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Unformatted text preview: ted value of MStreatment is σ2. Just as with MSregression in hypothesis testing with regression, MStreatment has a likelihood function with ! shape of a chi
square distribution (i.e., a distribution we know exactly), but the multiplied by σ2. Therefore, we need to divide by an estimate of σ2 to get a test statistic we can use. This estimate comes from MSresidual, which is the mean square obtained from the residual sum of squares. MSresidual = ! SSresidual
df residual (6) The expected value of MSresidual (according to either H0 or H1) is σ2. In fact, the sampling distribution for MSresidual also has a chi
square shape, again multiplied by σ2. Therefore, when we calculate the ratio of MStreatment and MSresidual, σ2 cancels out, and we end up with a test statistic that doesn’t depend on any unknown population parameters. F= MStreatment
MSresidual (7) F tells us how much the group means differ relative to how much they should differ just by chance. If F is large, then the group differences are larger than can be explained by chance. !
To know how large F must be to reject the null hypothesis, we need to know its likelihood function (i.e., its sampling distribution according to the null hypothesis). The distribution for F is called an F distribution. An F distribution arises any time you take the ratio of two chi
square variables, such as MStreatment and MSresidual. Because the distribution of any chi
square variable depends on its degrees of freedom, the F distribution depends on the degrees of freedom for both chi
square variables. In other words, to specify an F distribution, we must specify two df values: the degrees of freedom for the numerator and the degrees of freedom for the denominator. In this case, these are dftreatment and dfresidual. Once we know...
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This document was uploaded on 02/25/2014 for the course PSYC 3101 at Colorado.
 Spring '08
 MARTICHUSKI
 Psychology

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