Term
Factorial (multi-way) designs |
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Definition
• Allow us to investigate several IVs simultaneously. • It's a “crossed” one-way ANOVA design. |
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Term
Advantages of factorial designs |
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Definition
• A two-factor experiment with two levels of each factor will require only half the number of subjects as would be required in two different one factor-two level experiments. • No inflation of Type I error. • Allow us to examine the effects of interactions b/t the IVs. |
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Term
The logic of factorial designs |
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Definition
• Assumes that each score reflects the influence of both IVs. • These influences can be separated out by considering the marginals. • The means of the marginals are only affected by the main effects of the two treatments. • The variance within cells is not affected by any treatment that shifts the means. |
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Term
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Definition
• The simple structural model does NOT hold in factorial ANOVA. • Instead, the total sum-of-squares includes an addition source of variability called the interaction. • The interaction reflects nonlinear summation of the effects of the IVs. • Each score doesn’t reflect a constant contribution of the IVs. • Instead, the score depends on the specific levels of the IVs, and the weight of each IV depends on the level of the other IV. |
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Term
Within subjects (or repeated measures) ANOVA |
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Definition
• The intrinsic variability (sd of the sample) will usually be smaller in a within subjects design than it would be with a between subjects design. • If the denominator of the F ratio is smaller, then F will be larger and power will be greater. • The within-subjects ANOVA treats the subjects themselves as a separate factor to separate out the effect of the treatment from individual variability and sampling variability. |
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Term
Effects of subject variability |
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Definition
| • If subject variability increases, then...• Standard ANOVA:• SSwithin increases, SSbetween decreases.• Repeated measures ANOVA: • SSwithin decreases, SSbetween increases. |
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Term
| SS comparison for three types of ANOVA |
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Definition
• One factor (one-way) ANOVA SStotal=SSwithin+SSbetween • Factorial (multi-way) ANOVA SStotal=SSwithin+SSrows+SScols+SSin• Repeated measures (within subjects) ANOVA SStotal=SStreats+SSsubs+SSin |
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Term
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Definition
| • The structural model easily deals with situations in which the n of the treatment groups is not equal.• In this case the df’s reflect the differences in the n of each group.• The group means still reflect differences in the scores of the groups. • The grand mean reflects the total variability. |
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Term
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Definition
| • Type I error accumulates! • The more comparisons that are made, the more likely it is to make at least one Type I error. |
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Term
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Definition
| • Unplanned comparisons are not based on any prior expectations.• It is critical to avoid taking advantage of random variation between groups.• If you conduct several comparisons and wish to control Type I error, you can use a more stringent critical p value. • To make all possible pairwise comparisons, use the Bonferroni correction. |
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Term
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Definition
| • Planned comparisons are based on prior expectations about “interesting” comparisons between groups.• Planned comparisons must be specified before the data are inspected!• It is common not to correct the critical p value in making planned comparisons.• In such cases the experimenter is willing to suffer the potential inflation of Type I error in order to avoid making a Type II error. |
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