Question

The mice in the study had body mass measured throughout the study. Computer output showing body mass gain (in grams) after 4 weeks for each of the three light conditions is shown, and a dotplot of the data is given in Figure 8.6 . \(\begin{array}{lrrr}\text { Level } & \mathrm{N} & \text { Mean } & \text { StDev } \\ \text { DM } & 10 & 7.859 & 3.009 \\ \text { LD } & 8 & 5.926 & 1.899 \\ \text { LL } & 9 & 11.010 & 2.624\end{array}\) (a) In the sample, which group of mice gained the most, on average, over the four weeks? Which gained the least? (b) Do the data appear to meet the requirement of having standard deviations that are not dramatically different? (c) The sample sizes are small, so we check that the data are relatively normally distributed. We see in Figure 8.6 that we have no concerns about the DM and LD samples. However, there is an outlier for the LL sample, at 17.4 grams. We proceed as long as the \(z\) -score for this value is within ±3 . Find the \(z\) -score. Is it appropriate to proceed with ANOVA? (d) What are the cases in this analysis? What are the relevant variables? Are the variables categorical or quantitative?

Short answer

a) The LL group of mice gained the most weight on average and the LD group gained the least weight on average. b) The standard deviations are not dramatically different. c) Assuming we have calculated the Z-score for the outlier in the LL sample, if it is within ±3, we proceed with ANOVA. d) The cases are the different mice while the light conditions and body mass changes are the variables. Light conditions is a categorical variable and body mass change is a quantitative variable.

Step-by-step solution

Identify Body Mass Variation

We can identify which group of mice gained the most and the least mass by looking at the 'Mean' column in the table. The group with the highest mean gained the most weight, while the group with the lowest mean gained the least weight.

Check Standard Deviations

We need to see if the standard deviations are not dramatically different. We do this by checking the 'StDev' column in the table. If the standard deviations of each group are relatively close to each other, we can say that the requirement is met.

Calculating the Z-Score

The Z-score of a particular data point refers to how many standard deviations it's away from the mean. We need to calculate the Z-score for the outlier of the LL sample at 17.4 grams. The formula to calculate the Z-score is: Z = (X - μ) / σ, where X is the data point, μ is the mean, and σ is the standard deviation. If the Z-score is within ±3, we can proceed with ANOVA.

Identifying Cases and Variables

The cases in this analysis are the different mice, while the relevant variables are the light conditions (DM, LD, LL) and the body mass changes. Light conditions (DM, LD, LL) is a categorical variable as it places mice into distinct groups. Body mass change is a quantitative variable as it can be measured and exists on a numerical scale.