ch. 13_111109 - Lab 227 11/11/09 ANOVA Overview ANOVA is a...

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Lab 227 11/11/09 ANOVA Overview ANOVA is a procedure we use to test the null hypothesis when we want to evaluate the mean differences between two or more groups. The main advantage of ANOVA is that we can make multiple comparisons between groups while keeping the alpha level constant. Hypotheses H 0 : µ 1 = µ 2 = µ 3 H 1 : At least one population mean is different Definitions Factor: this is what we call the IV in ANOVA Level: the individual conditions that make up a factor o For example, when testing the effect of three types of therapy on depression, “type of therapy” is the factor while the specific types (e.g. cognitive, behavioral, or psychodynamic) are considered levels of the factor. The F statistic The ratio for the F statistic is similar to the t-statistic but uses variance differences instead of mean differences ܨ = ܸܽݎ݅ܽ݊ܿ݁ ܾ݁ݐݓ݁݁݊ ݏܽ݉݌݈݁ ݉݁ܽ݊ݏ ܸܽݎ݅ܽ݊ܿ݁ ݓ݅ݐℎ݅݊ ݃ݎ݋ݑ݌ݏ (݁ݔ݌݁ܿݐ݁݀ ݀ݑ݁ ݐ݋ ܿℎܽ݊ܿ݁ ݋ݎ ݁ݎݎ݋ݎ) This can also be stated in another way: ܨ = ܶݎ݁ܽݐ݉݁݊ݐ ݂݂݁݁ܿݐ + ݂݂݀݅݁ݎ݁݊ܿ݁ݏ ݀ݑ݁ ݐ݋ ܿℎܽ݊ܿ݁ ܦ݂݂݅݁ݎ݁݊ܿ݁ݏ ݀ݑ݁ ݐ݋ ܿℎܽ݊ܿ݁ If the null is true, the there will be no treatment effect and the ratio would be F=1 Notation K is the number of groups in the design N is the total sample size N is the sample size per group T is used instead of ∑X If we add up T for all groups we will get G If we compute ∑X 2 for each group and add it up, we will get σ ܺ ௧௢௧௔௟ MS is what we call the variance in ANOVA
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Formulas Sums of Squares ܵܵ ௧௢௧௔௟
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This note was uploaded on 02/24/2011 for the course PSYC 227 taught by Professor Shinkareva during the Fall '09 term at South Carolina.

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ch. 13_111109 - Lab 227 11/11/09 ANOVA Overview ANOVA is a...

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