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.

Table showing chest compression measurements by car size and SPSS ANOVA results with sum of squares, degrees of freedom, F-value, and significance.

P-VALUE If we use a 0.05 significance level in analysis of variance with the sample data given in Exercise 1, what is the P-value? What should we conclude? If the four populations have means that do not appear to be the same, does the analysis of variance test enable us to identify which populations have means that are significantly different?

Accepted Answer

Hello. In this video we are told that a researcher conducts an anova to compare the mean systolic blood pressure among four different diet groups. The SPSS output gives a P value of 0.012. Using a significance level of 0.05. What should the researcher conclude and how does the Inova test specify which diet groups differ in their means? So in order to approach this problem, what we first need to do is we need to go ahead and create a null and alternate hypothesis for the Enova test. Now, the null hypothesis usually includes some form of equality. Now, in the problem itself, we are comparing the systolic blood pressures among 4 different dietary groups. And so for the null hypothesis of this test we are going to assume that the systolic blood pressure between the four groups are going to be equal to each other. So this will be our null hypothesis. And for our alternate hypothesis, an alternate hypothesis is going to be the complement which states that at least. One group differs from the others. So this is going to be our null and alternate hypothesis for the AOA test. Now, what we want to do is we want to go ahead and compare the given P value to this given significance level in order to determine the significance. So, the problem tells us that the SPSS output gives a P value of 0.012. So we know that the given P value. Is 0.012 and they want us to compare this to the significance level of 0.05. So, if we compare these two values together, notice that 0.012 is less than 0.05. So what this means is that we are going to reject. Our null hypothesis. But since we are rejecting our null hypothesis, what does this tell us about the significance? Well, what this tells us is that there are statistically significant differences in the mean systolic blood pressure among the four dietary groups. But we want to note that the Enova test only indicates that at least one group mean is different. It does not specifically tell us which groups differ. In order to determine which groups differ, we would have to use a different test such as a post hoc test or Turkey's HSD test. So with that being said, the correct solution to this problem is going to be option A. So I hope this video helps you in understanding how to approach this problem, and we will go ahead and see you all in the next video.

Key Concepts

Analysis of Variance (ANOVA)

P-value and Significance Level

Post Hoc Tests

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