91Ó°ÊÓ

A study of genetic influences on diabetes compared normal mice with similar mice genetically altered to remove a gene called \(a P 2\). Mice of both types were allowed to become obese by eating a high-fat diet. The researchers then measured the levels of insulin and glucose in their blood plasma. Here are some excerpts from their findings. \({ }^{24}\) The normal mice are called "wild-type" and the altered mice are called " \(a P 2^{-1-. "}\) Each value is the mean \(\pm\) SEM of measurements on at least 10 mice. Mean values of each plasma component are compared between \(a P 2^{-/-}\)mice and wild-type controls by Student's \(t\) test \((* P<0.05\) and \(* * P<0.005)\). $$ \begin{array}{lcc} \hline \text { Parameter } & \text { Wild Type } & \mathrm{aP2^{-/- }} \\ \hline \text { Insulin (ng/mL) } & 5.9 \pm 0.9 & 0.75 \pm 0.2^{* *} \\ \hline \text { Glucose (mg/dL) } & 230 \pm 25 & 150 \pm 17^{*} \\ \hline \end{array} $$ Despite much greater circulating amounts of insulin, the wild-type mice had higher blood glucose than the \(a P 2^{-1}\) - animals. These results indicate that the absence of aP2 interferes with the development of dietary obesityinduced insulin resistance. Other biologists are supposed to understand the statistics reported so tersely. (a) What does "SEM" mean? What is the expression for SEM based on \(n, \mathrm{x}^{-} \bar{x}\), and s from a sample? (b) Which of the tests we have studied did the researchers apply? (c) Explain to a biologist who knows no statistics what \(P<0.05\) and \(P<0.005\) mean. Which is stronger evidence of a difference between the two types of mice?

Step by step solution

01

Understanding SEM

SEM stands for Standard Error of the Mean. It quantifies how much the sample mean (\(\bar{x}\)) is expected to vary from the true population mean. The formula for SEM is \(\frac{s}{\sqrt{n}}\), where \(s\) is the sample standard deviation and \(n\) is the sample size.

02

Identifying the Test Used

The researchers used the Student's \(t\)-test, which is a statistical test that compares the means of two groups to determine whether there is a statistically significant difference between them.

03

Explaining P-Values

In hypothesis testing, a \(P\)-value is a measure of the probability of obtaining an effect at least as extreme as the one in the sample data, assuming that the null hypothesis is true. A \(P<0.05\) means there's less than a 5% probability that the observed differences or something more extreme are due to random chance, suggesting statistically significant results. A \(P<0.005\) is even stronger evidence, indicating less than a 0.5% probability of the result occurring by random chance.

Unlock Step-by-Step Solutions & Ace Your Exams!

• Full Textbook Solutions

  Get detailed explanations and key concepts

• Unlimited Al creation

  Al flashcards, explanations, exams and more...

• Ads-free access

  To over 500 millions flashcards

• Money-back guarantee

  We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

Key Concepts

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

Standard Error of the Mean (SEM)

The Standard Error of the Mean, often abbreviated as SEM, is a fundamental statistical concept used extensively in biology to assess how well a sample mean estimates the true population mean. When conducting experiments, researchers often gather data from a sample rather than an entire population due to time or logistical constraints. The SEM helps in understanding how close this sample mean (\(\bar{x}\)) is expected to be to the actual population mean.

To calculate the SEM, you use the formula:\[SEM = \frac{s}{\sqrt{n}}\]where:

• \(s\) is the sample standard deviation, signifying how much data points deviate from the sample mean.
• \(n\) is the size of the sample, representing the total number of observations in the study.

A smaller SEM indicates that the sample mean is close to the real mean of the population, providing more confidence in the reliability of the sample data.

In experiments such as those on mice to learn about genetic influences on conditions like diabetes, SEM helps in concluding how much trust can be placed on the mean insulin or glucose levels measured.

Student's t-test

When researchers aim to determine whether there's a statistically significant difference between means from two groups, they often employ the Student's t-test. This test compares the means to see if any observed differences are likely due to a genuine effect rather than random variation.

The Student's t-test assumes that the data are normally distributed and allows scientists to assess hypotheses about population means based on sample data. In biological studies, such as those involving genetically modified mice, the t-test is invaluable for evaluating whether the differences in measured parameters like insulin or glucose levels between groups are statistically significant.

The t-test produces a t-value, which is then used to find the p-value. This p-value ultimately tells us whether the differences are significant or not. With the results from a t-test, scientists can claim a finding is statistically significant if the p-value meets a certain threshold, often set at 0.05 in biological experiments.

P-Value Interpretation

P-values play a crucial role in interpreting the results of statistical tests such as the Student's t-test. They essentially reveal the probability that the observed results occurred by random chance, given the null hypothesis is true.

In biological studies, a p-value less than 0.05 (\(P<0.05\)) indicates that there's less than a 5% probability the observed effect is due to chance. This threshold is a conventional marker for statistical significance, suggesting that the effect is strong enough to reject the null hypothesis, which states no difference or effect exists.

When a study reports a p-value of less than 0.005 (\(P<0.005\)), this indicates even stronger evidence against the null hypothesis, implying less than a 0.5% chance the result is due to random chance. In simple terms, the smaller the p-value, the stronger the evidence against the null hypothesis. In the context of comparing different groups of mice:

• A p-value of < 0.05 suggests a valid statistical difference in the variable being tested.
• A p-value of < 0.005 indicates an even more convincing argument for a genuine effect between the control and experimental groups.

Understanding these values helps biologists and other scientists assess the validity of their experimental conclusions and the likelihood that observed patterns reflect true differences in the population.