In Exercises 1–4, use the following listed measured amounts of...

Question

In Exercises 1–4, use the following listed measured amounts of chest compression (mm) from car crash tests (from Data Set 35 “Car Data” in Appendix B). Also shown are the SPSS results from analysis of variance. Assume that we plan to use a 0.05 significance level to test the claim that the different car sizes have the same mean amount of chest compression.

Anova

a. What characteristic of the data above indicates that we should use one-way analysis of variance?

Table showing chest compression data (mm) for small, midsize, large cars, and SUVs from crash tests.

Why Not Test Two at a Time? Refer to the sample data given in Exercise 1. If we want to test for equality of the four means, why don’t we use the methods of Section 9-2 “Two Means: Independent Samples” for the following six separate hypothesis tests?

Image showing six null hypotheses comparing means: μ1=μ2, μ1=μ3, μ1=μ4, μ2=μ3, μ2=μ4, μ3=μ4.

Accepted Answer

Hello there. Today we're gonna solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. In a study comparing the mean test scores of students from 4 different schools, a statician suggests using ANOVA rather than conducting all possible 2 sample T tests between schools. What is the main statistical reason for preferring ANOVA in this scenario? Awesome. So it appears for this particular problem, we're asked to determine what is the main statistical reason for preferring to use an ANOVA over two sample tests for this particular situation, for this particular scenario. So now that we know we're ultimately solving for and. Quickly noting that an ANOVA is an analysis of variance, let us read off our multiple choice answers to see what our final answer might be. A is ANOVA is less powerful than multiple T tests. B is ANOVA is only used when variances are unequal. C is ANOVA controls the overall type 1 error rate when comparing multiple means, and D is ANOVA can only be used for two groups. Awesome. So, first off, in order to solve this particular problem, we need to note and recall that comparing means from more than 2 groups will require multiple 2 sample T tests in order to compare all the pairs. And our second step is we need to note and recall that each additional test will increase the probability of making at least 1 type 1 error across all tests. Our third step is we need to note and recall that an ANOVA is designed to compare all group means at once at the same time, maintaining the overall type 1 error rate at the specified significance level. So that would mean for step 4, therefore, as a result, the main statistical reason to use an ANOVA is its ability to control. the overall type 1 error rate when comparing multiple means. So that will mean, without a doubt, our final answer has to be multiple choice answer letter C, which once again is ANOVA controls the overall type 1 error rate when comparing multiple means. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

Key Concepts

Analysis of Variance (ANOVA)

Null Hypothesis

Significance Level

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