The Significance Test in ANOVA (1 of 2)

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If the null hypothesis is true, then both MSB and MSE estimate the same quantity. If the null hypothesis is false, then MSB is an estimate of a larger quantity (click here to see what it is). The significance test involves the statistic F which is the ratio of MSB to MSE: F = MSB/MSE. If the null hypothesis is true, then the F ratio should be approximately one since MSB and MSE should be about the same. If the ratio is much larger than one, then it is likely that MSB is estimating a larger quantity than is MSE and that the null hypothesis is false. In order to conduct a significance test, it is necessary to know the sampling distribution of F given that the null hypothesis is true. From the sampling distribution, the probability of obtaining an F as large or larger than the one calculated from the data can be determined. This probability is the probability value. If it is lower than the significance level, then the null hypothesis can be rejected. The mathematics of the sampling distribution were worked out by the statistician R. A. Fisher and is called the F distribution in his honor. (Click here for information about the F distribution.)
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