PSYC 381 Statistics Arlo Clark-Foos, Ph.D.

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1 One-Way Within- Groups ANOVA PSYC 381 Statistics Arlo Clark-Foos, Ph.D.

2 Comparing Designs Pros of Between No order or carryover effects Between-Groups Design Pros of Within More costly Higher variability between groups than within (i.e., individual differences)

3 Used A Lot in Market Research! Taste Tests Odor Tests

4 Within Groups Designs What about order/carryover effects? Counterbalance! All participants experience all conditions/treatments/levels

5 Counterbalancing Minimization of order effects by varying the order of presentation of different levels of the independent variable from one participant (or group) to the next. An example of a counterbalanced within-subjects design with 3 conditions: 3 Conditions/Levels of IV 3! = 3 x 2 x 1 = 6 orders What if your IV had more levels? Example: IV = Year in School (4 levels) 4 x 3 x 2 x 1 = 24 orders!! You need a Latin Square Design!

6 Latin Square Design A technique to control for order effects without having all possible orders. A limited set of orders is constructed to ensure that (1) each condition appears at each ordinal position and (2) each condition precedes and follows each condition one time.

7 Within Groups ANOVA New Terminology SS Subjects df Subjects n A few new formulas (along with the old ones)

8 An Example with Beer! Do you have a love of lagers? A journalist (Fallows, 1999) wanted to know if self-proclaimed beer snobs would be able to distinguish between three classes/qualties of beers. There are over 50+ styles of beer, many of which are not available in lower quality versions so he chose lagers because of their widespread availability. The results below are their taste ratings for each beer. Cheap Beers e.g., Mid-Range Beers e.g., Budweise High-End Beers e.g.,

9 One-Way Within Groups ANOVA: Beer Taste Testing Six Steps to Hypothesis Testing 1. Identify the populations, 1. People who drink cheap beer 2. People who drink mid-range beer 3. People who drink high-range beer Distribution, F distribution (>2 groups) One-Way Within-Groups ANOVA Assumptions 1. Participants not selected randomly, careful generalizing 2. Data do not appear skewed 3. Homoscedasticity it [(largest variance) ) (2 x smallest variance)] 4. Are there order effects? Not counterbalanced

10 One-Way Within Groups ANOVA: Beer Taste Testing 2. State null and research hypotheses Null: People who drink cheap, mid-range, and high-end beer rate their beers the same, on average. Research: People who drink cheap, mid-range, and high-end beer do not rate their beers the same, on average.

11 One-Way Within Groups ANOVA: Beer Taste Testing 3. Determine characteristics of comparison distribution df Within ( df )( df ) = ( 2 )( 4) = 8 = Between Subjects df N 1 = 3 1 = 2 = n 1 = 5 1 = 4 f f Subjects 14 Between = Groups df Subjects df Total = df Between + df Subjects + dfwithin = = df Total = N Total or 1 = 15 1 = 14

12 One-Way Within Groups ANOVA: Beer Taste Testing 4. Determine the critical values or cutoffs (p = 05). df Between = 2 df Within = 8 F Critical = 4.46

13 One-Way Within Groups ANOVA: Beer Taste Testing 5. Calculate the test statistic SS Total = ( X GM ) 2

14 One-Way Within Groups ANOVA: Beer Taste Testing 5. Calculate the test statistic SS Between = ( M GM ) 2

15 One-Way Within Groups ANOVA: Beer Taste Testing 5. Calculate the test statistic SS = Σ ( M GM ) 2 Sbj Subjects Participan i t

16 One-Way Within Groups ANOVA: Beer Taste Testing 5. Calculate the test statistic SS Within = SS Total SS Between SS Subjects =

17 One-Way Within Groups ANOVA: Beer Taste Testing 6. Make a decision People who dink cheap, mid-range, and high-end beers do not rate their beers the same, on average, F(2, 14) = 14.77, p <.05 ( F ( 2,14) 14.77) > ( F = 4.46) = Critical

18 Effect Size 2 SSBetween R = R = = ( SS SS ) ( ) Total Subjects.787

19 Summary Pros & Cons of Within & Between Subjects Designs Order Effects Counterbalancing & Latin Square New Sums of Squares and Degrees of Freedom (Subjects) New Source of Variability Effect Size

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