Question

We have seen that light at night increases weight gain in mice and increases the percent of calories consumed when mice are normally sleeping. What effect does light at night have on glucose tolerance? After four weeks in the experimental light conditions, mice were given a glucose tolerance test (GTT). Glucose levels were measured 15 minutes and 120 minutes after an injection of glucose. In healthy mice, glucose levels are high at the 15 -minute mark and then return to normal by the 120 -minute mark. If a mouse is glucose intolerant, levels tend to stay high much longer. Computer output is shown giving the summary statistics for both measurements under each of the three light conditions. (a) Why is it more appropriate to use a randomization test to compare means for the GTT-120 data? (b) Describe how we might use the 27 data values in GTT-120 to create one randomization sample. (c) Using a randomization test in both cases, we obtain a p-value of 0.402 for the GTT-15 data and a p-value of 0.015 for the GTT-120 data. Clearly state the results of the tests, using a \(5 \%\) significance level. Does light at night appear to affect glucose intolerance?

Short answer

Yes, light at night appears to affect glucose intolerance, but it's only statistically significant in the longer term (based on GTT-120 data). There is no statistically significant effect in the short term (based on GTT-15 data).

Step-by-step solution

Understanding the Suitability of Randomization Test

A randomization test is based on the principle of permutation, and its strength lies in its distribution-free nature. It doesn't require data to follow any specific distribution and can precisely estimate population parameters. For GTT-120 data, due to the small sample size, non-normal data, or presence of outliers, it's more appropriate to use the randomization test as it is more robust in such situations.

Sample Creation Using GTT-120 Data

To create a single randomization sample of the GTT-120 data, shuffle the values without considering the light conditions they belong to. After randomization, the first n values could be considered as group one and the remaining as group two. Computing the difference of the means between these two groups gives one randomization sample.

Test Results Interpretation

The p-value for the GTT-15 data is 0.402 and GTT-120 data is 0.015. If the p-value is less than or equal to the significance level (here, \(5 \%\)), then the effect is statistically significant. So, for GTT-120, with a p-value less than 0.05, it is concluded that night light has a statistically significant effect on glucose intolerance. However, in the case of the GTT-15 data, since p-value is greater than 0.05, there is no significant effect of night light on glucose intolerance at the 15 minute mark post-injection.

Key concepts

Randomization Test

The randomization test, also known as a permutation test, is a non-parametric method used in statistics to test the hypothesis about the effect of an intervention. In our case, the intervention is light exposure at night and its potential impact on glucose tolerance in mice. Unlike traditional statistical tests which assume a specific data distribution (e.g., normal distribution), a randomization test does not require any such assumptions, making it an excellent choice for analyzing data that may not meet these assumptions due to small sample size, non-normal data distribution, or the presence of outliers.

Implementing a randomization test involves shuffling the data randomly and recalculating the statistic of interest (such as the mean) for the shuffled data. This process is repeated a large number of times to create a sampling distribution of the test statistic under the null hypothesis. Comparing the actual test statistic to this distribution provides an empirical p-value which indicates the likelihood of observing such a result if the null hypothesis were true. The strength of this test is in its simplicity and robustness, it can be applied to various types of data without concern for the underlying data distribution.

Glucose Intolerance

Glucose intolerance is a condition characterized by higher than normal blood glucose levels following ingestion of glucose. It is often a precursor to diabetes and indicates impaired glucose metabolism. In our exercise scenario, mice undergo a glucose tolerance test (GTT) to assess their body’s ability to manage glucose. Normally, healthy mice would present high glucose levels shortly after the glucose injection (at the 15-minute mark) which would then return to baseline by the 120-minute mark. If a mouse is glucose intolerant, its glucose levels would remain elevated for a longer duration, failing to normalize as expected.

This health parameter is crucial in studies involving metabolic processes and disease, as it can be an early indicator of disorders such as diabetes. Understanding and identifying glucose intolerance through tests like GTT is imperative for early intervention and management of potential metabolic syndromes. Given the importance of accurate measurement and interpretation, the GTT is a fundamental diagnostic tool in both human and veterinary medicine.

Statistical Significance

Statistical significance is the likelihood that a relationship between two or more variables is caused by something other than random chance. In the context of the exercise, statistical significance helps us determine whether light at night truly affects glucose intolerance in mice, as opposed to the observed effects being due to random variation in the data. The p-value is a crucial element in determining statistical significance; it quantifies the probability of obtaining results at least as extreme as those observed, under the assumption that the null hypothesis is true.

In the GTT-120 data from our exercise, a p-value of 0.015 is reported, which is below the commonly used significance level of 0.05. This means there is a 1.5% probability of obtaining the test results if the null hypothesis (that light at night does not affect glucose tolerance) were true. Since this p-value is less than 5%, we reject the null hypothesis and conclude that there is a statistically significant effect of light at night on glucose intolerance in mice. This conclusion assists researchers in validating experimental results and making informed decisions from studies and trials.