1. How to Start This PowerPoint® Tutorial
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2. 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.
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© 2016 Mark Mitchell & Janina Jolley

3. 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.

4. 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.

5. 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

6. 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

7. 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.

8. 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

9. 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

10. 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
<
>

11. 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 * =
>

12. 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 *
<
>

13. 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.

14. 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 **
***
<
>

15. 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
******
*****
<<
>>>
>

16. > 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
****
>

17. = 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 * =

18. **** 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
***

19. **** 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
*** *

20. 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

21. 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
* * *
* *
>

22. ≠ 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 *
**|**

23. 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
***
***
*** *
***
*** *
*** **

24. 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.

25. 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.

26. 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

27. 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

28. 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 *
<
>

29. 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.

30. 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.

31. 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 **
****

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

33. 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
***

34. 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 *
<<
>>>

35. 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
***
***
*** * **

36. 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 *
<<
>>>

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

38. 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 *
<<
>>>

39. 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

40. 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 *
<

41. 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) =
***
*** *
***

42. 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) =
***
*** * **

43. 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 =
***
*** * **

44. 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
***
***
*** * **

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

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

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

48. 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
***
***
*** * **

49. 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
***
***
*** * **

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

51. 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
***
***
*** * **

52. 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
***
***
*** *

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

54. 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 = =
***
***
***
>> * ** ** ** *

55. 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
***
***
*** * **

56. 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.

57. 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.

58. 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.

59. 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.

60. 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.

61. 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.

62. 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.

63. 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.

64. 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.

65. 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

66. 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

67. 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

68. 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

69. 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

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

71. 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

72. 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

73. 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

74. 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

75. 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

76. 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

77. 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)

78. 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

79. 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)

80. Get your results