Statistics for the Social Sciences Psychology 340 Spring 2005 Within Groups ANOVA

Statistics for the Social Sciences Outline Basics of within groups ANOVA –Repeated measures –Matched samples Computations Within groups ANOVA in SPSS

Statistics for the Social Sciences Example Suppose that you want to compare three brand name pain relievers. –Give each person a drug, wait 15 minutes, then ask them to keep their hand in a bucket of cold water as long as they can. The next day, repeat (with a different drug) Dependent variable: time in ice water Independent variable: 4 levels, within groups –Placebo –Drug A –Drug B –Drug C

Statistics for the Social Sciences Statistical analysis follows design The 1 factor within groups ANOVA: –One group –Repeated measures –More than 2 scores per subject

Statistics for the Social Sciences Statistical analysis follows design The 1 factor within groups ANOVA: –One group –Repeated measures –More than 2 scores per subject –More than 2 groups –Matched samples –Matched groups - OR -

Statistics for the Social Sciences Within-subjects ANOVA PlaceboDrug ADrug BDrug C XBXB XAXA XCXC XPXP n = 5 participants Each participates in every condition (4 of these)

Statistics for the Social Sciences Within-subjects ANOVA –Step 2: Set your decision criteria –Step 3: Collect your data –Step 4: Compute your test statistics Compute your estimated variances (2 steps of partitioning used) Compute your F-ratio Compute your degrees of freedom (there are even more now) –Step 5: Make a decision about your null hypothesis Hypothesis testing: a five step program –Step 1: State your hypotheses

Statistics for the Social Sciences Step 4: Computing the F-ratio Analyzing the sources of variance –Describe the total variance in the dependent measure Why are these scores different? Sources of variability –Between groups –Within groups XBXB XAXA XCXC XPXP Individual differences Left over variance (error) Because we use the same people in each condition, we can figure out how much of the variability comes from the individuals and remove it from the analysis

Statistics for the Social Sciences Partitioning the variance Total variance Stage 1 Between groups variance Within groups variance

Statistics for the Social Sciences Partitioning the variance Total variance Stage 1 Between groups variance Within groups variance Stage 2 Between subjects varianceError variance

Statistics for the Social Sciences Partitioning the variance Total variance Stage 1 Between groups variance Within groups variance Stage 2 Between subjects varianceError variance 1)Treatment effect 2)Error or chance (without individual differences) 1)Individual differences 2)Other error 1)Other error (without individual differences) 1)Individual differences Because we use the same people in each condition, none of this variability comes from having different people in different conditions

Statistics for the Social Sciences The F ratio –Ratio of the between-groups variance estimate to the population error variance estimate Step 4: Computing the F-ratio Observed variance Variance from chance F-ratio =

Statistics for the Social Sciences Partitioning the variance Total variance Stage 1 Between groups variance Within groups variance Stage 2 Between subjects varianceError variance 1)Treatment effect 2)Error or chance (without individual differences) 1)Individual differences 2)Other error 1)Other error (without individual differences) 1)Individual differences

Statistics for the Social Sciences Partitioning the variance Total variance Stage 1 Between groups varianceWithin groups variance

Statistics for the Social Sciences Partitioning the variance PlaceboDrug ADrug BDrug C

Statistics for the Social Sciences Partitioning the variance Total variance Stage 1 Between groups varianceWithin groups variance Stage 2 Between subjects varianceError variance

Statistics for the Social Sciences What is ? Partitioning the variance PlaceboDrug ADrug BDrug C The average score for each person Between subjects variance

Statistics for the Social Sciences Partitioning the variance PlaceboDrug ADrug BDrug C What is ? The average score for each person Between subjects variance

Statistics for the Social Sciences Partitioning the variance Total variance Stage 1 Between groups varianceWithin groups variance Stage 2 Between subjects variance Error variance

Statistics for the Social Sciences Partitioning the variance PlaceboDrug ADrug BDrug C Error variance

Statistics for the Social Sciences Partitioning the variance Total variance Stage 1 Between groups varianceWithin groups variance Stage 2 Between subjects variance Error variance

Statistics for the Social Sciences Partitioning the variance Mean Squares (Variance) Between groups varianceError variance Now we return to variance. But, we call it Means Square (MS) Now we return to variance. But, we call it Means Square (MS) Recall:

Statistics for the Social Sciences Partitioning the variance Total variance Stage 1 Between groups varianceWithin groups variance Stage 2 Between subjects variance Error variance

Statistics for the Social Sciences Within-subjects ANOVA The F tableThe F table –Need two df’s df between (numerator) df error (denominator) –Values in the table correspond to critical F’s Reject the H 0 if your computed value is greater than or equal to the critical F –Separate tables for 0.05 & 0.01 Do we reject or fail to reject the H 0 ? Do we reject or fail to reject the H 0 ? –From the table (assuming 0.05) with 3 and 12 degrees of freedom the critical F = –So we reject H 0 and conclude that not all groups are the same

Statistics for the Social Sciences Within-subjects ANOVA in SPSS –Setting up the file –Running the analysis –Looking at the output