put states into two categories on some basis. You could categorize them into whatever groups you wish—for example, states with nice climates vs. those without, or southern states vs. northern states, or states you would like to live in vs. those you would like to avoid. Include about 5–8 states in each group. Pick some outcome variable on which you want to compare the two groups. For example, is the murder rate different in southern states vs. northern states? Do an online search to find the necessary data. Then use an independent-samples t test to analyze the data. Report the results in APA format. Don’t forget to calculate an effect size.