If you assess the effects of two independent variables in one study, it's possible that combinations of their levels produce unique effects. In this video, learn about these possible effects.
- [Instructor] It's possible to have more than one independent variable in a study, let's see what can happen when independent variables combine. A factor is another name for an independent variable and as I just mentioned you can have more than one in a study. Each factor can have any number of levels. We'll cover the simplest case two factors and two levels of each, this is called a two by two design. Here's an example of this type of design. The study involves the effects of background silence versus music and light color red versus green on problem solving. 20 people are randomly assigned to one of four combinations silence and red light, silence and green light, music and red light, or music and green light. And five people are in each combination. The dependent variable is the time in seconds to solve a paper and pencil maze. We have a set of null and alternative hypotheses for each variable and as you'll see, something else. One null hypothesis is that the mean of performance under red light equals the mean of performance under green light and the alternative hypothesis is not H zero. Another null hypothesis is that the mean of performance during silence equals the mean of performance during music and the alternative hypothesis is again not H zero. We have another set of null alternative hypotheses that are about something else and I'll tell you about them in a moment. and music equals row two. Light color is the column variable, red equals column one and green is column two. we'll use the initials of levels to identify a cell. So silence and red is cell SR, silence and green is cell SG, Now to understand that something else in that third null hypothesis we have to think about cell means, in other words the average of all scores in a cell. We will also consider the row means, the average of all scores in a row regardless of the column. And we have to consider the column means, the average of all scores in a column regardless of the row. Now with all that in mind, let's graph some possible results. Levels of one factor light color are on the X axis, the dependent variable is on the Y axis, and cell means are inside the graph. The lower line in the graph represents the data for row one silence, the upper line represents the data for row two, music. Here's what this graph means. The relatively large distance between X bar for music and X bar for silence suggests that we can reject the null hypothesis about silence and music, this is referred to as a main effect of background. We'd also call it a row main effect. Of course we'd have to do the analysis to verify that we have this main effect. The relatively small distance between X bar for red and X bar for green suggests that we cannot reject null hypothesis about the mean of red and the mean of green. We would have to do the analysis to verify that too. The lines are parallel, this suggests that the levels of light color combine with silence and music in the same way, which is to say that regardless of silence or music, green light results in longer times than red light and regardless of red light or green light, music results in longer times than silence. And now for that something else. In this graph the lines are not parallel. This suggests that levels of light color combine with silence and music in different ways meaning that with music in the background, red light results in longer times than green light. And with silence in the background, green light results in longer times than red light. This is called a statistical interaction. A statistical interaction occurs when the different levels of one factor affect the different levels of another factor differently. The situation in this graph is called a row by column interaction, for this example it's a background by light So that third set of hypotheses is the null hypothesis is that there's no background by light color interaction and again H1 is not H zero. So here's the full set of hypotheses. The hypotheses about the light, the hypotheses about the background, and the hypotheses about the interaction. It's possible to do a multifactor study with more than two factors and with many possible combinations of levels of factors. And the possible results would include many potential combinations of main effects and interactions. So summing up, you can have more than one factor in a study, each one can yield a main effect or not, and the factors can combine to produce statistical interactions.
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