Question

Exercise 4.19 on page 269 describes a study investigating the effects of exercise on cognitive function. \({ }^{31}\) Separate groups of mice were exposed to running wheels for \(0,2,4,7,\) or 10 days. Cognitive function was measured by \(Y\) maze performance. The study was testing whether exercise improves brain function, whether exercise reduces levels of BMP (a protein which makes the brain slower and less nimble), and whether exercise increases the levels of noggin (which improves the brain's ability). For each of the results quoted in parts (a), (b), and (c), interpret the information about the p-value in terms of evidence for the effect. (a) "Exercise improved Y-maze performance in most mice by the 7 th day of exposure, with further increases after 10 days for all mice tested \((p<.01)\) (b) "After only two days of running, BMP ... was reduced \(\ldots\) and it remained decreased for all subsequent time-points \((p<.01)\)." (c) "Levels of noggin ... did not change until 4 days, but had increased 1.5 -fold by \(7-10\) days of exercise \((p<.001)\)." (d) Which of the tests appears to show the strongest statistical effect? (e) What (if anything) can we conclude about the effects of exercise on mice?

Short answer

Exercise appears to improve cognitive function in mice by improving Y-maze performance, reducing levels of BMP, and increasing levels of noggin. The effect on noggin levels, which did not manifest until 4 days into exercise but had increased 1.5-fold by 7-10 days, seems to be the most statistically significant.

Step-by-step solution

Interpretation of Part (a)

In part (a) of the exercise, a p-value of less than .01 indicates strong evidence against the null hypothesis that exercise does not improve Y-maze performance in mice. Consequently, it is very likely that exercise does improve Y-maze performance, particularly after 7 or more days of exposure.

Interpretation of Part (b)

In part (b), a p-value of less than .01 again indicates strong evidence against the null hypothesis, in this case that exercise does not reduce levels of BMP. Especially given that this effect was observed after only two days of running and remained for all subsequent time-points, it is very likely that exercise does indeed reduce levels of BMP.

Interpretation of Part (c)

In part (c), a p-value of less than .001 provides extremely strong evidence against the null hypothesis that exercise does not increase the levels of noggin. Given that this effect did not change until 4 days but had increased 1.5-fold by 7-10 days of exercise, we can conclude it is highly likely that exercise increases the levels of noggin, but only after a certain time point.

Determine the Strongest Statistical Effect

Given that the p-value for the effect on noggin levels was the smallest, part (c) appears to show the strongest statistical effect.

Conclusion on the Effects of Exercise on Mice

Given the results from parts (a), (b), and (c), it seems quite likely that exercise improves brain function in mice by boosting Y-maze performance, reducing levels of BMP, and increasing levels of noggin. However, the exact mechanism and timescales for these effects warrant further investigation.