The F-test statistic is formed by taking the of two separate estimates of , where the estimate in the numerator is derived from the and the estimate in the denominator is derived from the . The sampling distribution is the distribution with degrees of freedom within categories and degrees of freedom between categories.
Added by Ronald M.
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The F-test statistic is formed by taking the numerator derived from the sum of squares between categories and the denominator derived from the sum of squares within categories. The sampling distribution is the distribution with degrees of freedom between categories and degrees of freedom within categories. Once you compute the F (obtained) statistic for your data, you compare its value with F (determined by the given alpha level and the degrees of freedom). If the test statistic is in the critical region, you reject the null hypothesis and conclude that there is a significant difference between the means.
Samuel S.
The F-test is used to test the equality of variances for two or more groups. In this case, they want to know the probability that the variance of group 1 is equal to the variance of group 2. The F-statistic is calculated as the ratio of the variances, and it follows an F-distribution with degrees of freedom equal to the number of observations minus 1 for each group. The critical value for the F-test can be found in the F-table. If the calculated F-statistic is greater than the critical value, we reject the null hypothesis and conclude that the variances are not equal. Otherwise, we fail to reject the null hypothesis and conclude that the variances are equal.
Adi S.
A hypothesis test comparing two population variances uses the F distribution. The F distribution is not symmetric and its shape will depend on two values of degrees of freedom, a numerator and denominator degrees of freedom. It is important to note that the F values will never be negative. The F test statistic is calculated as follows where s1² is the variance from sample 1, s2² is the variance from sample 2, and s1² > s2². Since the F statistic is calculated using the larger variance as the numerator, only upper tail areas will be used when finding the p-value. The size of sample 1 is denoted by n1 and will have n1 – 1 degrees of freedom. The size of sample 2 is denoted by n2 and will have n2 – 1 degrees of freedom. It is given that a sample of 21 items from population 1 has a variance of s1² = 5.7. A sample of 26 items from population 2 has a variance of s2² = 2.35. Use these values to find the F test statistic, rounding the result to two decimal places. Step 2 The test statistic was found to be F = 2.43. Before the p-value can be found, the degrees of freedom for the numerator and denominator must be found. The sample from population 1 contained 21 items, so n1 = and n1 – 1 = . Thus, the degrees of freedom for the numerator is . The sample from population 2 contained 26 items, so n2 = and n2 – 1 = . Thus, the degrees of freedom for the denominator is .
Jon S.
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