Analysis of Variance
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| Inflation of Type I Error | Each t-test has a type I error of alpha, however over a series of multiple t-tests the overall type I error does not stay at alpha but grows w/ each new comparison.
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| Analysis of Variance (ANOVA) | Compares multiple pop. means that avoids the inflation of type I error rates. Test one null hypothesis to determine if any of the pop. mean differ from the rest. Type I error remains at alpha. Use w/ interval/ratio data.
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| One-Factor ANOVA | "One factor" mean that b/w all groups, there is only one source of variation investigated.
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| Independent Sample ANOVA Assumptions | Population: all pops. are normally dist., all pops. have same variance. Sampling: samples are independent of one another, each sample obtained by SRS from pop.
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| Mean Square Within/Error | Pool all the sample variances. When the sample sizes are the same the pooled variance is the average of the individual sample variances. DF=N-k N:total # of obs. k:# diff. pop. Good estimate of pop. variance when null is correct & incorrect.
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| Mean Square Among/Treatment | Based on the sample means. DF=k-1. Good estimate of pop. variance only when null is correct.
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| Two Main Points | MSW is based on variability w/n each sample. MSA only good when all sample means can be considered from same pop. If null is true, MSA & MSW should be similar & ratio should be close to 1.
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| Partitioning the Sum of Squares | SSA:among groups sum of squares df=k-1. SSW:w/n groups sum of squares df=N-k. SST:total sum of squares SSW+SSA df=N-1.
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| One-Factor ANOVA for Dependent Samples | Goal is to decide if there is a difference among the dependent pop. means. Randomized complete block (two-way) & repeated measures. MST has k-1 df & MSE has N-k-b+1 df. SSB has b-1 df. SST has N-1 df.
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| Dependent Samples Assumptions | Population: normally dist. pops., variances are same, scores in all pairs of pops. should have same degree of relationship. Sample: samples are dependent, observations come from SRS from pop.
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