While the t-test is limited to the comparison of two means, the ANOVA is an inferential statistic that can be used to compare two or more means. The ANOVA produces an F statistic that is a ratio of the variability of the means being compared to the variability of the observations within each set of data on which the means are based. The ANOVA can be used to compare two or more means (in theory the number of means is limitless) taken from different groups (resulting from a between-subjects design) or to compare means taken from the same group of subjects under varying conditions (resulting from a within-subjects or repeated-measures design) – the repeated measures ANOVA. The one-way ANOVA examines the effect of a single independent variable on a dependent variable. The two-way ANOVA examines the effects of two separate independent variables, as well as their interaction, on a dependent variable.

Consider an experimental investigation in which the effects of work environment on productivity are examined using a between-subjects design. A large corporation randomly assigns its workers to one of three different work environments; single closed office, single open cubby where the worker works alone but can see and hear other workers, or shared open cubby where the worker shares the work space with another worker and can see and hear other workers. They then measure each worker’s productivity on a standardized productivity schedule. The independent variable is the type of work environment and it has three levels rather than two as in the previous studying example. The dependent variable is productivity, and the null hypothesis is that work environment has no effect on productivity or that the productivity of all workers will be the same regardless of work environment. These data would be most appropriately analyzed with an ANOVA.

Learning Check #21:
Identify the independent variable, dependent variable, and the null hypothesis from the following scenario:

A researcher would like to know if highlighting a textbook helps students to score better on exams. She randomly selects one-half of the students in an introductory class and instructs them to highlight their textbooks as they read. The other students are instructed to do NO highlighting as they read.

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If the experimental manipulation has no effect, the experimental and control groups in the over-learning study would not differ significantly in their performance on the exam and the workers in the different work environments would all be equally productive. In those cases, we would fail to reject the null hypothesis. If, in the over-learning study, the experimental manipulation has an effect, the two groups would differ significantly in their performance on the exam. In that case, we would reject the null hypothesis. This would indirectly support the research hypothesis, which would predict that over-learning affects exam performance. But how large must a difference be between groups for it to be significant? How much more productive must one group of workers be than another for us to conclude that work environment affects productivity? To determine whether the difference between groups is large enough to minimize chance variation as an alternative explanation of the results, we must determine the statistical significance of the difference between them.