The manufacturer of Advil, a common headache remedy,...

The manufacturer of Advil, a common headache remedy, recently developed a new formulation of the drug that is claimed to be more effective. To evaluate the new drug, a sample of 200 current users is asked to try it. After a one-month trial, 180 indicated the new drug was more effective in relieving a headache. At the same time a sample of 300 current Advil users is given the current drug but told it is the new formulation. From this group, 261 said it was an improvement. At the .05 significance level can we conclude that the new drug is more effective?

Key Concepts

Hypothesis Testing

Hypothesis testing is a statistical method used to decide whether there is enough evidence in a sample of data to infer that a certain condition holds for the entire population. It involves formulating a null hypothesis, which represents a default position or a statement of no effect, and an alternative hypothesis, which represents the claim to be tested. The process then uses sample data to determine the likelihood of observing results as extreme as those obtained if the null hypothesis were true.

Null and Alternative Hypotheses

The null hypothesis (H0) is a statement that there is no difference or effect, while the alternative hypothesis (Ha) asserts that there is a difference or effect. In studies that compare formulations or treatments, the null hypothesis typically posits no improvement or no difference in effectiveness, whereas the alternative hypothesis suggests that one treatment is more effective than the other.

Significance Level

The significance level, commonly denoted as alpha (?), is the probability threshold set by the researcher for rejecting the null hypothesis. It represents the maximum allowable risk of a Type I error, which occurs when a true null hypothesis is incorrectly rejected. A common significance level is 0.05, meaning there is a 5% risk of incorrectly claiming a significant effect when none exists.

p-value

The p-value is the probability of observing results at least as extreme as the ones actually observed, assuming that the null hypothesis is true. It is used to measure the strength of the evidence against the null hypothesis. A p-value lower than the predetermined significance level suggests that the observed data is unlikely under the null hypothesis and provides grounds for its rejection.

Comparing Proportions

Comparing proportions is a statistical technique used to determine whether there is a significant difference between the proportions of outcomes (such as improvements or successes) in two or more groups. This technique is particularly useful in experiments and clinical trials where the response is categorical, and it often involves calculating a test statistic to compare the observed differences relative to what would be expected by chance.

Experimental Design and Bias

Experimental design refers to the framework of how an experiment is conducted, including the protocols for assigning participants to treatment groups, controlling for confounding variables, and minimizing bias. Blinding, placebo controls, and randomization are key aspects in ensuring that the results are due to the treatment effect rather than external factors or participant expectations.

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