1. When Can We Draw Conclusions?
Scope of Inference
When Can We Draw Conclusions?

2. Statistical Inferences
Researchers who conduct statistical studies often want to draw conclusions (make inferences) that go beyond the data they produce.
There are two types:
Inference About the Population – Observational Study
Inference About Cause and Effect - Experiment

3. The U.S. Census Bureau carries out a monthly Current Population Survey of about 60,000 households. Their goal is to use data from these randomly selected households to estimate the percent of unemployed individuals in the population.
Scientists performed an experiment that randomly assigned 21 volunteer subjects to one of two treatments: sleep deprivation for one night or unrestricted sleep. The experimenters hoped to show that sleep deprivation causes a decrease in performance two days later.

4. What type of inference can be made from a particular study?
The answer depends on the design of the study.
Inference about the population can be determined from an observational study
Inference about cause and effect can be determined by an experiment
BUT ONLY IF THE STUDY IS DONE CORRECTLY!

5. In the Census Bureau’s sample survey, the individuals who responded were chosen at random from the population of interest. Random sampling avoids bias and produces trustworthy estimates of the truth about the population. The Census Bureau should be safe making an inference about the population based on the results of the sample.

6. In the sleep deprivation experiment, subjects were randomly assigned to the sleep deprivation and unrestricted sleep treatments. Random assignment helps ensure that the two groups of subjects are as similar as possible before the treatments are imposed. If the unrestricted sleep group performs much better than the sleep deprivation group, and the difference is too large to be explained by chance variation in the random assignment, it must be due to the treatments. In that case, the scientists could safely conclude that sleep deprivation caused the decrease in performance. That is, they can make an inference about cause and effect.

7. However, since the experiment used volunteer subjects, this limits scientists’ ability to generalize their findings to some larger population of individuals.

8. Let’s recap what we’ve learned about the scope of inference in a statistical study.
Random selection of individuals allows inference about the population. An observational study that uses random sampling can make an inference about the population.
Random assignment of individuals to groups permits inference about cause and effect. Well-designed experiments randomly assign individuals to treatment groups.

9. However…
Most experiments don’t select experimental units at random from the larger population. That limits such experiments to inference about cause and effect.
Observational studies don’t randomly assign individuals to groups, which rules out inference about cause and effect.

10. Table of Inference Randomly Assigned to a Treatment? Yes No Population
Cause and Effect
None
Randomly Selected Individuals?