IX. Significance Testing

Several years ago, Arizona passed a law sparking a fierce debate about a controversial, new medical treatment. The treatment is intended to reverse the initial effects of an abortion and to allow the pregnancy to continue under otherwise healthy conditions. Ordinarily, about 40% of pregnancies continue after the first of two abortion pills have been taken. But in an experimental study, six women were given the new treatment, four of whom went on to deliver healthy babies. Critics say the result is not statistically significant to show that the treatment is effective.

Source: The Atlantic (2015): Can Abortion be Undone?

Use a normal approximation curve to assess the claims above.

a. What is the null hypothesis?

a. What is the mean () in the study?

b. What is the standard deviation ()?

c. Are the results of the study significant at the .05 (5%) level?

Now suppose that a much larger study were conducted with 150 participants receiving the treatment, two-thirds of whom continued their pregnancies without any major problems.

a. What is the mean () in this study?

b. What is the standard deviation ()?

c. Are the results significant at the .01 (1%) level?

d. How should the result be stated so as not to commit a Type-1 or a Type-2 error?

Suppose that you are the executive director for the U.S. Food and Drug Administration. You have decided, as a matter of policy, to only accept prescription drugs that have been shown to be effective at the 1% significance level. A pharmaceutical company submits experimental data in support of a new anti-depressant medication. Their experiment consists of two groups of 1,000 research participants who they tracked for a year. 200 participants within the control group recovered while 250 participants within the experimental group recovered.

How significant is this data?

Based on this data, should the F.D.A. approve the new medication for the general public?

X. Correlation and Causation

Directions: Read the graph below and answer the corresponding questions.

Describe the graph above and one conclusion that you could draw from it.

How might researchers test to see whether the increased consumption of organic food in fact increases the rate of autism?

What would they need to show to prove that the former is causally related to the latter?

The real cause of increasing autism prevalence? 25000- 300000 Autism 20000- Organic Food Sales 200000 15000 Individuals Diagnosed Sales ($ millions) 10000- 100000 5000- r=0.9971 (p