The amount of chromium in the diet has an effect on the way the body processes i

Question

The amount of chromium in the diet has an effect on the way the body processes insulin. In an experiment designed to study this phenomenon, four diets were fed to male rats. There were two factors. Chromium had two levels: low (L) and normal (N). The rats were allowed to eat as much as they wanted (M) or the total amount that they could eat was restricted (R). We call the second factor Eat. One of the variables measured was the amount of an enzyme called GITH. The means for this response variable appear in the following table.

A plot of the mean GITH for these diets, with the factor Chromium on the x axis and GITH on the y axis is given below. For each Eat group the points for the two Chromium means are connected.

(a) Describe the patterns you see. Does the amount of chromium in the diet appear to affect the GITH mean? Does restricting the diet rather than letting the rats eat as much as they want appear to have an effect? Is there an interaction?

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(b) Compute the marginal means. Compute the differences between the M and R diets for each level of Chromium. Use this information to summarize numerically the patterns in the plot.

Eat Chromium M R L 4.545 5.175 N 4.425 5.317 5.4 Eat-R 5.2 4.8 D 4.6 4.4 Eat-M Low Normal Chromium level

Explanation / Answer

a) Describe the patterns you see. Does the amount of chromium in the diet appear to affect the GITH mean? Does restricting the diet rather than letting the rats eat as much as they want appear to have an effect? Is there an interaction?

Since the amount of chromium in the diet appears to affect the GITH means, and the mean at the Low chromium level has mean values between those of the Medium, as indicated by the means plot, there is an interaction effect.

Restricting the diet rather than letting the rats to eat as much as they want appears to have an effect as at the Normal levels of chromium, there is a decline in the consumption.

(b) Compute the marginal means. Compute the differences between the M and R diets for each level of Chromium. Use this information to summarize numerically the patterns in the plot.

The marginal means at Low and Normal level are respectively 4.86 and 4.871. The differences between the M and R diest for each level of chromium level is

Thus, the interaction effect may be idenifiable.

-0.011

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