III. Application Knowing the cdf of the F-distribution, we can now use that knowledge to analyze problems such as the one of statistical significance presented above. In statistics, statistical significance is defined by a significance level This significance level is not the same for all problems and can α. be varied to suit the needs of the current study, but is often .1, .05, or .01. We also require a null hypothesis, which is an assumption made prior to analyzing the data, and if we have statistically significant evidence, we are able to reject the null. For example, in the problem presented in the introduction, the null hypothesis would be that the jointly tested independent variables have no effect on the dependent variable. If we were to find statistically significant evidence, we would then prefer the unrestricted model which takes these variables into account. To determine if there is sufficient evidence to be statistically significant at significance level we must first calculate the p-value. A p-value is the probability that the observed data would α, occur if the null hypothesis were true. If the p-value is very small, i.e. it is lower than the significance level, we have adequate evidence to reject the null. For an F-test, we can use the cdf to determine the p-value for a given set of data. For an F with m numerator degrees of freedom and n denominator degrees of freedom and cdf : p-value= where is a random F-variable with the same m and n degrees of freedom (Wooldridge 151). For example, if we had RSSr=195.31 RSSur=172.36 q=5 n=89 k=14 then
III. Application Knowing the cdf of the F-distribution, we can now use that knowledge to analyze problems such as the one of statistical significance presented above. In statistics, statistical significance is defined by a significance level α. This significance level is not the same for all problems and can be varied to suit the needs of the current study, but is often .1, .05, or .01. We also require a null hypothesis, which is an assumption made prior to analyzing the data, and if we have statistically significant evidence, we are able to reject the null. For example, in the problem presented in the introduction, the null hypothesis would be that the jointly tested independent variables have no effect on the dependent variable. If we were to find statistically significant evidence, we would then prefer the unrestricted model which takes these variables into account. To determine if there is sufficient evidence to be statistically significant at significance level α, we must first calculate the p-value. A p-value is the probability that the observed data would occur if the null hypothesis were true. If the p-value is very small, i.e. it is lower than the significance level, we have adequate evidence to reject the null. For an F-test, we can use the cdf to determine the p-value for a given set of data. For an F with m numerator degrees of freedom and n denominator degrees of freedom and cdf : p-value= where is a random F-variable with the same m and n degrees of freedom (Wooldridge 151). For example, if we had RSSr=195.31 RSSur=172.36 q=5 n=89 k=14 then
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