Factorial Designs. Outline. Definition. Factorial designs. Factorial designs. Higher order interactions

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1 1 Factorial Designs Outline 2 Factorial designs Conditions vs. levels Naming Why use them Main effects Interactions Simple main effect Graphical definition Additivity definition Factorial designs Independent samples Repeated measures Mixed Higher order interactions Definition 3 Condition one level of each IV paired together A factorial design has at least two IVs has all possible conditions IV # 1 Level 1 Level 2 Level 3 IV # 2 Level 1 Level 2 1

2 Factorial Example 4 A person acts as if he has a heart attack this happens in front of either 1, 3, or 5 other people the person can appear either drunk or elderly The time it takes for one of the people to summon help is recorded Factorial Example 5 What conditions were used? 1., 1 other person 2., 3 other people 3., 5 other people 4., 1 other person 5., 3 other people 6., 5 other people If all conditions are present, the study is a factorial design. What Conditions Are Used? 6 What are the conditions in the following factorial design? Factor#1 Males vs. females IV#2 Pictures of clothing vs. cars 2

3 Naming of Factorial Designs 7 Factorial designs are given a name which tells how many IVs are being used and the number of levels of each IV m X n X o X m = number of levels of first IV n = number of levels of second IV What is the name of the number of bystanders (1 vs. 3 vs. 5) and appearance (drunk vs. elderly) study? What is the name of the sex (male vs. female) and object (car vs. clothing) study? Number of Conditions 8 How many conditions are their in an m X n X o X design? Do the multiplication! The number of conditions in the number of bystanders (1 vs. 3 vs. 5) and appearance (drunk vs. elderly) study is 3 X 2 = 6 How many conditions are their in the sex (male vs. female) and object (car vs. clothing) study? X Why Use a Factorial Design? 9 Researchers often want to know if more than one IV influences the DV Is helping behavior influenced by the number of bystanders? Is helping behavior influenced by the appearance of the person needing help? The effect of each individual IV on the DV is called a main effect There can be as many main effects as there are IVs 3

4 Main Effects 1 A main effect occurs when the value of a DV is sufficiently different for different levels of an IV H : = 1 = = m H 1 : not H Main effects are worded with a single IV As the number of bystanders increases, the time to help increases People are more quick to help when a person appears elderly as compared to appearing drunk Main Effects 11 A main effect occurs if the average value of the DV for all the conditions at one level of an IV is sufficiently different from the average value of the DV for all the conditions at some other level of the IV The following example assumes equal sample size in each condition Balanced designs are good! Main Effects 12 # of bystanders Appearance Mean Effect -1 The effect tells us that when we move from the drunk level to the elderly level, there is, on average, a 1 second decrement in the time it takes someone to help 4

5 Main Effects 13 The larger the effect is, the more likely the main effect is to be statistically significant Main Effects 14 Appearance Mean Effect # of bystanders Mean Effect -1 Main Effects 15 The effect tells us that when we move from the 1 bystander level to the 5 bystanders level, there is, on average, a second increment in the time it takes someone to help 5

6 Main Effects 16 Main effects can be estimated graphically Find the mean value of all conditions at each level of an IV The more different the means are, the more likely the main effect is statistically reliable The following example assumes equal sample sizes in each condition Time to Help (s) # of Bystanders Main Effect of # of Bystanders 17 Find the mean value of all conditions at each level of an IV Mean value of 1 bystander = ( + 15) / 2 = 17.5 Mean value of 3 bystanders = ( ) / 2 = Mean value of 5 bystanders = (35 + 1) / 2 = 22.5 Time to Help (s) # of Bystanders Main Effects 18 The more different the means are from each other, the more likely the main effect is to be statistically reliable and the more likely there is to be a main effect of the number of bystanders Time to Help (s) # of Bystanders 6

7 Cats Dogs Dogs Cats Main Effect of Appearance 19 Find the mean value of all conditions at each level of an IV Mean value of elderly = ( ) / 3 = 15 Mean value of drunk = ( ) / 3 = 25 Time to Help (s) The more different the means are from each other (15 vs 25), the more likely there is to be a main effect of appearance # of Bystanders Are Main Effects Likely? # of Items Retrieved Recognition Recall Low High Word Frequency Liking Rating Introvert Personality Extravert Why Use a Factorial Design? 21 The hypothesized existence of a main effect is not a sufficient reason to use a factorial design We could perform two, single factor studies, one with one of the IVs and the other with the other IV 7

8 Why Use a Factorial Design? 22 Factorial designs also tell us whether the effect of each IV on the DV is independent of the effects of the other IVs Does the effect of the number of bystanders depend on the appearance of the person who needs help? Such an effect is called an interaction effect H : There is no interaction H 1 : There is an interaction Interactions 23 Interactions are important because they tell us that we cannot generalize our results to all situations the effect of one IV depends on the level of another IV limit our ability to make simple statements main effects do not fully describe the effect Definitions of Interactions 24 An interaction occurs when the simple main effect of an IV depend on the level of one or more other IVs the lines on a graph of the results of an experiment are not statistically parallel the effect of two or more IVs are not additive All three definitions are logically equivalent to each other 8

9 Definition of Interaction 25 The simple main effect of an IV depends on the level of one or more other IVs If no interaction exists: As the number of bystanders increases, helping behavior decreases If an interaction exists: As the number of bystanders increases, helping behavior decreases if the person appears drunk, otherwise it increases if the person appears elderly Examples 26 Is an interaction likely? High frequency words are easier to recall than low frequency words. Low frequency words are easier to recognize than high frequency words Relative to silence, listening to Mozart improves spatial abilities equally in both men and women People who wear thick glasses are more introverted than people who do not wear glasses, but this is true only if the person is less than 25 years of age Definitions of Interaction 27 An interaction occurs when the lines on a graph of the results of an experiment are not statistically parallel The greater the difference in the slopes of the lines, the more likely the interaction is present Time to Help (s) # of Bystanders 9

10 Examples 28 Are interactions likely? 8 8 Time to Help (s) 6 4 Time to Help (s) # of Bystanders # of Bystanders Definitions of Interaction 29 An interaction occurs when the effect of two or more IVs are not additive That is, you cannot add the simple effects of each IV together to predict what will happen when both treatments are simultaneously present Definitions of Interaction 3 Appearance Mean Effect # of bystanders Mean Effect

11 Are the Effects Additive? 31 If the effects of the IVs are additive, we should be able to predict the mean value of n - 1 conditions given the effect sizes and 1 condition n = number of conditions Factorial Designs 32 Factorial designs can occur in three varieties Independent samples designs Repeated measures designs Mixed designs Independent Samples, Factorial Designs 33 An independent samples, factorial design has all of its IVs manipulated as independent samples IVs each person participates in a single condition 1 Person 5 People 11

12 Independent Samples, Factorial Designs 34 Independent samples designs should be used when sequence effects are likely to occur in all IVs eliminate the possibility of carry-over effects have low statistical power hard to reject H when H is false can be offset by increasing sample size must have block random assignment or matching for all IVs Repeated Measures, Factorial Designs 35 A repeated measures, factorial design has all of its IVs manipulated as repeated measures IVs each person participates in every condition 1 Person 5 People Repeated Measures, Factorial Designs 36 Repeated measures designs should be used when sequence effects are not likely to occur in any IV have high statistical power easier to reject H when H is false can have a smaller sample size must have counterbalancing for all IVs 12

13 Mixed, Factorial Designs 37 A mixed, factorial design has at least one of its IVs manipulated as an independent samples IV and at least one IV manipulated as a repeated measures IV each person participates in all levels of the repeated measures IVs, but only one level of the independent samples IV 1 Person 5 People Mixed Factorial Designs 38 Mixed designs should be used when sequence effects are likely to occur in some, but not all IVs IVs with potential sequence effects are made independent samples IVs, and IVs with little potential of sequence effects are made repeated measures IVs have intermediate statistical power must have counterbalancing for all repeated measures IVs must have block random assignment or matching for all independent samples IVs More Than Two IVs 39 When there are more than two IVs in an experiment, there can be As many main effects as there are IVs Multiple two way interactions Two way interaction = interaction of two IVs One or more higher order interaction(s) Higher order interaction = interactions of n 1 IVs are different at different levels of n th IV n!/(r! (n r)!) n = number of IVs r = level of interaction 13

14 More Than Two IVs 4 Number of IVs # of 2 Way Interactions # of 3 Way Interactions # of 4 Way Interactions # of 5 Way Interactions # of 6 Way Interactions No 3 Way Interaction 41 3 Way Interaction 42 14

15 Abstract 43 The APA abstract is a summary of the entire manuscript Problem under investigation Brief description of participants Essential methodology Basic findings Conclusions Abstract 44 Always page 2 Level 1 heading Abstract Written as a single paragraph Never indented Word count limit 15 for us Keywords: centered at bottom, followed by keywords for the manuscript 15