11-08 math

# Degrees of freedom you dont need to memorize degrees

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Unformatted text preview: those, we know the distribution of F exactly. Hypothesis testing with ANOVA. The last step of ANOVA is to use the test statistic to decide between hypotheses. In this case, we do a one ­tailed test because F is only interesting when it’s large. A large value of F indicates that the group means differ more than would be expected by chance; this is evidence against the null hypothesis and in favor of some real difference among the populations. However, a small value of F indicates that the group differences are less than would be expected even by chance, and there is nothing interesting that would cause this to happen. Therefore, the critical value and p ­value are both based on probabilities in the upper tail of the distribution. ( ) p Fdf treatment , df residual " Fcrit = # ( ) p = p Fdf treatment , df residual " F ! (8) (9) ! Fdf treatment , df residual represents a random variable whose probability distribution is an F distribution with dftreatment and dfresidual degrees of freedom. Equation 8 says that Fcrit is ! defined as the value that has a probability α of being exceeded. Equation 9 says that the p ­ value is the probability of a result exceeding the actual F ­value obtained from the data. Both of these equations work just as in one ­tailed t ­tests. As with other one ­tailed tests, if F > Fcrit and p < α (if one is true then the other is also true), then you reject the null hypothesis, because F is too big to be explained by chance. Degrees of freedom. You don’t need to memorize degrees of freedom for ANOVA, but this may help you see how everything fits together. The total variability in the data, SStotal, is based on the diff...
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## This document was uploaded on 02/25/2014 for the course PSYC 3101 at Colorado.

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