Statistical Inference Module 7

Inferential Statistics We start with a question about a group or groups. The group(s) we are interested in is(are) called the population(s). Examples What is the average number of car accidents for a person over 65 in the United States? Which is more effective at lowering the heartrate of mice, no drug (control), drug A, drug B, or drug C? For the entire world, is the IQ of women the same as the IQ of men?

Inferential Statistics Example 1: What is the average number of car accidents for a person over 65 in the United States? –How many populations are of interest? –What is the population of interest?

Inferential Statistics Example 2: For the entire world, is the IQ of women the same as the IQ of men? –How many populations are of interest? –What are the populations of interest?

Inferential Statistics Example 3: Which is more effective at lowering the heartrate of mice, no drug (control), drug A, drug B, or drug C? –How many populations are of interest? –What are the populations of interest?

Inferential Statistics Suppose we have no previous information about these questions. How could we answer them? –Census: Obtain information about every individual in the population. Advantages –We get everyone, we know the truth. Disadvantages –Expensive, Difficult to obtain, may be impossible. –Sample: Select a subset of individuals from the population. Advantages –Less expensive. Feasible. Disadvantages –Uncertainty about the truth. Instead of surety we may have error.

Inferential Statistics Population

Inferential Statistics Census vs. Sample –If we take a census, we have everyone and we have no need for inference. We know. –If we take a sample, we make inference from the sample to the whole population. –For the 3 examples, it is not likely we can get a census. We will need to use a sample. –Obviously, for each population we are interested in, we must get a separate sample.

Inferential Statistics General Idea of Inferential Statistics –We take a sample from the whole population. –We summarize the sample using important statistics. –We use those summaries to make inference about the whole population. –We realize there may be some error involved in making inference.

Inferential Statistics Example (1988, the Steering Committee of the Physicians' Health Study Research Group) –Question: Can Aspirin reduce the risk of heart attack in humans? –Sample: Sample of 22,071 male physicians between the ages of 40 and 84, randomly assigned to one of two groups. One group took an ordinary aspirin tablet every other day (headache or not). The other group took a placebo every other day. –Summary statistic: The rate of heart attacks in the group taking aspirin was only 55% of the rate of heart attacks in the placebo group. –Inference to population: Taking aspirin causes lower rate of heart attacks in humans.