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PSY200 CH11 - 11.1-3 11.6-9 t for two F for more when...

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11.1-3, 11.6-9 “t for two, F for more” – when comparing two means, use t test ( t=2, F=2+) Limitations of F test o Single variable ANOVA test if statistically significant F, independent variable had pushed means apart o Three+ levels of independent variable, F test tells us Independent variable pushed means apart Two groups with highest and lowest means differed significantly from each other o We do not know from F test whether any of the other groups (not highest/lowest) differed from each other Compare 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 population T test = more limited in application but more definitive in implication Computing s involved distances of scores from a central point o If 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 hypothesis o If 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 affect Both numerator (MSb) and denominator (MSw) of F test use squared distance from a central point to determine distance—means compared to overall mean (MSb), scores to their own group mean (MSw) o Numerator (MSb) = overestimination of sigma 2 —affected by independent variable and random sampling fluctuation o Denominator (MSw) = least squares, unbiased estimate of sigma 2 —affected by random sampling fluctuation ( null hypothesis ) Direct comparison method o Comparing mean of a single sample to actual population mean (mu) or theoretical population mean (muT) o Comparing means resulting from two measurements of single group o Comparing means of two unrelated groups o
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