Slides to accompany Weathington, Cunningham & Pittenger (2010), Chapter 12: Single Variable Between- Subjects Research 1

Objectives Independent Variable Cause and Effect Gaining Control Over the Variables The General Linear Model Components of Variance The F-ratio ANOVA Summary Table Interpreting the F-ratio Effect Size and Power Multiple Comparisons of the Means 2

Multi-level Independent Variable More than 2 levels of the IV Permits more detailed analysis –Can’t identify certain types of relationships with only two data points (Figure 12.1) Can increase a study’s power by reducing variability within the multiple treatment condition groups 3

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Searching for Cause and Effect Identifying differences among multiple groups is a starting point for causal study Control is the key: –Through research design –Through research procedure 5

Control through Design Most easily secured in a true experiment You manipulate and control the IV –Control groups are possible  isolating effects of IV You control random assignment of participants –Helps to reduce confounding effects 6

Control through Procedure Each participant needs to experience the same process (except the manipulation) –Systematic Identifying and trying to limit as many confounding factors as possible Pilot studies are a great way to test your process and your control strategies 7

General Linear Model X ij = µ + α j + ε ij A person’s performance (score = X ij ) will reflect: –Typical score in that group (µ) –Effect of the treatment/manipulation (α j ) –Random error (ε ij ) H o : all µ i equal 8

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GLM and Between-Subj. Research Goal is to determine proportion of total variance due to IV and proportion due to random error Size of between-groups variance is due to error (ε ij ) and IV (α j ) If b-g variance > w-g variance  IV has some effect 10

ANOVA Compares different types of variance –Total variance = variability among all participants’ scores (groups do not matter) –Within-groups variance = average variability among scores within a group or condition (random) –Between-groups variance = variability among means of the different treatment groups Reflects joint effects of IV and error 11

F-ratio Allows us to determine if b-g variance > w-g variance F = Treatment Variance + Error Variance Error Variance F = MS between /MS within 12

F-ratio: No Effect Treatment group M may not all be exactly equal, but if they do not differ substantially relative to the variability within each group  nonsignificant result When b-g variance = w-g variance, F = 1.00, n.s. 13

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F-ratio: Significant Effect If IV influences DV, then b-g variance > w-g variance and F > 1.00 Examining the M can highlight the difference(s) 15

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F-ratio Distribution Represents probability of various F-ratios when H o is true Shape is determined by two df –1 st = b-g = (# of groups) - 1 –2 nd = w-g = (# of participants in a group) – 1 Positive skew, α on right extreme region 17

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Summarizing ANOVA Results Figure 12.7 Using the critical value from appropriate table in Appendix B, if F obs > F crit  significant difference among the M Rejecting H o requires further interpretation –Follow-up contrasts 19

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Interpreting F-ratio Omega squared indicates degree of association between IV and DV f is similar to d for the t-test Typically requires further M comparisons –t-test time, but with reduced α to limit chances of committing a Type I error 21

Multiple Means Comparisons You could consider lowering α to.01, but this would increase your Type II probability Instead use a post-hoc correction for α: – α e = 1 – (1 – α p ) c – Tukey’s HSD = difference required to consider M statistically different from each other 22

What is Next? **instructor to provide details 23