Transformations of Data Example 1 illustrated the use of two-w...

Question

Transformations of Data Example 1 illustrated the use of two-way ANOVA to analyze the sample data in Table 12-3. How are the results affected in each of the following cases?

c. The format of the table is transposed so that the row and column factors are interchanged.

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. In a two-way A N O V A. A data table is initially set up with diet type as the rows and exercise level as the columns. If the table is transposed such that exercise level becomes the row factor and diet type the column factor, what happens to the results of the statistical analysis? Awesome. So it appears for this particular prom, we're asked to figure out how our statistical analysis will change if our table is transposed in such a fashion that the exercise level will become the row factor and that the diet type will become the column. Factor. So if the exercise level becomes the row factor and if the diet type becomes the calm factor if our table is transposed, how so what would happen to the results of our statistical analysis? So how will our statistical analysis change if these events take place? So with that in mind, now that we know what we're ultimately trying to solve for, let's take a moment to note, just in case we can't remember, that ANOVA, so this ANOVA represents the analysis of variance. So with that Mind, let us know that our first step that we need to take in order to solve this particular problem is we need to identify the factors and their roles. So let us note that our two factors that we're focusing our attention on are the diet type and the exercise level. So with that in mind, now that we know that we're focusing on the exercise level and the diet type, let us note that the diet type and the exercise level are the two factors within our two-way ANOVA that we're focused on. Our second step now is we need to understand the effect of transposing the table. So as we should recall and note, when we transpose the table, so so when we're transposing the table, that will mean it'll swap the row. The rolls of the rows and the columns. So once again, transposing the table will swap the rolls of the rows and columns. Therefore, as a result, the exercise level will become the row factor and the diet type will become the column factor. Our third step we need to note is we need to perform an analysis of the impact on the statistical results, so we need to analyze what the impact will be on the statistical results. So as we should recall a note, the statistical analysis results, which will be the F values, P values, and interaction effects. Depend only on the data and the factors, not on which is assigned to the rows or columns. Our fourth step is we need to make our final conclusions, so we need to state our conclusion. So as we should note, the results of the two-way ANOVA will remain unchanged. Only the labeling of the output, which factor is called row or column, is switched. So therefore, without a doubt, our final answer would have to be. The statistical results remain the same, but the factor labels are interchanged. 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.

Transformations of Data Example 1 illustrated the use of two-way ANOVA to analyze the sample data in Table 12-3. How are the results affected in each of the following cases?

c. The format of the table is transposed so that the row and column factors are interchanged.

Key Concepts

Two-Way ANOVA

Factor Interaction

Data Transposition

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