Issue link: https://iconnect007.uberflip.com/i/1530610
66 PCB007 MAGAZINE I DECEMBER 2024 e number of observations should be ≥ 12 for each sample. With ≥ 12 observations, precision is maximized by decreasing the width of the confidence interval of the variance. is provides enough power for the F-test. Power is the conditional probability that you will avoid a Type II error, accept- ing the null hypothesis when, in fact, it's false. e data set in Table 1 is used here. e ToolPak two-sample F-test output is shown in Table 4, and the output explanations are given in Table 5. Of particular note in Table 4 is that only the one-tail output exists. Because our interest is in parity, we want the two-tail output. All we need to do is double the one-tail p-value out- put: 0.370 X 2 = 0.740. Table 1 provides a data set, Table 2 shows the ToolPak two-sample t-Test (assuming unequal variances) output, and Table 3 gives the output explanations. F-test e F-test is used to test if the variances of two populations are equal (we need to work in units of variance when calculating F statis- tics; variance = standard deviation squared [σ 2 ]). A typical application tests if a new pro- cess or treatment is superior to a current one. When comparing two populations, we typi- cally hypothesize that their variances are the same. en, we calculate the test statistic from the data and compare it to a theoretical value from the F-distribution. Depending on the outcome, we either accept the null or alterna- tive hypothesis based on a probability value (alpha). An alpha value of 0.05 is commonly used to accept the alternative hypothesis 2, 4 . Although F-tests are relatively robust, they are based on several assumptions: e data are continuous, not categorical. e sample data have been randomly sampled from a popula- tion. e distributions are approximately nor- mal, free from severe skewness and outliers. e samples are independent 2, 4 . Table 3: t-Test output explanations Table 5: F-test output explanations Table 4: F-test: two-sample