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Unformatted text preview: 11.1-3, 11.6-9t for two, F for more when comparing two means, use t test ( t=2, F=2+)Limitations of F testoSingle variable ANOVA test if statistically significant F, independent variable had pushed means apartoThree+ levels of independent variable, F test tells usIndependent variable pushed means apartTwo groups with highest and lowest means differed significantly from each otheroWe do not know from F test whether any of the other groups (not highest/lowest) differed from each otherCompare two means with t test with statistical significance, you know the difference between the two means is being affected by the independent variable = may generalize to populationT test= more limited in application but more definitive in implicationComputing s involved distances of scores from a central pointoIf the only thing that makes two means different is random sampling fluctuation, the means will be fairly close to the population mean and to each other = null hypothesisoIf independent variable is pushing the means apart, their distance apart (or central point for more means) will tend to be too great to be explained by null hypothesis = independent variable has a statistically significant affectBoth numerator (MSb)and denominator (MSw)of F testuse squared distance from a central point to determine distancemeans compared to overall mean (MSb), scores to their own group mean (MSw)oNumerator (MSb) = overestimination of sigma2affected by independent variable and random sampling fluctuationoDenominator (MSw) = least squares, unbiased estimate of sigma2affected by random sampling fluctuation(null hypothesis)Direct comparison methodoComparing mean of a single sample to actual population mean (mu) or theoretical population mean (muT)oComparing means resulting from two measurements of single groupoComparing means of two unrelated groupsoComparing mean of each of two or more treatment groups to control groupoMaking all possible pairwise comparisons between 3+ meanscomparing two...
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- Spring '11