Question

Research question: Do patients given a new drug experience greater weight loss over the course of 8 weeks than patients given a placebo?

Researchers have developed a new drug to support weight loss in adults. They have designed an experiment in which patients will be randomly assigned to either the treatment or control group. The amount of weight lost by each patient over the course of 8 weeks will be recorded.

If they find that their new drug does contribute to weight loss, they will mass produce it and sell it across the country. If there is not evidence that their new drug contributes to weight loss, they will abandon this project, which they have been working on for years and spent nearly a million dollars developing.

A. State the null and alternative hypotheses that should be used to address the given research question.

What does a Type I error mean in this situation? What are the consequences of making a Type I error in this specific scenario?

What does a Type II error mean in this situation? What are the consequences of making a Type II error in this specific scenario?  

In this scenario, is a Type I or Type II error more serious? Or, are they equally serious? Explain your reasoning.

If you were working with this research team, what alpha level would you use? Explain your reasoning.

B.

A sample consisting of 30 patients was randomly split between the treatment and control groups. After weight loss data were collected, the research team conducted a randomization test for the difference in two means. In the samples, the treatment group lost an average of 7.2 pounds and the control group lost an average of 4.4 pounds. The pooled standard deviation was 2.59 pounds. A p value of 0.0038 was computed using StatKey.

Using the alpha level you selected in part A, are the results statistically significant? Explain why or why not. [5 points]

Compute Cohen’s d. Remember to show all work using the equation editor. [10 points]

Are the results practically significant. Explain why or why not. [5 points]

Answer 1

(A) The hypothesis are :

Null hypothesis H0: The weight loss in new drug is less than or equal to weight loss in placebo.

Alternate Hypothesis H1: The weight loss in new drug is greater than weight loss in placebo

Type 1 error : Rejecting H0 when it is true

In this case, if we make a type 1 error, that is, we reject  H0 i.e The weight loss in new drug is less than or equal to weight loss in placebo and accept H1 i.e that new drug works better than placebo. This means you are making a drug which does not work actually and this will eventually result in low sales and bad reputation of the company.

Type 2 error : Accepting H0 when it is false

In this case, if we make a type 2 error, that is , we accept H0 The weight loss in new drug is less than or equal to weight loss in placebo and reject H1 i.e that new drug works better than placebo. This means you are wasting your money spent on the experiment to make a new drug and this consequence can be a huge loss to the company.

Type 1 error is considered more serious in almost every situation. In our case, selling a drug that does not work creates a long term damage to the company rather than losing 1 million dollars.

The significance level is the probability of rejecting the null hypothesis when it is true. So, a 5% level of significance can be appropriate of this kind of experiment, meaning we are ready to accept 5% of time when the drugs do not work and this is not a big number.

(B) We selected the level of significance to be 5% or 0.05 and the p - value obtained by the test is 0.0038.

We know if p- value is <= level of significance, we reject the null hypothesis and

if p-value > level of significance, we accept the null hypothesis.

In our case, 0.0038 < 0.05, so we reject the null hypothesis and accept the alternate hypothesis. This means that the weight loss by the new drug is more than the placebo, hence, the new drug works.

The results are statistically significant.

The cohen's d is given by :

where,

M₁ = mean of group 1 = 7.2 pounds

M₂ = mean of group 2 = 4.4 pounds

s_pooled = pooled standard deviations for the two groups = 2.59 pounds

N = Sample size = 30

Hence, we have,

d =  

d = 1.08108 * 0.97297 * 0.93333

d = 0.98173

Approximately d = 1

This means that the two groups differ by 1 standard deviation i.e. the two groups are significantly different.

A cohen's d greater 0.8 or more signifies large difference. Therefore, we conclude that the new drug is practically significant because it has large difference compared to placebo.