How to Start This PowerPoint® Tutorial Before getting started, you need to know 3 things: If you are given the option to click on a button that says “Enable Content,” “Enable Macros,” or “Enable Editing,” please do so. That button may appear at the top of your screen and look like this: Run this presentation in PowerPoint’s “Slide Show” mode. One way to get into “Slide Show” mode is to click on the “Slide Show” tab and select “From Beginning.” Alternatively, you could click on the button near the bottom of your screen that looks like a picture of a computer monitor (it looks like the icon we have highlighted below in yellow). Once in “Slide Show” Mode, click the green button below to go to the next slide. On the next slide, you will again click on a green button. This button will work once you are in PowerPoint’s slide show mode

Visualizing an Experiment That Manipulates Two Variables: Part 2 Click here to begin! If the green button above does not work, quit Powerpoint®. Then, restart Powerpoint. When Powerpoint restarts, be sure to click any buttons that say “Enable macros.” Then, put the program in “Slide Show” mode. Quit © 2016 Mark Mitchell & Janina Jolley

What This Tutorial Can Do For You If you did the previous tutorial, you learned about factorial experiments and simple main effects. In this tutorial, you will learn how to average a factor’s simple main effects to estimate that factor’s overall main effect and how to subtract a factor’s simple main effects to estimate the factor’s interaction effect: the degree to which its effect is affected by the other manipulated factor. By the end of this tutorial, not only will you know what main effects and interactions are but you will also be able to interpret the results of factorial experiments—when those results are presented as a table of means. To continue, click your keyboard’s right arrow button.

Working Through the Tutorial The first time through the tutorial, you should click through the slides (you can use either the right arrow button or your mouse)—except when you are asked a question. When you are asked a question, you should answer it. After your first time through the tutorial, you can use the “Menu” slide to skip to a particular part of the tutorial. The “Menu” slide is the next slide, but you can always get to the Menu by clicking on the orange “home” button on the bottom left of any slide. To continue, click your keyboard’s right arrow button.

Choose an item from the menu below—or just click your keyboard’s right arrow button. Combining (averaging) a factor’s simple main effects to estimate overall main effects Comparing (subtracting) a factor’s simple main effects to look for interactions Quiz Quit

The experiment above can produce 4 simple main effects The experiment above can produce 4 simple main effects. Can these 4 simple main effects also be looked at as 2 pairs of main effects: a pair of main effects for each factor? Yes No

In the 2 X 2, we have 2 pairs of simple main effects In our example, we have A pair of simple main effects for white text vs. black text White text vs. black text on light backgrounds and White text vs. black text on dark backgrounds A pair of simple main effects for dark vs. light background Light background vs. dark background for white text, and Light background vs. dark background for black text. To continue, click your keyboard’s right arrow button.

Can we combine and compare each factor’s pair of simple main effects? Yes, because the data come from the same experiment. No A B

Right! We can look at pairs of main effects. We would pair up The two row effects with each other and the two column effects with each other. Each column effect with its corresponding row effect. A B

Background Dark Light Text color Black ** **** White < > Right! We can can pair up the 2 row simple main effects and the 2 column simple main effects. But before we pair up our main effects, let’s review. The blue row can be used to estimate: The simple main effect of background for the black text conditions. The simple main effect of black text. A B Background Dark Light Text color Black ** **** White < >

Background Dark Light Text color Black ** **** White * = > The bottom row can be used to estimate: The simple main effect for background for the white text conditions: This effect is four stars. The simple main effect of background for the white text conditions: This effect is three stars. The simple main effect of white text: This effect is four stars. A B C Background Dark Light Text color Black ** **** White * = >

So, the two simple main effects we found by comparing cells within rows represent The effects of the background on the readability of black text (a 2 star edge to light backgrounds) and the effects of background on the readability of white text (a 3 star edge to dark backgrounds). The effect of text color. A B Background Dark Light Text color Black ** **** White * < >

You now know how to estimate a factor’s simple main effects. Combining a Factor’s Pair of Simple Main Effects to Get That Factor’s Overall Main Effect You now know how to estimate a factor’s simple main effects. To find the average effect that a factor has in a study, average its simple main effects. This average effect is called the factor’s overall main effect (Often, just called a main effect). Main Menu To continue, click your keyboard’s right arrow button.

Combining (averaging) the two simple main effects that we found by comparing cells within the black and white rows would give us The overall main effect of background, combined across both black and white text. The effect of text color. The background by text interaction. A B C Background Dark Light Text color Black ** **** White * Dark - Light ** *** < >

From averaging/combining the two row simple main effects, you would conclude that Dark backgrounds are, on average, slightly more readable than light backgrounds. Light backgrounds are, on average, more readable than dark backgrounds. White text is more readable than black text. A B C Background Dark Light Text color Black ** **** White * Totals ****** ***** << >>> >

> Background Dark Light Text color Before we start combining our two simple column main effects, let’s look at each individual column. First, let’s look at the dark background column. For that column, how much more effective is white print than black print? One star Two stars Three stars Four stars A B C D Background Dark Light Text color Black ** White **** >

= Background Dark Light Text color Now, let’s look at the light background column. For that column, how much more visible is black text than white text? One star Two stars Three stars Four stars A B C D Background Dark Light Text color Black **** White * =

**** Background Dark Light Text color Black White Averaging/combining the two simple main effects we found by comparing cells within the two background columns would give us The main (average) effects of varying background The main (average) effect of varying text color The background by text interaction A B C Background Dark Light Text color Black ** **** White * Black/ White difference ***

**** Background Dark Light Text color Black White The main effect of varying text color from black to white is, on average, to Have no effect Decrease readability (black text is more readable) Increase readability (white text is more readable) A B C Background Dark Light Text color Black ** **** White Black/ White difference *** *

Another Way to Find Main Effects You now know one way to detect main effects: See whether the average of the factor’s simple main effects is different from 0. Another way to detect main effects, a way that some students find easier, is to see whether the average for groups that have one level of the factor (e.g., the average of the black text groups) differs from the average of the groups that have another level of the factor (e.g., the average of the white text groups). To explore this other way to find main effects, click your keyboard’s right arrow button. If you want to skip learning about this other way to determine whether there is a main effect, click the “Skip” button below. Skip

Hint: How do the labels for the 2 columns differ? Finding that the average scores of the dark background column differ from average scores of the light background column suggests Hint: How do the labels for the 2 columns differ? a main effect for text color a main effect for background darkness an interaction A B C Background Dark Light Text color Black ** White **** Totals ** **** ** ** Averages * * * * * >

≠ Background Dark Light Totals Averages ** **** ***|*** *** * **|** Finding that there is a difference between the average scores of two rows suggests (Hint: How do the two rows—and even their labels—differ?) a main effect for the column variable (e.g., background) a main effect for the row variable (e.g., text color) an interaction A B C Background Dark Light Totals Averages Text color Black ** **** ***|*** *** ≠ White * **|**

On the average, in this experiment, is a dark background better than a light background? Yes Background color Dark Light Text color Black White Totals Averages No *** *** *** * *** *** * *** **

Summary: Overall Main Effects You know how to estimate a factor’s overall main effect. For example, you know that, by taking the average of a factor’s simple main effects, you can estimate that factor’s overall main effect. But how do you tell whether there is an interaction? To continue, click your keyboard’s right arrow button.

Defining interactions First, let’s be sure we know what we mean by an interaction. An interaction means that the effect of one factor depends on the level of another factor. Changing a factor will have one effect under some conditions but a different effect under other circumstances. That is, with an interaction, we cannot say what difference varying one factor will make unless we also know the level of the other factor. In other words, if we have an interaction, a factor’s simple main effects will differ. For example, the difference in readability when we change from black text to white text would be negative when we had a light background, but positive when we had a dark background. If variables interact, combining those variables produces effects that differ from the sum of their individual effects. Combining variables may result in effects that are greater than the sum of the individual effects (think Mentos and diet Coke), less than the sum of their individual effects, or even opposite of the sum of the individual effects (e.g., you might generally like turkey and smore-flavored pop tarts, but not like putting them together into a turkey pop tart sandwich.). light background dark background See more examples of interactions To continue, click your keyboard’s right arrow button.

Understanding interactions If there is an interaction, a factor’s simple main effects differ from each other. True False Example of an interaction Background Dark Light Background simple main effects Text color Black ** **** +2 White *** * -2

Understanding interactions If there is an interaction, a factor’s simple main effects differ from the factor’s overall main effect. True False Example of an interaction Background Dark Light Background simple main effects Overall background main effect Text color Black ** **** +2 White *** * -2

Finding that the difference between the two cells in one row is different from the difference between the two cells in another row suggests a main effect for the row variable a main effect for the column variable a simple main effect of the column variable in that row an interaction nothing A B C D E Background Dark Light Text color Black ** **** White * < >

Detecting interactions You determine whether you have an interaction by comparing a factor’s pair of simple main effects. If a factor’s simple main effects differ significantly from each other, there is an interaction. Warning 1: Only compare simple main effects from the same factor. Warning 2: If the overall main effects of two different factors differ, that does not mean anything about whether there is an interaction. To continue, click your keyboard’s right arrow button.

In which case, would there be an interaction? The effect of changing text from black to white was different in the dark background condition than in the light background. A B The most visible condition was the black text on a light background condition. C Both A and B. No, not necessarily. If we have a main effect of background such that light backgrounds are better than dark backgrounds and a main effect for black text being better than white text, those main effects would normally cause black text to be most visible on light backgrounds.

Which experiment(s) found an interaction? Experiment A Experiment B Both Experiments A and B A B C Experiment A Background Dark Light Text color Black ** **** White * Experiment B Background Dark Light Text color Black * *** White ** ****

Black/ White difference Do the two black/white simple main effects differ? Yes No Background Dark Light Text color Black ** **** White * Black/ White difference ***

Yes No Background Dark Light Text color Black White Is there an interaction between text color and background? Yes No Is the effect of going from black text to white text different in the dark background condition than in the light background condition? Background Dark Light Text color Black ** **** White * Black/ White difference ***

We could also uncover the interaction by comparing the pair of row main effects. Recall that the two row simple main effects represent The effects of background on the readability of black text and the effects of background on the readability of white text. The effect of text color (black versus white). A B Background Dark Light Text color Black ** **** White * << >>>

Black/white difference Does the effect of text color (black being more visible than white) differ depending on the background? There is a text by background interaction. There is not a text by background interaction. Yes No Background color Dark Light Text color Black White Black/white difference *** *** *** * **

In the table below, does it seem like the two row effects (the effects of background) differ? Yes No Background Dark Light Text color Black ** **** White * << >>>

Does there seem to be an interaction? Yes No Background Dark Light Text color Black ** **** White * << >>>

Background Dark Light Text color Black White To review, finding a significant difference between background’s two simple main effects would tell us that there was a(n) Background main effect: On average, the background has an effect. Text color main effect: On average, text color has an effect. Background by text color interaction: Background has one effect for black text, but a different effect for white text. A B C Background Dark Light Text color Black ** **** White * << >>>

Averaging the two simple main effects for background would tell us whether there was a(n) Text color main effect: On average, text color has an effect. Background main effect: On average, the background has an effect. Text by background interaction: Background has one effect for black text, but a different effect for white text. A B C

Background Dark Light Text color Black White < Finding a difference between two cells in the black text row suggests a text main effect. background main effect. simple main effect of background in the black text condition. simple main effect of black text. text by background interaction. A B C D E Background Dark Light Text color Black ** **** White * <

Difference (Effect of varying color) = Now, let’s look at a different set of results. In the experiment below, when the background is dark, does varying the text color matter? Yes No Background color Dark Light Text color Black White Difference (Effect of varying color) = *** *** * ***

When the background is light, does varying the text color matter? Yes No Background Dark Light Text color Black White Difference (Effect of varying color) = *** *** * **

When the background is light, what is our best guess about the effect of varying the text color? 1 star (*) 2 stars (**) 3 stars (***) A B C Background Dark Light Text color Black White Difference = *** *** * **

Black/white difference On the average, in this experiment, is black text more readable than white? There seems to be a text overall main effect. There does not seem to be a text overall main effect. Yes No Background color Dark Light Text color Black White Black/white difference *** *** *** * **

When the text color is black, does varying the background matter? Yes No Background Dark Light Text color Black White *** *** *** *

When the text color is white, does varying the background matter? Yes No Background Dark Light Text color Black White *** *** *** *

Is there a text color by background darkness interaction? Yes No Background Dark Light Text color Black White *** *** *** *

The “Differences” Column could also be labeled Differences between dark and light backgrounds. Effects of varying the background. Both A and B. A B C Background Dark Light Differences Text color Black White *** *** *** * **

There is a difference in readability (number of stars) between the dark and the light background in the black text condition. Yes No Background Dark Light Differences Text color Black White *** *** *** * **

There seems to be a simple main effect of background in the black text condition. True False Background Dark Light Text color Black White *** *** *** *

There is a difference in readability between the dark and the light background in the white text condition. True False Background Dark Light Differences Text color Black White *** *** *** * **

The difference in readability (in number of stars) between the dark background and the light background in the white text condition is 0 stars 1 stars 2 stars 3 stars A B C D Background Dark Light Text color Black White *** *** *** *

There seems to be a simple main effect of background in the white text condition. True False Background Dark Light Text color Black White *** *** *** *

Overall (averaged over both text colors), there seems to be a main effect of background. True False Background Dark Light Differences Text color Black White Total= Average = /2 = = *** *** *** >> * ** ** ** *

In this experiment, on average, is black text more readable than white In this experiment, on average, is black text more readable than white? There seems to be a text main effect. There does not seem to be a text main effect. Yes No Background Dark Light Text color Black White Black - White *** *** *** * **

Review: What 3 things do we find from looking at this study? Background Dark Light Text color Black Black *** Black **** White White *** White * To continue, click your keyboard’s right arrow button.

1. There is a main effect for text color. That is… Background Dark Light Text color Black Black *** Black **** White White *** White * What I want: In terms of visibility, 1=3, 2 better than 4. And 2 better than 1 and 4 worse than 3. To continue, click your keyboard’s right arrow button.

1. The difference in readability of black and white text is not zero 1. The difference in readability of black and white text is not zero. Put another way… Background Dark Light Text color Black Black *** Black **** White White *** White * Black - White *** To continue, click your keyboard’s right arrow button.

1. The average of the black text is different from the average of the white text. Background Dark Light Text color Black Black *** Black **** White White *** White * To continue, click your keyboard’s right arrow button.

2. Over all, the dark background is more effective than the light background. In other words,… Text color Black Black *** Black **** White White *** White * Background totals *** ** What I want: In terms of visibility, 1=3, 2 better than 4. And 2 better than 1 and 4 worse than 3. > To continue, click your keyboard’s right arrow button.

2. The difference between the readability of dark and light backgrounds is not zero. Put another way, Background Dark Light Dark – Text color Black White * *** **** *** ** * * To continue, click your keyboard’s right arrow button.

2. The average of the dark background is different from the average of the light background (a background main effect). Background Dark Light Text color Black White *** **** What I want: In terms of visibility, 1=3, 2 better than 4. And 2 better than 1 and 4 worse than 3. *** * To continue, click your keyboard’s right arrow button.

3. But the effect of the text color depends on the background color 3. But the effect of the text color depends on the background color. In other words, … Background Dark Light Text color Black Black *** Black **** White White *** White * < What I want: In terms of visibility, 1=3, 2 better than 4. And 2 better than 1 and 4 worse than 3. > To continue, click your keyboard’s right arrow button.

3. There is a background by text interaction. Dark Light Text color Black Black *** Black **** White White *** White * < > To continue, click your keyboard’s right arrow button.

Review of the terms Black text, on average, is better than white text. This would be described as An overall main effect for background. An overall main effect for text. A text by background interaction. A B C

Review of the terms 2. Dark background, on average, is better than light background. This would be described as An overall main effect for background. An overall main effect for text. A text by background interaction. A B C

Review of the terms 3. Depending on the background, black text may be more effective than white text. This would be described as An overall main effect for text. An overall main effect for background. A text by background interaction. A B C

Click on the calculation that would give you the simple main effect of background in the black text condition: Darkness of Background Dark Light Text color Black Black (A) Black (B) White White (C) White (D) Average of A-B and C- D A B A- B C - D C D A- C B - D Average of A-C and B- D

If the simple main effects of the same factor differ (as in the example below), there is an interaction. True False Background Dark Light Text color White White (A) White (B) Gray Gray (C) Gray (D) 5 4 1 Do a bunch of these 2 4 2 1 2

Quiz Click on the green arrow button to go to the quiz. Quiz Quit

To determine the overall main effect of line thickness, you would Take the difference between 5 and 4. Take the difference between 3 and 2. Take the difference between 4 and 2 and the difference. between 5 and 3, then average those differences. Take the difference between 5 and 4 and the difference between 3 and 2, then average those differences. Take the difference between 5 and 4 and 3 and 2, then subtract those differences. 4 Blue 5 Text Color 2 3 Green Thin Thick Line Thickness

4 5 2 3 To find the interaction between line thickness and color, Take the difference between 5 and 4. Take the difference between 3 and 2. Take the difference between 5 and 3. Take the difference between 5 and 4 and 3 and 2, then average those differences. If that average is significantly greater than zero, there is an interaction. Take the difference between 5 and 4 and the difference between 3 and 2, then subtract those two differences. Because that result is 0 (1-1 = 0), there is not an interaction. 4 Blue 5 Text Color 2 3 Green Thin Thick Line Thickness

Click on the calculation that would give you the overall main effect of text color: Darkness of Background Dark Light Text color Black Black (A) Black (B) White White (C) White (D) Average of A-B and C- D A B A- B Do a bunch of these C - D C D A- C B - D Average of A-C and B- D

Click on the calculation that would give you the overall main effect of background: Darkness of Background Dark Light Text color Black White Average of A-B and C- D A B A- B Do a bunch of these C - D C D A- C B - D Average of A-C and B- D

Darkness of Background If the two simple main effects for text color are the same (i.e., A-C = B-D), there is no interaction. True False Darkness of Background Dark Light Text color Black Black (A) Black (B) White White (C) White (D) Average of A-B and C- D A B A- B Do a bunch of these C - D C D A- C B - D Average of A-C and B- D

Darkness of Background If the two simple main effects of background are the same (i.e., A-B = C-D), there is no interaction. True False Darkness of Background Dark Light Text color Black Black (A) Black (B) White White (C) White (D) Average of A-B and C- D A B A- B Do a bunch of these C - D C D A- C B - D Average of A-C and B- D

If the simple main effects of 2 different factors differ (as in the example below), there is an interaction. True False Background Dark Light Text color White White (A) White (B) Gray Gray (C) Gray (D) 5 4 1 (A- B); (5-4) Do a bunch of these 1 (C – D); (3-2) 3 2 2 (A-C); (5-3) 2 (B-D); (4-2)

Overall background main effect If the overall main effects of 2 different factors differ (as in the example below), there is an interaction. True False Background Overall background main effect Dark Light Text color White Gray Overall text color main effect 5 4 1 Do a bunch of these 3 2 2

If the simple main effects of the same factor differ (as in the example below), there is an interaction. True False Background Dark Light Text color White White (A) White (B) Gray Gray (C) Gray (D) 5 4 1 (A- B); (5-4) Do a bunch of these 2(C – D); (4-2) 4 2 1 (A-C); (5-4) 2 (B-D); (4-2)

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