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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

Expert verified
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

01

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.
02

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.
03

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.
04

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.
05

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.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Cognitive Function Testing
Cognitive function testing is a critical process used to measure the brain's performance in various tasks. In the context of this exercise, one of the tests used was the "Y-maze" test, a tool used to assess cognitive abilities in animals like mice. The basic principle involves monitoring the ability of the mice to navigate a Y-shaped maze. This requires the use of memory and the ability to adapt to changing circumstances.

In cognitive function testing, especially in experimental settings, it is important to consider the different parameters being measured. With mice, such tests reveal how certain treatments or interventions, like exercise, affect cognitive performance over time. The study in the exercise measured improvements in the Y-maze performance as a direct indicator of enhanced cognition.

These improvements were linked to various biochemical changes within the brain. Specifically, increased exercise was analyzed for its potential to modify specific brain proteins like BMP and noggin. Higher maze performance scores after days 7 and 10 suggest significant enhancements in cognitive capacities due to these molecular changes.

Observing these results provides insights not just for the role of exercise in cognitive development, but also into underlying molecular mechanisms. Such information allows researchers to design better interventions for cognitive impairments in various settings.
P-value Interpretation
P-value interpretation is a cornerstone of statistical analysis in experiments. The p-value helps us determine the significance of our results against a null hypothesis.

In research, a p-value represents the probability that the observed results could have occurred under the null hypothesis. A low p-value (typically less than 0.05) suggests that the results are statistically significant, meaning there is strong evidence against the null hypothesis.

In the context of the exercise, p-values were reported in three different scenarios: improvements in maze performance, reduction in BMP, and increase in noggin levels. Each case presented a p-value of less than 0.01 or in the case of noggin levels, less than 0.001. These low values indicate strong evidence supporting the effects of exercise on brain functions by rejecting the null hypothesis that exercise has no effect.

It is essential to correctly interpret these values to understand the study's results. For example, a p-value of less than 0.01 implies that there's less than a 1% probability that the improvements noted are due to random chance. Even more so, a p-value of less than 0.001 shows extremely strong evidence that changes like increases in noggin levels are directly attributed to the exercise regimen.
Statistical Significance in Experiments
Statistical significance is a concept that helps researchers determine if their findings reflect real-world phenomena rather than random variations. In experiments, establishing statistical significance means that the results observed are unlikely to have occurred if there were no true effect or relationship.

When examining the effects of exercise on cognitive function, statistical significance is crucial. It helps confirm that the patterns observed, such as improved maze performance, are not due to mere chance. This validation is achieved through statistical tests that calculate p-values. A result is often considered statistically significant if its p-value falls below a predetermined threshold (commonly 0.05), demonstrating a strong likelihood that the findings are true.

In our exercise, each reported finding surpassed this threshold, with p-values less than 0.01 and as low as 0.001. This confirmed that the exercise had real, measurable effects on the mice's cognitive functions.

Understanding statistical significance allows researchers to make informed conclusions from the experimental data and apply these findings in developing strategies that can have practical applications. It plays a pivotal role in advancing scientific knowledge by providing a framework through which the reliability of results can be assessed.

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Most popular questions from this chapter

Indicate whether it is best assessed by using a confidence interval or a hypothesis test or whether statistical inference is not relevant to answer it. (a) What percent of US voters support instituting a national kindergarten through \(12^{\text {th }}\) grade math curriculum? (b) Do basketball players hit a higher proportion of free throws when they are playing at home than when they are playing away? (c) Do a majority of adults riding a bicycle wear a helmet? (d) On average, were the 23 players on the 2014 Canadian Olympic hockey team older than the 23 players on the 2014 US Olympic hockey team?

The data in Hurricanes contains the number of hurricanes that made landfall on the eastern coast of the United States over the 101 years from 1914 to 2014 . Suppose we are interested in testing whether the number of hurricanes is increasing over time. (a) State the null and alternative hypotheses for testing whether the correlation between year and number of hurricanes is positive, which would indicate the number of hurricanes is increasing. (b) Describe in detail how you would create a randomization distribution to test this claim (if you had many more hours to do this exercise and no access to technology).

Match the four \(\mathrm{p}\) -values with the appropriate conclusion: (a) The evidence against the null hypothesis is significant, but only at the \(10 \%\) level. (b) The evidence against the null and in favor of the alternative is very strong. (c) There is not enough evidence to reject the null hypothesis, even at the \(10 \%\) level. (d) The result is significant at a \(5 \%\) level but not at a \(1 \%\) level. I. 0.00008 II. 0.0571 III. 0.0368 IV. \(\quad 0.1753\)

Influencing Voters Exercise 4.39 on page 272 describes a possible study to see if there is evidence that a recorded phone call is more effective than a mailed flyer in getting voters to support a certain candidate. The study assumes a significance level of \(\alpha=0.05\) (a) What is the conclusion in the context of thisstudy if the p-value for the test is \(0.027 ?\) (b) In the conclusion in part (a), which type of error are we possibly making: Type I or Type II? Describe what that type of error means in this situation. (c) What is the conclusion if the p-value for the test is \(0.18 ?\)

For each situation described, indicate whether it makes more sense to use a relatively large significance level (such as \(\alpha=0.10\) ) or a relatively small significance level (such as \(\alpha=0.01\) ). A pharmaceutical company is testing to see whether its new drug is significantly better than the existing drug on the market. It is more expensive than the existing drug. Which significance level would the company prefer? Which significance level would the consumer prefer?

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