Two-Way Anova If we have a goal of using the data given in Exe...

Question

Two-Way Anova If we have a goal of using the data given in Exercise 1 to (1) determine whether the femur side (left, right) has an effect on the crash force measurements and (2) to determine whether the vehicle size has an effect on the crash force measurements, should we use one-way analysis of variance for the two individual tests? Why or why not?

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. Researchers are analyzing the durability of plastic panels used in construction. They collect crash stress data from tests using different panel positions, top, bottom, and panel types, type X, Type Y, Type Z. The goal is to determine one, whether the panel position affects the measured stress. 2, whether the panel type affects the measured stress. Should a one-way ANOVA be used for each of these two tests? Explain your reasoning. Awesome. So it appears for this particular prom we're asked to take all the information that is provided to us, and we're asked to determine should a one-way ANOVA be used for each of these two tests and explain our reasoning. So, as we should recall, ANOVA denotes analysis of variance. So with that in mind, now that we know that we're trying to figure out whether or not a one-way ANOVA should be used for each of these two tests and to explain our reasoning, let's read off our multiple choice answers to see what our final answer might be. A is no one way A N O V A cannot handle multiple factors and their interaction. B is yes one way A N O V A is appropriate for testing any number of variables. C is yes 21 way A N O VA tests both effects independently and accurately. And D is no one way ANOVA works only if the sample size is larger than 30. OK. So, first off, in order to solve this particular problem, we need to understand the structure of the study. So, once again, we need to note that the researchers are analyzing two factors, the panel position, which I'll call PP, and the panel position is equal to either top, which I'll call T or bottom B. Awesome. So we have two different types of panel positions, top or bottom, and then we also have panel type, which I'll call PT and the panel type is either equal to type, and then I'll put in parentheses equal to type. X, Y, or Z. Awesome. So once again, so for panel type, it's either going to be X, Y, or Z. Fantastic. So now we need to recall and note the one-way ANOVA limitations. So we need to note and recall once again that a one-way ANOVA is designed to test only one factor at a time, assuming all other conditions are the same. So, once again, so we need to note that it's only for one factor. So I'll call one F for one factor. So we need to note that once again, a one-way ANOVA is designed to test only one factor at a time, assuming all other conditions are the same. And we also at this at this point, we need to note and recall the problem with doing two one-way ANOVAs. So, if we perform separate one-way ANOVAs, the interaction between panel type and panel position will be ignored as a result, and the effects might be confounded as a result, leading to incorrect interpretations. So with that in mind, The correct approach, as we should note, would be, since the study involves two independent variables, such as the panel type and position, we want to examine both their main effects and any interaction. A two-way ANOVA is the correct method, so we can't use a one-way ANOVA. We have to use a two-way ANOVA, and that would be the correct method. So, Without a doubt, we need to note and recall that the interaction means the effect of one factor might be dependent or will depend on the level of the other. So, once again, interaction means the effect of one factor might depend on the level of the other. So with that in mind, without a doubt, our correct answer has to be multiple choice answer letter A, which once again is no. One way A N O V A cannot handle multiple factors and their interaction. 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

One-Way ANOVA

Interaction Effects

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