Psych 110 Final - New

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Analysis of variance

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ANOVA, a technique for testing differences in the means of several groups

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One-way ANOVA

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an analysis of variance wherein groups are defined on only one independent variable

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Omnibus null hypothesis

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the hypothesis that all population means are equal

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Assumption of normality

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sampling distribution is normal

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Assumption of heterogeneity of variance

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each population has same variance

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Assumption of independence of samples

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all observations are independent of each other

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Logic of ANOVA

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average value of sample variances is an estimate of population variances, does not depend on the truth or falsity of the null

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MSwithin

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aka MSerror, variability among subjects in the same treatment group

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MSbetween groups

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aka MSgroups or MS treatment, variability among group means

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Average of the sample variances

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MSerror

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Variance of the sample means multiplied by the sample size

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MSgroup

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MSerror

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estimate of pop mean independent of the truth of the null, average variance of each sample in treatment

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MS group

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pop variance estimate only when the null is true, variance of groups corrected by n to produce estimate of population variance

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When MS error and MS group agree

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support for the truth of the null

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Sum of squares

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the sum of the squared deviations about the mean

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SStotal

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the sum of squared deviations of all the scores, regardless of group membership

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SSgroup

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the sum of squared deviations of the group means from the grand mean, multiplied by the number of observations

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SSerror

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the sum of squared residuals or the sum of the squared deviations within each group

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SSerror formula

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SSerror = SStotal – SSgroup

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SStotal formula

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SStotal = SSerror + SSgroup

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dftotal for ANOVA

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N-1, N = number of total participants

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dfgroup for ANOVA

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k-1, k = number of groups

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dferror

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k(n-1)

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F ratio/statistic

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the ratio of MS group over MS error

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Logic of F ratio

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closer to 1 = null is true because MSerror and MSgroup will be approximately the same

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Bonferroni procedure

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a multiple comparisons procedure in which the familywise error rate is divided by the number of comparisons

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Logic of Bonferroni

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omit requirement that F be significant, run all tests at α over c, where c = number of comparisons

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Tukey procedure

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a multiple comparison procedure designed to hold the familywise error rate at α for a set of comparisons, compares every mean with every other mean

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Violations of assumptions

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if the largest variance is no more than four or five times the smallest = no problem

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Heterogeneity and unequal sample sizes

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do not mix

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Eta squared

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ηˆ2, a measure of the magnitude of effect, SSgroup over SStotal

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Bias of eta squared

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tends to overestimate the value we would obtain if we were able to measure the whole population

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Omega squared

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ω^2, a less biased measure of magnitude of effect

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Factors

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independent variables in ANOVA world

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Two-way factorial design

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a design involving two independent variables in a way in which every level of every variable is paired with every level of the other variable

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Factorial design

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an experimental design in which every level of each variable is paired with every level of every variable

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Interaction

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a situation in a factorial design in which the effects of one independent variable depend on the level of another independent variable

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Notation: i and j

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i = row and j = column

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Main effect

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the effect of one independent variable averaged across the levels of the other independent variable

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Simple effect

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the effect of one independent variable at one level of another

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Notation: nc

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n = number of participants in the group, c = level

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SScells

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the sum of squares assessing the differences among the cell means

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Differences in cell means

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other than sampling error, coming from different levels of the same variable, different levels of differing variables or because of an interaction

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Parallel lines

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means that there is NO interaction effect present