Chapter Eleven: Designing, Conducting, Analyzing, and Interpreting Experiments with More Than Two Groups The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

Objectives Review project assignment How do we design multiple group studies? How do we analyze multiple group studies? The logic of analysis of variance Review exam The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

Experimental Design: Adding to the Basic Building Block The two-group design is the basic building block. Researchers typically want to move beyond two-group designs so they can ask more complicated and interesting questions. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

Example What is the effect of background noise during study time on recall? Two basic groups? More than two? Which is the control group? The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

What is the effect of delay on recall Start with basic two group experiment? What additional groups could you add? What is the control group? The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

The Multiple-Group Design How Many Groups? This question marks the difference between the multiple-group design and the two-group design. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

The Multiple-Group Design How Many Groups? This question marks the difference between the multiple-group design and the two-group design. A multiple-group design compares three or more levels or amounts of an IV. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

The Multiple-Group Design How Many Groups? This question marks the difference between the multiple-group design and the two-group design. A multiple-group design compares three or more levels or amounts of an IV. A multiple-group design can have a control group and two or more experimental groups. We can compare three, four, five, or even more differing levels or amounts of an IV. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

The Multiple-Group Design How Many Groups? This question marks the difference between the multiple-group design and the two-group design. A multiple-group design compares three or more levels or amounts of an IV. A multiple-group design can have a control group and two or more experimental groups. We can compare three, four, five, or even more differing levels or amounts of an IV. A multiple-group design does not have to have a control group. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

The Multiple-Group Design Assigning Participants to Groups After we decide to conduct a multiple-group experiment, we must decide about assignment or research participants to groups. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

The Multiple-Group Design Assigning Participants to Groups After we decide to conduct a multiple-group experiment, we must decide about assignment or research participants to groups. We may choose between independent groups or correlated groups. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

The Multiple-Group Design Independent Groups Groups of participants that are formed by random assignment. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

The Multiple-Group Design Independent Groups Groups of participants that are formed by random assignment. Correlated Samples (Nonrandom Assignment to Groups) The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

The Multiple-Group Design Independent Groups Groups of participants that are formed by random assignment. Correlated Samples (Nonrandom Assignment to Groups) Matched sets Participants are matched on a variable that will affect their performance on the DV (matching variable). Then sets of participants are created who are essentially the same on the matching variable. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

The Multiple-Group Design Independent Groups Groups of participants that are formed by random assignment. Correlated Samples (Nonrandom Assignment to Groups) Matched sets Natural sets Analogous to using natural pairs except that sets must include more than two research participants. Many animal researchers use littermates as natural sets. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

The Multiple-Group Design Independent Groups Groups of participants that are formed by random assignment. Correlated Samples (Nonrandom Assignments to Groups) Matched sets Natural sets Analogous to using natural pairs except that sets must include more than two research participants. Many animal researchers use littermates as natural sets. Repeated measures Each participant must participate in all of the treatment conditions. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

Comparing Multiple-Group and Two-Group Designs All you have to do to change your two-group design into a multiple-group design is add another level (or more) to your IV. A two-group design can tell you whether your IV has an effect. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

Comparing Multiple-Group and Two-Group Designs A two-group design can tell you whether your IV has an effect. If you find no answer in a library search, then you should consider conducting a two-group (presence vs. absence) study. A multiple-group design is appropriate when you find the answer to your basic question and wish to go further. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

Variations on the Multiple-Group Design Comparing Different Amounts of an IV If we already know that a particular IV has an effect, then we can use a multiple-group design to help us define the limits of that effect. In this type of experiment, we often add an important control in order to account for a possible placebo effect. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

Variations on the Multiple-Group Design Comparing Different Amounts of an IV Dealing with measured IVs Ex post facto research deals with measured rather than manipulated IVs. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

Analyzing Multiple-Group Designs Multiple-Groups designs are measured with the analysis of variance (ANOVA). The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

Analyzing Multiple-Group Designs Multiple-Groups designs are measured with the analysis of variance (ANOVA). The ANOVA procedure used to analyze a multiple-group design with one IV is known as a one-way ANOVA. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

Analyzing Multiple-Group Designs Multiple-Groups designs are measured with the analysis of variance (ANOVA). The ANOVA procedure used to analyze a multiple-group design with one IV is known as a one-way ANOVA. A one-way ANOVA for independent groups is known as a completely randomized ANOVA. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

Analyzing Multiple-Group Designs Multiple-Groups designs are measured with the analysis of variance (ANOVA). The ANOVA procedure used to analyze a multiple-group design with one IV is known as a one-way ANOVA. A one-way ANOVA for independent groups is known as a completely randomized ANOVA. A one-way ANOVA for correlated groups is known as a repeated-measures ANOVA. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

ANOVA The null hypothesis: The independent variable had no effect – any differences between treatment levels are due to chance The alternative hypothesis: The independent variable effected at least one of the groups The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

Rationale of ANOVA Between-Groups Variability Variability in DV scores that is due to the effects of the IV. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

Rationale of ANOVA Between-Groups Variability Variability in DV scores that is due to the effects of the IV. Error Variability (Within-Groups Variability) Variability in DV scores that is due to factors other than the IV (individual differences, measurement error, and extraneous variation). The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

Rationale of ANOVA The notion that has evolved for the ANOVA is that we are comparing the ratio of between-groups variability to within-groups variability. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

Rationale of ANOVA The notion that has evolved for the ANOVA is that we are comparing the ratio of between-groups variability to within-groups variability. F = between-groups variability within-groups variability The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

Rationale of ANOVA When the IV has a significant effect on the DV, the F ratio will be large. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

Rationale of ANOVA When the IV has a significant effect on the DV, the F ratio will be large. When the IV has no effect or only a small effect, the F ratio will be small (near 1). The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

Hypothetical experiment Three groups – A, B, and C Each with 5 participants Do the groups differ significantly The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

Understanding within-group and between-group variance Group B Group C 1 The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

Answers Group Means = 1, 1, and 1 Within Group Variance = 0 Between Group Variance = 0 F is not significant The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

Understanding within-group and between-group variance Group B Group C 1 3 The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

Answers Group Means = 1, 1 and 3 Between Group Variance = 6.67 Within Group Variance = 0 F is infinitely large The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

Understanding within-group and between-group variance Group B Group C 1 3 2 The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

Answers Between Group Variance = 6.67 Within Group Variance = .17 F = 40 significant The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

Understanding within-group and between-group variance Group B Group C 3 1 2 The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

Answers Group Means = 1, 1, and 3 Between Group Variance = 6.67 Within Group Variance = .33 F significant The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

Understanding within-group and between-group variance Group B Group C 1 2 3 4 5 The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

Answers Group Means = 1, 1, and 3 Between Group Variance = 6.67 Within Group Variance = 1.17 F significant = 5.71 The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

Interpretation: Making Sense of Your Statistics Adding a third group (or more) creates an interesting statistical problem for us so that we often need to compute an extra statistical test to explore significant findings. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

Interpreting Computer Statistical Output One-way ANOVA for Independent Samples Source table A table that contains the results of ANOVA. Source refers to the source of the different types of variation. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

Hypothetical experiment In the following study, participants were randomly assigned to receive humanistic therapy, psychodynamic therapy, or behavioral therapy for their depression. Six months after therapy ended, participants’ levels of depression were rated on a Likert scale from 1 (not at all depressed) to 15 (extremely depressed). The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

Sample source table GROUP N MEAN STD DEV STD ERROR 1 (humanistic) 10 5.40 2.17 0.69 2 (psychodynamic) 10 7.50 2.84 0.90 3 (behavioral) 10 5.60 3.13 0.99 ONE-WAY ANOVA: THERAPY by DEPRESSION SOURCE SS DF MS F RATIO PROB. BETWEEN GROUPS 26.87 2 13.73 1.78 .187 WITHIN GROUPS 203.30 27 7.53 TOTAL 230.17 29 POST HOC TEST: Tukey-HSD with significance level .05 * Indicates significant differences shown for pairings G G G r r r p p p 1 2 3 Mean THERAPY 5.40 Grp 1 7.50 Grp 2 5.60 Grp 3 The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

Interpreting Computer Statistical Output One-way ANOVA for Independent Samples Source table A table that contains the results of ANOVA. Source refers to the source of the different types of variation. Sum of squares The amount of variability in the DV attributable to each source. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

Interpreting Computer Statistical Output One-way ANOVA for Independent Samples Mean square The “averaged” variability for each source = Same as variance The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

Interpreting Computer Statistical Output One-way ANOVA for Independent Samples Mean square The “averaged” variability for each source. The mean square is computed by dividing each source’s sum of squares by its degrees of freedom. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

Interpreting Computer Statistical Output One-way ANOVA for Independent Samples Mean square F = mean square between groups mean square within groups The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

Interpreting Computer Statistical Output One-way ANOVA for Independent Samples Mean square Variance A single number that represents the total amount of variation in a distribution. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

Interpreting Computer Statistical Output One-way ANOVA for Independent Samples Mean square Variance A single number that represents the total amount of variation in a distribution. The square of the standard deviation. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

Interpreting Computer Statistical Output One-way ANOVA for Independent Samples To discern where the significance lies in a multiple-group experiment, we must do additional statistical tests known as post hoc comparisons (also known as follow-up tests). The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

Interpreting Computer Statistical Output One-way ANOVA for Independent Samples Post hoc comparisons Statistical comparisons made between group means after finding a significant F ratio. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

Hypothetical Experiment A researcher was interested in determining the effectiveness of humanistic therapy for alleviating depression. He administered a depression inventory to a sample of clients with depression on three occasions: before therapy started, two months after therapy began, and four months into therapy. Depression scores could range from 1 (not at all depressed) to 15 (extremely depressed). The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

Sample source table GROUP N MEAN STD DEV STD ERROR 1 (Time 1) 10 13.50 1.58 0.50 2 (Time 2) 10 9.40 2.88 0.91 3 (Time 3) 10 7.30 4.06 1.28 ONE-WAY ANOVA: DEPRESSION by TIME (CORR SAMP) SUM OF MEAN SOURCE SQUARES DF SQUARES F RATIO PROB. TIME 198.87 2 99.43 18.43 .000 SUBJECTS 147.88 9 16.43 185.04 .000 WITHIN CELLS 97.13 18 5.40 TOTAL 443.88 29 POST HOC TEST: Tukey-HSD with significance level .05 * Indicates significant differences shown for pairings G G G r r r p p p 1 2 3 Mean TIME 13.50 Grp 1 * * 9.40 Grp 2 7.30 Grp 3 The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

Interpreting Computer Statistical Output One-way ANOVA for Independent Samples Translating Statistics into Words (text example): The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

Interpreting Computer Statistical Output One-way ANOVA for Independent Samples Translating Statistics into Words (text example): The effect of different clothing on salesclerks’ response time was significant F(2, 21) = 4.71, p = .02. The proportion of variance accounted for by the clothing effect was .31. Tukey tests indicated (p < .05) that clerks waiting on customers dressed in sloppy clothes (M = 63.25, SD = 11.73) responded more slowly than clerks waiting on customers in dressy (M = 48.38, SD = 9.46) or casual clothes (M = 48.88, SD = 9.55). The response times of clerks waiting on customers in dressy and casual clothes did not differ from each other. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

Interpreting Computer Statistical Output Translating Statistics into Words (text example): The effect of three different clothing styles on clerks’ response times was significant, F(2, 14) = 19.71, p < .001. The proportion of variance accounted for by the clothing effect was .74. Tukey tests showed (p < .01) that clerks took longer to respond to customers dressed in sloppy clothes (M = 63.25, SD = 11.73) than to either customers in dressy clothes (M = 48.38, SD = 9.46) or customers in casual clothes (M = 48.88, SD = 9.55). Response times did not differ between the clerks waiting on customers in dressy or casual clothing. The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education