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?

d. The first sample value in the first cell is changed so that it becomes an outlier.

Accepted Answer

Hello there. Today we're going to 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. Suppose you are conducting a two-way ANOVA on a data set with 3 treatments and 4 blocks. If the last observation in the 3rd treatment and the 2nd block is altered to be an extreme outlier, what is the most likely effect on the results of the two-way ANOVA? Awesome. So it appears for this particular prompt we're asked to determine what is the most likely effect on the results of this specific two way ANOVA, which, as we should recall, an ANOVA means an analysis of variance. So we're trying to figure out what is the most likely effect on this two-way. Analysis of variances considering all the conditions set to us by the prom itself. So we're asked to focus on the condition where the last observation is in the 3rd treatment and 2nd block is altered to be an extreme outlier. So what would be the effect on the results of this two-way ANOVA due to these conditions. So now that we know what we're ultimately trying to solve for. Our first step is we need to identify the structure of the two-way ANOVA. So we need to note that there are 3 treatments, which I'll denote this as T for treatments. So there's 3 treatments and 4 blocks, which I'll call blocks B for short. So that will mean because there's 3 treatments and 4 blocks, that would mean that the data isn't will be arranged in a 3 x 4 table, which I'll put that in parenthesis, so 3 times 4 table. Awesome. Our second step now is we need to understand the role of an outlier in an ANOVA situation. So as we should recall and note, A A N O V A, which once again is an analysis of variance, compares group means and partitions total variance into components due to treatments, blocks, and error. Awesome. So now our third step is we need to predict the effect of an extreme outlier. So as we should recall, an extreme outlier increases the overall variability, how it varies in the data, especially the error or the residual sum of squares. So now our 4th step is we need to explain the impact on F statistics. So as we should recall, since the F statistics or treatments and blocks are calculated as the ratio of mean squares or the treatment of the block to mean square error. Increasing the error mean square, which will be the denominator, will decrease the F values as a result. So that will mean that our 5th step is we need to state the most likely effect on the statistical significance. And as we should recall, with lower F values, it becomes less likely that the ANOVA will detect significant differences among treatments or blocks. So that will mean, without a doubt, our final answer would have to be that The within group errors of squares will increase, causing the F statistics to decrease and reducing the chance of finding significance. So that is our final answer. Hooray, we did it. So once again, our final answer without a doubt has to be the within group error sum of squares will increase. causing the F statistics to decrease and reducing the chance of finding significance. So this particular problem is fairly simple to solve for as long as you have a strong understanding of the conceptual topics that are associated with this type of statistics problem. So once you have a strong understanding of your chapter for all the concepts that are involved, solving this particular problem is very simple. And that's it. 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?

d. The first sample value in the first cell is changed so that it becomes an outlier.

Key Concepts

Two-Way ANOVA

Outliers

Effect on ANOVA Results

Watch next