Question

Donating Blood to Grandma? Can young blood help old brains? Several studies \(^{32}\) in mice indicate that it might. In the studies, old mice (equivalent to about a 70 -year-old person) were randomly assigned to receive blood plasma either from a young mouse (equivalent to about a 25 -year-old person) or another old mouse. The mice receiving the young blood showed multiple signs of a reversal of brain aging. One of the studies \(^{33}\) measured exercise endurance using maximum treadmill runtime in a 90 -minute window. The number of minutes of runtime are given in Table 2.17 for the 17 mice receiving plasma from young mice and the 13 mice receiving plasma from old mice. The data are also available in YoungBlood. $$ \begin{aligned} &\text { Table 2.17 Number of minutes on a treadmill }\\\ &\begin{array}{|l|lllllll|} \hline \text { Young } & 27 & 28 & 31 & 35 & 39 & 40 & 45 \\ & 46 & 55 & 56 & 59 & 68 & 76 & 90 \\ & 90 & 90 & 90 & & & & \\ \hline \text { Old } & 19 & 21 & 22 & 25 & 28 & 29 & 29 \\ & 31 & 36 & 42 & 50 & 51 & 68 & \\ \hline \end{array} \end{aligned} $$ (a) Calculate \(\bar{x}_{Y},\) the mean number of minutes on the treadmill for those mice receiving young blood. (b) Calculate \(\bar{x}_{O},\) the mean number of minutes on the treadmill for those mice receiving old blood. (c) To measure the effect size of the young blood, we are interested in the difference in means \(\bar{x}_{Y}-\bar{x}_{O} .\) What is this difference? Interpret the result in terms of minutes on a treadmill. (d) Does this data come from an experiment or an observational study? (e) If the difference is found to be significant, can we conclude that young blood increases exercise endurance in old mice? (Researchers are just beginning to start similar studies on humans.)

Short answer

The results of the calculations should be written as: (a) The mean run time for mice receiving young blood is \(\bar{x}_{Y}\). (b) The mean run time for mice receiving old blood is \(\bar{x}_{O}\). (c) The difference in means is \(\bar{x}_{Y} - \(\bar{x}_{O}\) which should be interpreted in term of minutes on treadmill. (d) This data comes from an experiment. (e) If the difference found is significant, it suggests young blood could potentially improve exercise endurance in older mice, although further research and analysis are necessary before making definitive conclusions.

Step-by-step solution

Calculate the Mean of the Young Group

First, sum up all the run times for the mice receiving young blood and divide by the total number of mice. Using the data given \(\frac{27+28+31+35+39+40+45+46+55+56+59+68+76+90+90+90+90}{17}\) will provide the mean run time, denoted as \(\bar{x}_{Y}\).

Calculate the Mean of the Old Group

Using the same method as in Step 1, calculate the mean for the mice receiving old blood. Sum all the run times for these mice and divide by the total number of these mice. We calculate \(\frac{19+21+22+25+28+29+29+31+36+42+50+51+68}{13}\) to get the mean run time, \(\bar{x}_{O}\).

Calculate the Difference in Means

Subtract the mean of the older group from the mean of the younger group. We use the formula \(\bar{x}_{Y} - \(\bar{x}_{O}\) to find the difference in means, which measures the effect size of the young blood.

Interpret the Result

The result of Step 3 should be interpreted in terms of minutes on a treadmill. A positive difference would indicate that young blood can potentially improve exercise endurance in old mice, as they are able to run for a longer time.

Identify the Type of Study

Based on the problem description, this is an experiment since the mice were deliberately administered either young or old blood and observed for changes in their exercise endurance.

Significance Result Interpretation

If the difference in means is significant, this would imply that young blood could help increase exercise endurance in older mice. However, it's important to note that statistical significance does not guarantee the result would be equally substantive in real-world applications. Researchers consider additional factors, including practical significance, biological plausibility, ethics, and potential side-effects, before drawing any definitive conclusions.

Key concepts

Experimental Design

Experimental design is a critical aspect of scientific research that involves organizing an experiment to ensure accurate and dependable results. In the context of determining whether young blood can improve exercise endurance in older mice, a controlled experiment was conducted. This involved randomly assigning old mice to receive either young or old blood. The level of endurance was measured using treadmill run times over a 90-minute period. By keeping conditions consistent—such as the duration of the test—and only varying the age of the blood received, the design minimizes confounding variables. This approach allows researchers to make stronger inferences about causality; if significant differences are observed in treadmill times, the design supports the hypothesis that the age of the blood plasma may be responsible.

The use of random assignment in the experimental design is especially important as it helps to ensure that any differences in endurance between the two groups can be attributed to the treatment (young blood) rather than other factors. This foundational principle of scientific study design is crucial when interpreting the results and understanding the implications of the research on potential treatments for aging.

Mean Calculation

Mean calculation is a basic statistical method used to summarize the central value of a dataset. In the described exercise, calculating the mean treadmill run time for each group of mice (those receiving young blood and those receiving old blood) provides a clear way to compare overall endurance levels between the two groups. The mean is calculated by adding all individual values and dividing by the number of observations. For instance, the mean endurance time for the young blood group is denoted as \(\bar{x}_{Y}\), and for the old blood group as \(\bar{x}_{O}\).

The mean is highly relevant because it reflects the central tendency of the data, but it can sometimes be misleading if the data are skewed or if outliers are present. Understanding how to calculate and interpret the mean is fundamental for proper data analysis in experimental studies.

Effect Size

Effect size is a quantitative measure that provides insight into the magnitude of a treatment effect within an experiment. In our example, the effect size is represented by the difference in means (\(\bar{x}_{Y} - \bar{x}_{O}\)) between mice receiving young blood and those receiving old blood. This measure is crucial as it helps researchers evaluate the practical significance of their findings, beyond mere statistical significance.

For instance, a large effect size suggests that the change in endurance times due to the treatment (young blood) is both statistically significant and practically meaningful. In contrast, a small yet statistically significant effect size might call into question the practical usefulness of the treatment. By calculating the effect size, researchers can discern whether the observed differences in exercise endurance are likely to have tangible implications for anti-aging treatments.

Data Interpretation

Data interpretation is a vital step in research that involves making sense of the numbers and figuring out what they tell us about the world. After calculating the mean values and effect size, interpreting the data is crucial in drawing conclusions from the experiment. The difference in mean treadmill times between the two groups suggests that receiving young blood may improve the exercise endurance in old mice.

Interpretation goes beyond the figures; it requires understanding the experimental context and considering the findings' biological relevance, ethical ramifications, and reproducibility. If the difference in means demonstrates statistical significance, researchers must then consider if the effect is meaningful in a real-world scenario. They must ask if the benefits observed are substantial enough to suggest a potential treatment for humans, and whether further experimentation is justified. Data interpretation bridges the gap between statistical results and real-world relevance, guiding future research directions and applications.