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DECEMBER 2024 I PCB007 MAGAZINE 65 t-Test ere are three t-Tests to compare means: a one-sample t-Test, a two-sample t-Test, and a paired t-Test. e two-sample t-Test is used to determine if two population means are equal. A typical application tests if a new process or treatment is superior to a current one. When comparing two populations, we typically hypothesize that their means are the same. en, we calculate the test statistic from the data and compare it to a theoretical value from the t-distribution. Depending on the outcome, we either accept the null or alternative hypoth- esis based on a probability value (alpha). An alpha value of 0.05 is commonly used to accept the alternative hypothesis 2, 4 . Although t-Tests are relatively robust, they are based on sev- eral assumptions: e data are continuous, not categorical. e sample data have been randomly sampled from a population. e variance is assumed to be equal (similar in each group). However, this is no longer an issue with computers, and we can default to test with unequal variances. e distributions are approximately nor- mal. For two-sample t-Tests, we must have independent samples. If the samples are not independent, then a paired t-Test may be appropriate 2, 4 . e number of observations should be ≥ 12 for each sample. With ≥ 12 observations, pre- cision is maximized by decreasing the width of the confidence interval of the mean. is pro- vides enough power for the t-Test. Power is the conditional probability that you will avoid a Type II error, accepting the null hypothesis when, in fact, it's false. Figure 1: Analysis tools. Table 2: t-Test: two-sample assuming unequal variances Table 1: Data, Sample A and Sample B