"[DATA] Measuring Reaction Time Researchers wanted to determin...

Question

"[DATA] Measuring Reaction Time Researchers wanted to determine whether the reaction time (in seconds) of males differed from that of females to a go/no go stimulus. The researchers randomly selected 20 females and 15 males to participate in the study. The go/no go stimulus required the student to respond to a particular stimulus and not to respond to other stimuli. The results are as follows:

a. Is it reasonable to use Welch’s t-test? Why? Note: Normal probability plots indicate that the data are approximately normal and boxplots indicate that there are no outliers.

a. Is it reasonable to use Welch’s t-test? Why? Note: Normal probability plots indicate that the data are approximately normal and boxplots indicate that there are no outliers.

Accepted Answer

Welcome back, everyone. In this problem, a study compares systolic blood pressure measurements between two independent clinics. Clinic X sampled 22 patients, and Clinic Y sampled 16 patients. Diagnostic plots indicate the measurements are roughly normal and no extreme outlayers are present. Should the analyst use Welch's tea test to test for a mean difference? Explain briefly. A says no. Welch's T test is inappropriate because it assumes equal variances across groups. B says no. Welch's T test is inappropriate because sample sizes exceed 15, so a Z test is required instead. C says yes, independence, approximate normality, and allowance for unequal variances make Welch's T test suitable. And the D says no. Welch's tea test is inappropriate because diagnostic plots must show perfect normality before using any tea test. So here we're considering if the analyst should use Welch's tea test, OK? So we want reasons to understand if they should. Now what do we know about Welch's tea test that could help us to solve this problem? Well, recall, OK. That in Welch's tea test. OK. We can apply it or it would be appropriate for two independent samples. Alright, it is appropriate. 4 To independent samples. OK. When populations are approximately normal. It doesn't have to be perfect normality, but approximately normal. And the variances may be unequal variances. May be an equal. Now let's look at what we know about this study to see if Welch'sT test would be best if it fulfills these conditions. Now in our problem statement, notice we're told that we're comparing the measurements between two independent clinics, 2 independent samples, so we can check that off our list. Next, we're also told that the diagnostic plots indicate the measurements are roughly normal. So we can take approximate normality of our list. And then we are also told that no extreme outliers are present. So in that case. This tells us that variances may be unequal. So since it satisfies these conditions, the analysts should use Welch's T test for these three reasons. And if we look back at our answer choices, C would best explain why they should use Welch's tea test. We can be sure by reviewing the other choices. For example, in choice A, it says no it's an inappropriate because it assumes equal variances across groups. But Welch's T test does not assume equal variances. It relaxes that assumption. So A is incorrect. In B, it says it's inappropriate because sample sizes exceed 15, so a Z test is required instead. But the choice between T and Z depends on known population variants, not solely on sample size. So because the population variances are not known, the Z test is not required and. That means B is also incorrect. Finally, he says it's inappropriate because the plots must show perfect normality. But remember, as we said earlier, Welch's T test only requires approximate normality. Therefore, D is also incorrect. So that's why we're sure that C is the correct answer. Thanks a lot for watching everyone. I hope this video helped.

Key Concepts

Welch’s t-test

Normality Assumption

Outliers and Their Impact

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