may be used to analyze data. Typically, one set of statistical techniques is used to test hypotheses from data collected in experimental methods, and another set is used to analyze data from correlational research.
normal distribution (bell-shaped curve) a distribution of scores along a continuum with known properties F I G U R E A . 2 A Normal Distribution Approximate percent of scores in each segment
Number of standard deviations from the mean Mean –3 –2 –1 +1 +2 +3 2% 2% 13.5% 13.5% 34% 34%
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The simplest type of experimental design would have a treatment group, a control group, and a single dependent variable. Whether or not a group receives the treatment represents levels of the independent variable. The most common statistical technique for this type of study is the t-test, which examines the difference between the means on the dependent variable for the two groups, taking into account the variability of scores in each group. In the example of trained and untrained salespersons used earlier, a t-test would determine whether the difference in the two means (250 units vs. 242 units) is statistically significant, that is, not due to chance fluctuations. If the difference is significant, the researcher may conclude that the training program did have a positive effect on sales.
When an experimental design moves beyond two group comparisons, a statistical method called analysis of variance, or ANOVA, is often used. Analysis of variance looks at differences among more than two groups on a single dependent variable. For example, if we wanted to examine differences in sales performance between a group of salespersons exposed to 2 weeks of “sales influence tactic training,” a group exposed to 2 days of training, and a group with no training, analysis of variance would be the appropriate technique. In this instance, we still have one dependent variable and one independent variable as in the two-group case; however, the independent variable has three, rather than two, levels. Whenever a research design involves a single independent variable with more than two levels and one dependent variable, the typical statistical technique is referred to as a one-way analysis of variance (it is called a “one-way” because there is a single independent variable). The one-way ANOVA would tell us whether our three groups differed in any meaningful way in sales performance.
When a research design involves more than one independent variable, which is very common, the technique that is typically used is the factorial analy- sis of variance. For example, we may wish to examine the effect of the three levels of our influence training program on sales performance for a group of salespersons that receives a sales commission compared to one that does not. This design involves a single dependent variable (sales performance) and two independent variables, one with three levels (training) and one with two levels (commission vs. no commission). The number of different groups in a research study is determined by the number of independent variables and their levels. In this case, our design would result in six groups of salespersons (2 × 3 = 6), and the analysis would involve a 2 × 3 factorial analysis of variance.
There is a major advantage to examining more than one independent vari- able in a research study, and it involves the types of effects that may be detected. Suppose that in our study we find that influence tactic sales training significantly increases sales performance. This change in the dependent variable due to the independent variable of training is called a main effect. Similarly, we may find a main effect of the sales commission variable, such that salespersons who receive a commission have significantly higher sales performance than those who do not. This type of effect could not be detected if we were examining either independent variable alone. However, by examining both independent variables at the same time, we may detect a different type of effect called an interaction.
t-test
a statistical test for examining the difference between the means of two groups
Stop & Review
How would a researcher use descriptive and inferential statistics?
Two variables are said to interact when the effect of one independent variable on the dependent variable differs, depending on the level of the second independent variable. In our study, an interaction between influence tactic sales training and sales commission would be indicated if our training program only increased the sales performance of salespersons who received a commission and did not affect the performance of salespersons who did not receive commissions.
An even more sophisticated technique, multivariate analysis of variance (MANOVA), examines data from multiple groups with multiple dependent variables. The logic of MANOVA is similar to that of ANOVA, but there is more than one dependent variable investigated at a time. For instance, we may want to investigate the effects of training or receiving a sales commission (or both) on sales performance and worker job satisfaction. MANOVA procedures would tell us about differences between our groups on each of these dependent variables. Understanding how these complex statistical techniques work and how they are calculated is not important for our discussion. These terms are presented only to familiarize you with some of the statistics that you might encounter in research reports in I/O psychology or in other types of social science research and to increase your understanding of the purposes of such procedures.