APS - 4.3

Sampling Variability

The fact that different random samples of the same size from the same population produce different estimates.

Estimates from larger samples…

Are more precise, but not necessarily more accurate.

Statistically Significant

The observed results of a study are too unusual to be explained by solely chance.

Explanations for Variation in Responses between Treatment Groups

1. The treatment doesn’t have a different effect, and the difference occurred because of chance variation.

2. The treatment causes a difference in the average response.

The Scope of Inference

1. Random selection of individuals allows inference only about the population from which the individuals were chosen.

2. Random assignment of individuals to groups allows inference about cause and effect.

Retrospective

Observational studies that examine existing data.

Prospective

Observational studies that track individuals into the future.

Establishing Causation Wen an Experiment Cannot Be Done

• Has a strong, consistent association.

• Larger values of the explanatory variable are associated with stronger responses.

• Cause precedes the effect in time.

• Cause is plausible.

Determining if Data is Statistically Significant

The data is statistically significant when the average difference in the proportion of treatment groups overall is greater than any individual difference in proportion between treatment groups.