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Mice and Pain Can you tell if a mouse is in pain by looking at its facial expression? A new study believes you can. The study \(^{12}\) created a "mouse grimace scale" and tested to see if there was a positive correlation between scores on that scale and the degree and duration of pain (based on injections of a weak and mildly painful solution). The study's authors believe that if the scale applies to other mammals as well, it could help veterinarians test how well painkillers and other medications work in animals. (a) Define the relevant parameter(s) and state the null and alternative hypotheses. (b) Since the study authors report that you can tell if a mouse is in pain by looking at its facial expression, do you think the data were found to be statistically significant? Explain. (c) If another study were conducted testing the correlation between scores on the "mouse grimace scale" and a placebo (non-painful) solution, should we expect to see a sample correlation as extreme as that found in the original study? Explain. (For simplicity, assume we use a placebo that has no effect on the facial expressions of mice. Of course, in real life, you can never automatically assume that a placebo has no effect!) (d) How would your answer to part (c) change if the original study results showed no evidence of a relationship between mouse grimaces and pain?

Step by step solution

01

Identify Relevant Parameter and Formulate Hypotheses

The relevant parameter in this case is the degree of correlation between the mouse grimace scale and the level of reported pain. The null hypothesis (\(H_0\)) would be 'there is no correlation between the grimace scale and level of pain'. And the alternative hypothesis (\(H_a\)) would be 'there is a correlation between the grimace scale and the level of pain'.

02

Understand Statistical Significance

Statistical significance refers to the likelihood that the observed correlation in the data was not due to chance. If the authors report that the grimace scale can predict pain levels, it implies that the data shows a significant correlation, implying that the null hypothesis can be rejected and the alternative hypothesis is likely.

03

Discuss Outcome of a Placebo-Controlled Study

If a follow-up study with a non-painful placebo solution is performed and the placebo does not affect the facial expression of the mice, then it is expected that the correlation would not be as extreme as found in the original study. This is because, in theory, a placebo should not cause a grimace according to the grimace scale.

04

Consequence of No Observed Relationship

If the original study showed no evidence of a relationship between grimaces and pain, then the null hypothesis could not have been rejected. Therefore, in a subsequent placebo-controlled trial, we should expect similar results of no correlation between variables.

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Key Concepts

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

Null Hypothesis

In statistical hypothesis testing, the **Null Hypothesis** (\( H_0 \) ) is a fundamental concept. It represents the default position that there is no relationship or effect in the study. In the context of the mouse grimace scale study, the null hypothesis states that "there is no correlation between the grimace scale scores and the level of pain experienced by the mice." This assumption acts as a starting point for the investigation.

The reason for adopting a null hypothesis is to provide an objective baseline. Researchers can test this hypothesis against collected data to determine its validity.
Statistics and certain tests can show if the observed results are unlikely under the null hypothesis, leading to a rejection of it in favor of an alternative hypothesis.

Alternative Hypothesis

The **Alternative Hypothesis** (\( H_a \) ) is the statement that researchers aim to support with their data. It suggests that there is a notable effect or relationship present. In this exercise, the alternative hypothesis posits that "there is a correlation between the grimace scale scores and the level of pain."

Whenever data provides sufficient evidence to reject the null hypothesis, the alternative hypothesis gains support. This hypothesis is vital for driving scientific inquiry, as it challenges existing understanding and encourages new discoveries.

• The alternative hypothesis does not equal proof. It suggests a high likelihood that the relationship or effect exists, based on statistical analysis.
• Determining which hypothesis is supported depends on the significance of the data, assessed through statistical significance tests.

Statistical Significance

**Statistical Significance** is a crucial concept in determining whether the findings of a study are credible or simply due to random chance. It involves calculating the probability that the observed data would occur if the null hypothesis were true.

If the data is statistically significant, it implies that the results are unlikely to have occurred by chance alone, suggesting that the alternative hypothesis might be true. For example, in the mouse grimace study, if the findings show a significant correlation between grimace scores and pain, it means the results are likely valid, and the null hypothesis can be rejected.

A common threshold for significance is a p-value of less than 0.05, which indicates that there is less than a 5% probability that the results happened by chance. Consistently achieving statistical significance strengthens the argument for the validity of the findings. However, it is also important to consider the study design, data quality, and other factors to ensure comprehensive understanding.