1. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Chapter Twelve: Designing, Conducting, Analyzing, and Interpreting Experiments with Multiple Independent Variables Chapter Twelve: Designing, Conducting, Analyzing, and Interpreting Experiments with Multiple Independent Variables

2. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Experimental Design: Doubling the Basic Building Block A factorial design gives us the power we need to devise an investigation of several factors ( IVs ) in a single experiment.

3. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Experimental Design: Doubling the Basic Building Block Factors Synonymous with IVs

4. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Experimental Design: Doubling the Basic Building Block Factors Synonymous with IVs Independent Variables (IVs) Stimuli or aspects of the environment that are directly manipulated by the experimenter to determine their influences on behavior.

5. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Experimental Design: Doubling the Basic Building Block Factorial designs are the lifeblood of experimental psychology because they allow us to look at combinations of IVs at the same time, a situation that is quite similar to the real world.

6. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Experimental Design: Doubling the Basic Building Block Factorial designs are the lifeblood of experimental psychology because they allow us to look at combinations of IVs at the same time, a situation that is quite similar to the real world. A factorial design is more like the real world because there are probably few, if any, situations in which your behavior is affected by only a single factor at a time.

7. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education How Many IVs? The factorial design gets its name because we refer to each IV as a factor. Multiple IVs yield a factorial design.

8. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education How Many IVs? The factorial design gets its name because we refer to each IV as a factor. Multiple IVs yield a factorial design. Theoretically, there is no limit to the number of IVs that can be used in an experiment. Practically speaking, however, it is unlikely that you would want to design an experiment with more than two or three IVs.

9. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education How many Groups or Levels? Once you have two or more IVs, you will use a factorial design. The number of levels of each factor is unimportant at this point.

10. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education How many Groups or Levels? The simplest possible factorial design is known as a 2 X 2 design. This 2 X 2 shorthand notation tells us that we are dealing with a design that has two factors (IVs) because there are two digits given and that each of the two factors has two levels because each digit shown is a two.

11. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education How many Groups or Levels? The number of numbers tells us how many IVs there are. The value of each number tells us how many levels each IV has.

12. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education How many Groups or Levels? Various factors are often designated by letters, so the first factor is labeled Factor A, the second as Factor B, and so on.

13. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education How many Groups or Levels? Various factors are often designated by letters, so the first factor is labeled Factor A, the second as Factor B, and so on. The levels within a factor are often designated by the letter that corresponds to the factor and a number to differentiate the different levels. Thus, the two levels within the first factor would be labeled A1 (A sub 1) and A2 (A sub 2).

14. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education How many Groups or Levels? Main Effect A main effect refers to the sole effect of one IV in a factorial design.

15. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Assigning Participants to Groups We have two options for this assignment – independent groups or correlated groups.

16. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Assigning Participants to Groups We have two options for this assignment – independent groups or correlated groups. However, this question is not answered in such a simple manner as in the two-group and multiple-group designs, each of which had only one IV. All IVs could have participants assigned randomly or in a correlated fashion, or we could have one IV with independent groups and one IV with correlated groups. This possibility is referred to as mixed assignment.

17. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Assigning Participants to Groups Mixed Assignment A factorial design that has a mixture of independent groups for one IV and correlated groups for another IV. In larger factorial designs, at least one IV has independent groups and at least one has correlated groups (also known as mixed groups ).

18. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Random Assignment to Groups Factorial designs in which both IVs involve random assignment may be called between-subjects factorial designs or completely randomized designs Random Assignment to Groups

19. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Nonrandom Assignment to Groups In this section, we deal with factorial designs in which participant groups for all IVs have been formed through nonrandom assignment.

20. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Nonrandom Assignment to Groups In this section, we deal with factorial designs in which participant groups for all IVs have been formed through nonrandom assignment. We refer to such designs as completely within-groups (or within- subjects) designs.

21. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Nonrandom Assignment to Groups In this section, we deal with factorial designs in which participant groups for all IVs have been formed through nonrandom assignment. We refer to such designs as completely within-groups (or within- subjects) designs. We may want to resort to nonrandom assignment in order to assure the equality of participant groups before we conduct the experiment.

22. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Nonrandom Assignment to Groups Matched Pairs or Sets Matching can take place in either pairs or sets because factorial designs can use IVs with two or more levels.

23. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Nonrandom Assignment to Groups Matched Pairs or Sets Matching can take place in either pairs or sets because factorial designs can use IVs with two or more levels. The more levels an IV has, the more work matching for that variable takes.

24. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Nonrandom Assignment to Groups Matched Pairs or Sets Matching can take place in either pairs or sets because factorial designs can use IVs with two or more levels. The more levels an IV has, the more work matching for that variable takes. The more precise the match that is necessary, the more difficult matching becomes.

25. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Nonrandom Assignment to Groups Repeated Measures In a completely within-groups experiment using repeated measures, participants would take part fully and completely. Participants take part in every possible treatment combination.

26. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Nonrandom Assignment to Groups Repeated Measures In a completely within-groups experiment using repeated measures, participants would take part fully and completely. Participants take part in every possible treatment combination. This requirement makes it difficult or impossible to conduct an experiment with repeated measures on multiple IVs. The smaller the design, the more feasible it is to include all participants in all conditions of the experiment.

27. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Nonrandom Assignment to Groups Natural Pairs or Sets Using natural groups in a totally within-subjects design has the same difficulties as the matched pairs or sets variation of this design, but it would be even harder. The difficulty lies in being able to find an adequate number of naturally linked participants.

28. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Nonrandom Assignment to Groups Mixed Assignment to Groups Mixed assignment designs involve a combination of random and nonrandom assignment, with at least one IV using each type of assignment to groups.

29. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Nonrandom Assignment to Groups Mixed Assignment to Groups Mixed assignment designs involve a combination of random and nonrandom assignment, with at least one IV using each type of assignment to groups. In a two-IV factorial design, mixed assignment involves one IV with random assignment and one IV with nonrandom assignment. In such designs, the use of repeated measures is probably more likely than other types of nonrandom assignment.

30. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Nonrandom Assignment to Groups Mixed Assignment to Groups Mixed assignment designs involve a combination of random and nonrandom assignment, with at least one IV using each type of assignment to groups. Mixed designs combine the advantages of the two types of designs.

31. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Nonrandom Assignment to Groups Mixed Assignment to Groups Mixed assignment designs involve a combination of random and nonrandom assignment, with at least one IV using each type of assignment to groups. Mixed designs combine the advantages of the two types of designs. The conservation of participants through the use of repeated measures for a between-subjects variable makes for a popular and powerful design.

32. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Comparing the Factorial Design to Two-Group and Multiple- Group Designs Two-group designs are ideal for a preliminary investigation of a particular IV in a presence-absence format. In a similar fashion, 2 X 2 factorial designs may be used for preliminary investigations of two IVs.

33. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Comparing the Factorial Design to Two-Group and Multiple- Group Designs The multiple-group design may be used to conduct more in- depth investigations of an IV that interests us. We took the basic two-group design and extended it to include more levels of our IV. We can make the same type of extension with factorial designs.

34. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Comparing the Factorial Design to Two-Group and Multiple- Group Designs The multiple-group design may be used to conduct more in- depth investigations of an IV that interests us. We took the basic two-group design and extended it to include more levels of our IV. We can make the same type of extension with factorial designs. Just as with the multiple-group design, there is no limit to the number of levels for any IV in a factorial design. The number of levels of the IVs can be equal or unequal.

35. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Comparing the Factorial Design to Two-Group and Multiple- Group Designs The multiple-group design may be used to conduct more in- depth investigations of an IV that interests us. We took the basic two-group design and extended it to include more levels of our IV. We can make the same type of extension with factorial designs. Just as with the multiple-group design, there is no limit to the number of levels for any IV in a factorial design. Interaction effects must be interpreted in factorial designs but not in two-group or multiple-group designs.

36. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Comparing the Factorial Design to Two-Group and Multiple- Group Designs The multiple-group design may be used to conduct more in- depth investigations of an IV that interests us. We took the basic two-group design and extended it to include more levels of our IV. We can make the same type of extension with factorial designs. Just as with the multiple-group design, there is no limit to the number of levels for any IV in a factorial design. Interaction effects must be interpreted in factorial designs but not in two-group or multiple-group designs. A good rule of thumb to follow is to choose the simplest research design that will adequately test your hypothesis.

37. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Choosing a Factorial Design Experimental Questions

38. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Experimental Questions Factorial designs provide considerable flexibility in devising an experiment to answer your questions.

39. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Experimental Questions Factorial designs provide considerable flexibility in devising an experiment to answer your questions. The number of questions we can ask in a factorial experiment increases dramatically, but….

40. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Experimental Questions Factorial designs provide considerable flexibility in devising an experiment to answer your questions. The number of questions we can ask in a factorial experiment increases dramatically, but…. When we ask additional questions, we must make certain that the questions coordinate with each other…experimental questions should not clash. (e.g., it would not make sense to propose an experiment to examine the effects of self-esteem and eye color on test performance)

41. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Control Issues We need to consider independent versus correlated groups in factorial designs. A complicating factor for factorial designs is that we need to make this decision (independent vs. correlated groups) for each IV we include in an experiment.

42. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Practical Considerations You are well advised to keep your experiment at the bare minimum necessary to answer the question(s) that most interest(s) you. Bear in mind that you are complicating matters when you add IVs and levels.

43. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Variations on Factorial Designs Comparing Different Amounts of an IV

44. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Variations on Factorial Designs Comparing Different Amounts of an IV When you add a level to an IV in a factorial design, you add several groups to your experiment because each new level must be added under each level of your other independent variable(s).

45. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Comparing Different Amounts of an IV When you add a level to an IV in a factorial design, you add several groups to your experiment because each new level must be added under each level of your other independent variable(s). For example, expanding a 2 X 2 to a 3 X 2 design requires six groups rather than four. Adding levels in a factorial design increases groups in a multiplicative fashion.

46. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Using Measured IVs Using a measured rather than a manipulated IV results in ex post facto research. A research approach in which the experimenter cannot directly manipulate the IV but can only classify, categorize, or measure the IV because it is predetermined in the participants (e.g., IV = sex).

47. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Using Measured IVs Using a measured rather than a manipulated IV results in ex post facto research. Without the control that comes from directly causing an IV to vary, we must exercise extreme caution in drawing conclusions from such studies.

48. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Using Measured IVs Using a measured rather than a manipulated IV results in ex post facto research. Without the control that comes from directly causing an IV to vary, we must exercise extreme caution in drawing conclusions from such studies. We can develop an experiment that uses one manipulated IV and one measured IV at the same time.

49. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Dealing with More than Two IVs Designing an experiment with more than two IVs is probably the most important variation of the factorial design.

50. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Dealing with More than Two IVs The simplest possible factorial design with three IVs (often referred to as a three-way design ) has three IVs, each with two levels. This design represents a 2 X 2 X 2 experiment. This design would require eight different groups if it is planned as a completely between-groups design.

51. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Statistical Analysis: What Do Your Data Show? Naming Factorial Designs Labels you may hear that reflect the size of the design include:

52. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Statistical Analysis: What Do Your Data Show? Naming Factorial Designs Labels you may hear that reflect the size of the design include: Factorial ANOVA Two-way ANOVA Three-way ANOVA X by Y

53. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Naming Factorial Designs For designs that use random assignment for all IVs, labels that describe how participants are assigned to groups might include:

54. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Naming Factorial Designs For designs that use random assignment for all IVs, labels that describe how participants are assigned to groups might include: Independent groups Completely randomized Completely between-subjects Completely between-groups Totally between-subjects Totally between-groups

55. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Naming Factorial Designs Designs that use matching or repeated measures may be called: Randomized block Completely within-subjects Completely within-groups Totally within-subjects Totally within-groups

56. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Naming Factorial Designs Designs that use a mixture of “between” and “within” assignment procedures may be referred to as:

57. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Naming Factorial Designs Designs that use a mixture of “between” and “within” assignment procedures may be referred to as: Mixed factorial Split-plot factorial

58. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Planning the Statistical Analysis Suppose you are examining the data from the previous (Chapter 11) experiment and you think you detected an oddity in the data: It appears that salesclerks may have responded differently to female and male customers in addition to the different styles of dress.

59. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Planning the Statistical Analysis You decide to investigate this question in order to find out whether both customer sex and dress affect salesclerks’ response times to customers. Because there was no difference between responses to customers in dressy and casual clothing (see Chapter 11), you decide to use only casual and sloppy clothes.

60. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Planning the Statistical Analysis Thus, you have designed a 2 X 2 experiment in which the two IVs are clothing style (casual and sloppy) and customer sex (male and female).

61. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Rationale of Factorial ANOVA The rationale behind ANOVA for factorial designs is basically the same as we saw in Chapter 11, with one major modification. We still use ANOVA to partition (divide) the variability into two sources – treatment variability and error variability.

62. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Rationale of Factorial ANOVA With factorial designs, the sources of treatment variability increase. Instead of having one IV as the sole source of treatment variability, factorial designs have multiple IVs and their interactions as sources of treatment variability. The actual distribution of the variance among the factors would depend, of course, on which effects were significant.

63. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Rationale of Factorial ANOVA For a two-IV factorial design we use the following equations: Factor A = IV A variability error variability

64. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Rationale of Factorial ANOVA For a two-IV factorial design we use the following equations: Factor B = IV B variability error variability

65. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Rationale of Factorial ANOVA For a two-IV factorial design we use the following equations: Factor A by B = interaction variability error variability

66. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Understanding Interactions When two variables interact, their joint effect may not be obvious or predictable from examining their separate effects. For example, drinking a glass or two of wine may be a pleasurable and relaxing experience and driving may be a pleasurable and relaxing experience but is drinking wine and driving an extremely pleasurable and relaxing experience?

67. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Understanding Interactions When two variables interact, their joint effect may not be obvious or predictable from examining their separate effects. Combinations of drugs, in particular, are likely to have synergistic effects so that a joint effect occurs that is not predictable from either drug alone.

68. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Understanding Interactions Synergistic Effects Dramatic consequences that occur when you combine two or more substances, conditions, or organisms. The effects are greater than what is individually possible.

69. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Understanding Interactions A significant interaction means that the effects of the various IV’s are not straightforward and simple. For this reason, we virtually ignore our IV main effects when we find a significant interaction. Sometimes interactions are difficult to interpret, particularly when we have more than two IVs or many levels of an IV.

70. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Understanding Interactions A strategy that often helps us to make sense of an interaction is to graph it. By graphing your DV on the y axis and one IV on the x axis, you can depict your other IV with lines on the graph (see Chapter 9). By studying such a graph, you can usually deduce what happened to cause a significant interaction.

71. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Understanding Interactions When you graph a significant interaction, you will often notice that the lines of the graph cross or converge. This pattern is a visual indication that the effects of one IV change as the second IV is varied.

72. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Understanding Interactions When you graph a significant interaction, you will often notice that the lines of the graph cross or converge. This pattern is a visual indication that the effects of one IV change as the second IV is varied. Nonsignificant interactions typically show lines that are close to parallel. Remember: an interaction is present when the effects of one IV depends on the specific level of the other IV

73. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Interpretation: Making Sense of Your Statistics Our statistical analyses of factorial designs will provide us more information than we got from two-group or multiple-group designs. The analyses are not necessarily more complicated than those we saw in Chapters 10 and 11, but they do provide more information because we have multiple IVs and interaction effects to analyze.

74. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Interpreting Computer Statistical Output We will deal with 2 X 2 analyses in these three different categories to fit our clothing-by-customer-sex experiment: Two-way ANOVA for independent samples Two-way ANOVA for correlated samples Two-way ANOVA for mixed samples

75. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Two-Way ANOVA for Independent Samples The two-way ANOVA for independent samples requires that we have two IVs (clothing style and customer sex) with independent groups.

76. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Two-Way ANOVA for Independent Samples The two-way ANOVA for independent samples requires that we have two IVs (clothing style and customer sex) with independent groups. To create this design we would use four different randomly assigned groups of salesclerks.

77. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Two-Way ANOVA for Independent Samples The two-way ANOVA for independent samples requires that we have two IVs (clothing style and customer sex) with independent groups. To create this design we would use four different randomly assigned groups of salesclerks. The DV scores represent clerks’ response times in waiting on customers.

78. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Two-Way ANOVA for Independent Samples Source Table In the body of the source table, we want to examine only the effects of the two IVs (clothing and customer sex) and their interaction. The remaining source (w. cell or Within) is the error term and is used to test the IV effects. Different statistical programs will use a variety of different names for the error term.

79. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Two-Way ANOVA for Independent Samples Source Table The effect of sex shows an F ratio of 3.70, with a probability of.07. This IV shows marginal significance.

80. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Two-Way ANOVA for Independent Samples Marginal Significance Marginal significance refers to statistical results with a probability of chance between 5% and 10% (almost significant but not quite). Researchers often talk about such results as if they reached the p =.05 level. Dealing with marginally significant results means you run an increased risk of making a Type I error (accepting the experimental hypothesis when the null hypothesis is true).

81. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Two-Way ANOVA for Independent Samples Source Table The effect of sex shows an F ratio of 3.70, with a probability of.07. This IV shows marginal significance. The probability of “clothes” falls below.01 in the table. The interaction between clothing and customer sex produced an F ratio of 6.65 and has p =.02, therefore denoting significance.

82. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Two-Way ANOVA for Independent Samples Source Table A significant interaction renders the main effects moot because those main effects are qualified by the interaction and are not straightforward.

83. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Two-Way ANOVA for Independent Samples Source Table A significant interaction renders the main effects moot because those main effects are qualified by the interaction and are not straightforward. The first step in interpreting an interaction is to draw a graph of the results from the descriptive statistics (from source table).

84. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Two-Way ANOVA for Independent Samples Crossing lines, in conjunction with the low probability of chance for the interaction term, denote a significant interaction. When we examine the figure, the point that seems to differ most represents the clerks’ response times to male customers in sloppy clothes. This mean is considerably higher than the others.

85. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Two-Way ANOVA for Independent Samples Thus, we would conclude that clerks take longer to wait on men who are sloppily dressed than other customers. Notice that our explanation of an interaction effect must include a reference to both IVs in order to make sense.

86. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Two-Way ANOVA for Independent Samples If you attempt to interpret the main effects in a straightforward fashion when you have a significant interaction, you end up trying to make a gray situation into a black-and-white picture. In other words, you will be guilty of oversimplifying the results.

87. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Two-Way ANOVA for Independent Samples Here is one way you could present the results from this experiment: The effect of the clothing on the clerks’ response times was significant, F(1, 20) = 11.92, p =.003. The customer sex effect was marginally significant, F(1, 20) = 3.70, p =.069. However, the main effects were qualified by a significant interaction between clothing and customer sex, F(1, 20) = 6.65, p =.018. The proportion of the variance accounted for by the interaction was 0.25. The results of the interaction are graphed in Figure 1. Visual inspection of the graph shows that clerks’ response times for the sloppy clothes- male customer condition were higher than the other conditions.

88. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Two-Way ANOVA for Correlated Samples The two-way ANOVA for correlated samples requires that we have two IV’s with correlated groups for both IVs. Most often these correlated groups would be formed by matching or by using repeated measures.

89. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Two-Way ANOVA for Correlated Samples In our example of the clothing-customer sex experiment, repeated measures on both IVs would be appropriate. We would merely get one sample of salesclerks and have them wait on customers of both sexes wearing each style of clothing.

90. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Two-Way ANOVA for Correlated Samples Computer Results The clothing effect is significant at the.001 level and the sex effect is significant at the.014 level. However, both main effects are qualified by the significant clothing-by-sex interaction (p = 0.001). To make sense of the interaction, we must plot the means for the combinations of clothing and customer sex.

91. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Two-Way ANOVA for Correlated Samples One possible way of summarizing these results follows: Both the main effects of clothing and customer sex were significant, F(1, 5) = 24.69, p =.001 and F(1, 5) = 7.66, p =.014, respectively. However, the interaction of clothing and customer sex was also significant, F(1, 5) = 13.77, p =.001. The proportion of variance accounted for by the interaction was.48. This interaction appears in Figure 1. Salesclerks waiting on sloppily attired male customers were considerably slower than clerks with any other combination of customer sex and clothing. You would provide a fuller explanation and interpretation of this interaction in the discussion section of your experimental report.

92. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Two-Way ANOVA for Mixed Samples The two-way ANOVA for mixed samples requires that we have two IVs with independent groups for one IV and correlated groups for the second IV.

93. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Two-Way ANOVA for Mixed Samples The two-way ANOVA for mixed samples requires that we have two IVs with independent groups for one IV and correlated groups for the second IV. One possible way to create this design in our clothing-customer sex experiment would be to use a different randomly assigned group of salesclerks for each customer sex. Clerks waiting on each sex, however, would assist customers attired in both types of clothing.

94. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Two-Way ANOVA for Mixed Samples Computer Results Once again, the descriptive statistics did not change from our first and second analysis. We are still analyzing the same data.

95. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Two-Way ANOVA for Mixed Samples Source Table The source table appears at the bottom of Table 12-4 in your text. As you can see from the headings, the between-subjects effects (independent groups) and the within-subjects effects (repeated measures) are divided in the source table.

96. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Two-Way ANOVA for Mixed Samples Source Table This division is necessary because the between-subjects effects and the within-subjects effects use different error terms. The interaction appears in the within-subjects portion of the table because it involves repeated measures across one of the variables involved.

97. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Two-Way ANOVA for Mixed Samples Here’s one possibility for communicating the results of this study in APA format: Results from the mixed factorial ANOVA showed no effect on the customer sex, F(1, 10) = 2.42, p =.15. The clothing effect was significant, F(1, 10) = 25.21, p =.001. This main effect, however, was qualified by a significant customer-sex-by-clothing interaction, F(1, 10) = 14.06, p =.004. The proportion of variance accounted for by the significant interaction was.58. This interaction is shown in Figure 1, indicating that salesclerks who waited on sloppily dressed male customers were slower in responding than clerks who waited on casually dressed men or women dressed in either manner.

98. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education A Final Note Assuming that a significant main effect is not qualified by an interaction, you need to calculate a set of post hoc tests to determine exactly where the significance of that IV occurred.

99. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education The Continuing Research Problem Pursuing a line of programmatic research is challenging, invigorating, and interesting. Programmatic research refers to a series of experiments that deal with a related topic or question. Remember that pursuing such a line of research is how most famous psychologists have made names for themselves.

100. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education The Continuing Research Problem Let’s review the steps we took in designing the experiments in this chapter: After our preliminary research in Chapters 10 and 11, we decided to use two IVs (clothing and customer sex) in these experiments.

101. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education The Continuing Research Problem Let’s review the steps we took in designing the experiments in this chapter: After our preliminary research in Chapters 10 and 11, we decided to use two IVs (clothing and customer sex) in these experiments. Each IV had two levels (clothing  casual, sloppy; customer sex  men, women).

102. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education The Continuing Research Problem Let’s review the steps we took in designing the experiments in this chapter: After our preliminary research in Chapters 10 and 11, we decided to use two IVs (clothing and customer sex) in these experiments. Each IV had two levels (clothing  casual, sloppy; customer sex  men, women). This design allows us to determine the effects of the clothing, the effects of the customer sex, and the interaction between clothing and customer sex.

103. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education The Continuing Research Problem Let’s review the steps we took in designing the experiments in this chapter: The DV was the time it took salesclerks to respond to customers.

104. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education The Continuing Research Problem Let’s review the steps we took in designing the experiments in this chapter: With large numbers of clerks, we randomly formed four groups of clerks, with each waiting on one sex of customer in one type of clothing, resulting in a factorial between-groups design. We analyzed the response times using a factorial ANOVA for independent groups and found that clerks were slower to wait on male customers in sloppy clothing than all other customers.

105. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education The Continuing Research Problem Let’s review the steps we took in designing the experiments in this chapter: In a hypothetical situation with fewer clerks for the experiment, we used repeated measures on both IVs; that is, each salesclerk waited on both sexes of customers attired in both types of clothing, so that each clerk waited on four different customers. Thus, this experiment used a factorial within-groups design. We analyzed the data with a factorial ANOVA for correlated groups and found that clerks were slowest in waiting on sloppily dressed men.

106. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education The Continuing Research Problem Let’s review the steps we took in designing the experiments in this chapter: In a third hypothetical situation, we randomly assigned salesclerks to the two customer sex groups but used repeated measures on the clothing IV so that clerks waited either on men in both types of clothing or women in both types of clothing.

107. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education The Continuing Research Problem Let’s review the steps we took in designing the experiments in this chapter: In a third hypothetical situation, we randomly assigned salesclerks to the two customer sex groups but used repeated measures on the clothing IV so that clerks waited either on men in both types of clothing or women in both types of clothing. This arrangement resulted in a factorial mixed-groups design (one IV using independent groups, one using correlated groups).

108. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education The Continuing Research Problem Let’s review the steps we took in designing the experiments in this chapter: In a third hypothetical situation, we randomly assigned salesclerks to the two customer sex groups but used repeated measures on the clothing IV so that clerks waited either on men in both types of clothing or women in both types of clothing. This arrangement resulted in a factorial mixed-groups design (one IV using independent groups, one using correlated groups). We analyzed the response times with a factorial ANOVA for mixed groups and found the slowest response times to male customers in sloppy clothes (see Table 12-4 and Figure 12-13).

109. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education The Continuing Research Problem Let’s review the steps we took in designing the experiments in this chapter: We concluded that clothing and customer sex interacted to affect salesclerks’ response times.

110. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education The Continuing Research Problem Let’s review the steps we took in designing the experiments in this chapter: We concluded that clothing and customer sex interacted to affect salesclerks’ response times. Women received help quickly regardless of their attire, but men received help quickly only if they were not sloppily dressed.

111. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education The Continuing Research Problem Let’s review the steps we took in designing the experiments in this chapter: We concluded that clothing and customer sex interacted to affect salesclerks’ response times. Women received help quickly regardless of their attire, but men received help quickly only if they were not sloppily dressed. Men attired in sloppy clothes had to wait longer for help than the other three groups.