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Chapter 9 Jennifer Winquist 9.1 Introduction to the t-Test In the previous chapters we examined relationships among variables to assess covariation between the variables. In this chapter we consider research concerning differences between groups. Experiments are designed to establish cause-effect relationships. In the simplest experiment there are two groups of participants created by the manipulation of an independent variable (the cause). The two groups are measured on the same dependent variable (the effect) in order to compare their scores. Data analyses are needed to determine whether the independent variable manipulation produced significant differences in scores between the two groups on the dependent variable. The t-test is used to determine whether the difference between means of two groups or conditions is due to the independent variable, or if the difference is simply due to chance. Thus, this procedure establishes the probability of the outcome of an experiment, and in doing so enables the researcher to reject or retain the null hypothesis (in this case, Ho is that any observed differences are not significant, but rather, are due to chance). The null hypothesis states that the experimental manipulation has no effect, therefore the means of the groups will be equal. In this respect, the t-test is an inferential statistic used to test hypotheses. Under ideal conditions, these types of inferential statistics allow the researcher to infer a causal relationship between the independent and dependent variable. There are two distinct applications of the t-test. When a between-subjects design is used, the independent-samples t-test is the appropriate test. Use of a within-subjects design (sometimes called a repeated measures design) or a participant-by-participant matched design requires analysis with the paired samples t-test (also known as the correlated or paired-samples t-test). In this chapter we will introduce the independent samples t-test. We will address the correlated samples t-test in the next chapter. There are many hypotheses we could test as part of this project using the t-test. For example, we are interested in any gender differences that might exist among EZ employees. Note that in this context, gender is considered to be a quasi-independent variable because we cannot actually manipulate gender. Nevertheless, the t-test can be applied to examine differences between men and women on various dependent variables. For example, we might want to test for gender differences in scores on the task skills scale and/or the social skills scale (both would be considered dependent variables in this context). You might hypothesize that men would score higher than women on task skills, because research indicates that task orientation in leadership is a stereotyped male characteristic. Comparing the scores of women on task skills against those of men on independent-samples t-test would enable you to determine whether this was indeed the case. On the other hand, you might expect women to exhibit greater social skills (a stereotyped female characteristic) than men, a hypothesis that could also be tested with the independent-samples t-test. But let's not stop there. Ultimately we're interested in understanding leadership performance (perform) of employees, so why not determine if there are gender differences in overall performance? Although in this instance there may be no clear a priori reason to suspect that there should be gender differences in performance, it is certainly a question worth investigating. We will use the independent samples t-test to examine gender differences in performance for the example in this chapter. You will be asked to examine gender differences in social skills for the exercise at the end. |