Two-Way Anova The measurements of crash test forces on the fem...

Question

Two-Way Anova The measurements of crash test forces on the femur in Table 12-3 from Example 1 are reproduced below with fabricated measurement data (in red) used for the left femur in a small car. What characteristic of the data suggests that the appropriate method of analysis is two-way analysis of variance? That is, what is “two-way” about the data entered in this table?

Table showing crash test forces on left and right femurs for different car sizes, with red data for left femur.

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. A nutritionist is studying the effects of two different diets, Diet A and Diet B, and two exercise routines, routine X and routine Y on weight loss in adults. Each participant is assigned to one diet and one exercise routine. What feature of this experimental design indicates that a two-way ANOVA is the appropriate statistical test. Awesome. So it appears for this particular prom, we're asked to take all the information that is provided to us by the prom itself. And we're asked to determine what feature of this particular experimental design indicates that a two-way ANOVA is the appropriate statistical test. And as we should recall, an ANOVA is an analysis of variance. Awesome. So with that in mind, now that we know what 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 each participant's weight loss is classified by both diet and exercise routine, allowing analysis of both factors and their interaction. B is the groups are not independent, so ANOVA is not suitable. C is the outcome is not numerical, so ANOVA cannot be used, and D is only one factor is being tested, so a one way ANOVA is sufficient. Awesome. So it appears for this particular prompt, our first step that we need to take is we need to identify the independent variables. So we need to note and recall there are two independent variables, the diet, which I'll call D, with two levels, diet A and Diet B, and exercise routine, which I'll call ER. And that also has two levels, it has routine X and routine Y. Our second step is we need to recognize the factorial design. So as we should note, each participant is assigned to one combination of diet and exercise routine, creating groups for all possible combinations, which is A and X. A and Y. B and X and B and Y. Which is a factorial design. Awesome. So now with that in mind, our third step is we need to determine the dependent variable. So as we should note and recall, for this particular case, the dependent variable will be weight loss, a continuous outcome measured for each participant. Awesome. So I'll do WL for weight loss, so we'll know that once again that weight loss is our dependent variable. So dependent, so I'll call it DEP for short, so dependent variable. So now, our fourth step is we need to connect the two-way ANOVA. So with that in mind, we need to recall a note that a two-way ANOVA is appropriate because it tests for the main effects of each independent variable and their interaction effect on a continuous dependent variable in a factoral. Or a factorial design. So that will mean, without a doubt, that our multiple choice answer that has to be correct for this particular problem is multiple choice answer letter A. Which states that each participant's weight loss is classified by both diet and exercise routine, allowing analysis of both uh both factors and their interaction. And that's it. That is our final answer. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

Key Concepts

Two-Way ANOVA

Interaction Effects

Factorial Design

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