Weights from ANSUR I and ANSUR II The following table lists we...

Question

Weights from ANSUR I and ANSUR II The following table lists weights (kg) of randomly selected U.S. Army personnel obtained from the ANSUR I study conducted in 1988 and the ANSUR II study conducted in 2012. If we use the data with two-way analysis of variance and a 0.05 significance level, we get the accompanying display. What do you conclude?

Table showing weights in kg of male and female U.S. Army personnel from 1998 and 2012, with ANOVA results for gender and study.

Accepted Answer

Hello. In this video, we are told that a researcher collects data on blood pressure from a random sample of adults in 2 different cities and across 2 different age groups. The data is analyzed using a two-way Enova and a significance level of 0.05. The Enova output gives the following P values. City has a P value 0.033. The age group has a P value 0.001, and the interaction has a P value of 0.210. Which factors have a statistically significant effect on blood pressure. So in order to approach this problem, the first thing we want to do is we want to determine a null hypothesis for each of the different factors and the interaction. So starting with the city. What is going to be the null hypothesis for the city? Well, the null hypothesis is going to be that there is no difference. In blood pressure. Between cities. So this is going to be our null hypothesis for the city, and the P value for the city is given to us as 0.033. Now let's go ahead and develop the null hypothesis for the age group. The null hypothesis for the age group is going to be that there is no difference. In blood pressure. Between age groups. And the p value given to us for the age group is 0.001. Finally, let's go ahead and determine the null hypothesis for the interactions. Now the null hypothesis for the interactions is going to be that there is no interaction. Between City. And age group. On blood pressure. And the P value given to us for the interactions is 20.210. Now, in order for us to determine whether each of these have a significant or insignificant effect, we want to compare each of their P values to the significance level, and the significance level given to us is 0.05. So let's go ahead and start by comparing the city's P value to the significance level. Now, 0.033 is less than the significance level of 0.05. What this tells us is that we are going to reject the null hypothesis. So we reject the no hypothesis. For the age group comparing the p value to the significance level shows that the p value is less than the significance level, so we also reject the null hypothesis. And comparing the interactions, we again reject or we fail to reject because 0.210 is greater than 0.05. So we fail to reject. On the interactions. Now, what is the significance for these, for these values? So what this tells us is that both the city and age group have a statistically significant effect on their blood pressure, and the interactions between the city and age group do not have a statistically significant effect. And so with that being said, the correct option here is going to be option C. Both city and age group have significant effects, while the interactions don't. So I hope this video helps you in understanding on how to approach this problem, and we will go ahead and see you all in the next video.

Key Concepts

Two-Way Analysis of Variance (ANOVA)

F-Statistic and P-Value

Interaction Effect in ANOVA

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