Analysis of Variance 3 -Hypothesis Test with F-Statistic
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Statistics make it possible to analyze real-world business problems with actual data so that you can determine if a marketing strategy is really working, how much a company should charge for its products, or any of a million other practical questions. The science of statistics uses regression analysis, hypothesis testing, sampling distributions, and more to ensure accurate data analysis.
Hypothesis testing is the use of statistics to determine the probability that a given hypothesis is true. The usual process of hypothesis testing consists of four steps.
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3. Compute the , which is the probability that a test statistic at least as significant as the one observed would be obtained assuming that the were true. The smaller the -value, the stronger the evidence against the null hypothesis.
Iyanaga, S. and Kawada, Y. (Eds.). "Statistical Estimation and Statistical Hypothesis Testing." Appendix A, Table 23 in Cambridge, MA: MIT Press, pp. 1486-1489, 1980.
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The and are used to determine if the null hypothesis should be rejected. The that is followed is that an “extreme” test statistic results in rejection of the null hypothesis. Here, an extreme test statistic is one that lies outside the bounds of the critical value or values.
The critical value approach involves determining "likely" or "unlikely" by determining whether or not the observed test statistic is more extreme than would be expected if the null hypothesis were true. That is, it entails comparing the observed test statistic to some cutoff value, called the "critical value." If the test statistic is more extreme than the critical value, then the null hypothesis is rejected in favor of the alternative hypothesis. If the test statistic is not as extreme as the critical value, then the null hypothesis is not rejected.
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