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When analyzing scores in a bell-shaped distribution [link widoczny dla zalogowanych], one might observe that two groups with high variability might have the same difference in means as two groups with low variability. However, we could conclude that in spite of the similarity in mean differences, the two groups with low variability appear more distinct or different from the groups with high variability, which overlap a great deal.
Viewing these bell curves helps us to understand that when looking for differences between scores for two groups, we must judge the difference between their means relative to the spread of the score. Researchers assume that good randomization in selecting or assigning events is in place before utilizing the t-test.
Reinard [link widoczny dla zalogowanych], J. (1998). Introduction to Communication Research, 2nd Ed. McGraw-Hill: Boston.
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Instead of having four groups to examine all possible scenarios, a factorial design allows researchers to cross each of the time conditions with the setting conditions. In this example, the researchers can develop a two-by-two factorial design to depict how many factors and levels there are.
An interaction effect exists when differences on one factor depend on the level of another factor. An interaction exists between factors, not levels. Therefore, researchers could say there is an interaction between length of time and classroom setting, and then describe the specific levels involved.
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Determining Statistical Significance
Once researchers ascertain the t value, they must look it up in a table of critical t values to say whether the difference between the groups is likely to have been a chance finding. The risk level, which is called the alpha level [link widoczny dla zalogowanych], is usually set at .05. This means that five times out of one hundred you could find a statistically significant difference between the means by chance.
Beyond Two Means
class="dynamic">Why Use the T-Test?
Researchers use the t-test to compare two samples so that they can make an inference about the populations from which they drew the samples. Specifically, the t-test assesses whether the means of two groups are statistically different from one another.
Factorial analysis of variance identifies main effects and interaction effects. A main effect is an outcome that is a consistent difference between levels of a factor. For example, if there’s a statistical difference between the means for the classroom and online groups at all levels of instruction time researchers can say there is a main effect.
Researchers must also determine the degrees of freedom (df), which is n-2. Given the alpha level, t value, and df, researchers can use the critical value table to determine whether the t value is large enough to be significant. If so, one can conclude that the difference between the means for the two groups is statistically significant, even given the variability.
Factorial analysis of variance has some useful features when researchers want to study multiple independent variables, each with different levels. For example, one study might involve looking at a biology course taught two hours a week versus one taught four hours a week and measuring which is more effective. Additionally, one class is taught in the classroom and another is taught in an online format.
Distinguishing Main and Interaction Effects