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

b. If the objective is to test the claim that the four car sizes have the same mean chest compression, why is the method referred to as analysis of variance?

Table showing chest compression measurements (mm) for small, midsize, large, and SUV car sizes from crash tests.

Anova

b. If the objective is to test the claim that the four car sizes have the same mean chest compression, why is the method referred to as analysis of variance?

Accepted Answer

Below 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. A researcher collects data on reaction times in units of milliseconds from drivers using 4 different types of dashboard displays. The goal is to test whether the mean reaction times are the same for all display types. The researcher uses ANOVA for the analysis. Why is this method called analysis of variance when the objective is to compare means? Awesome. So it appears for this particular problem we're asked to determine why is this specific method for ANOVA called analysis of variance when the objective is to compare means. So now that we know we're ultimately trying to solve for, let's read off our multiple choice answers to see what our final answer might be. A is because it compares the variances of the groups directly. B is because it uses the variances within and between groups to determine if the means differ significantly. C is because it only analyzes the means of the groups and finally D is because it ignores the differences in means and focuses on medians awesome. So first off, in order to solve this particular problem, we need to note and recall that the researcher, particularly, wants to know if the mean reaction times are the same for all four display types, and Our second step now is to note that the method used is called analysis of variance or ANOVA. So ANOVA once again is analysis of variance. Awesome. Our third step is we need to note that although the goal is to compare means, ANOVA, as we should recall, works by examining the variances between group, means. And within the groups. So, our 4th step is we need to note that it compares the variance due to the differences among group means to the variance within each group. So, fifthly, If the variance, as we should note, between groups is much larger than the variance within groups, it will suggest that the means are not all equal to one another. So that would mean that our 6th and final step, therefore, the method is called the analysis of variance because it uses variances to Test for different differences in means. So it will test for differences in the means. So that means without a doubt, our final answer has to be multiple choice answer letter B, which once again is because it uses the variances within and between groups to determine if the means differ significantly. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video.

Key Concepts

Analysis of Variance (ANOVA)

Null Hypothesis

Significance Level

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