Unit 3: Collecting Data

The distribution of measures for individuals within a sample or population describes variation.

The value of a statistic varies from sample to sample. How can we determine whether differences between measures represent random variation or meaningful distinctions?

Statistical methods based on probabilistic reasoning provide the basis for shared understandings about variation and about the likelihood that variation between and among measures, samples, and populations is random or meaningful.

Data-based regression models describe relationships between variables and are a tool for making predictions for values of a response variable. Collecting data using random sampling or randomized experimental design means that findings may be generalized to the part of the population from which the selection was made. Statistical inference allows us to make data-based decisions.

Describe methods of randomized data collection

Describe components of experimental design

Select a random sample using a Table of Random digits

Students will prove their mastery by designing and critiquing study structures to determine if a claim is scientifically valid. They will demonstrate the ability to distinguish between observational studies and experiments, specifically explaining that only random assignment in an experiment allows for a cause-and-effect conclusion.

A primary way students show understanding is by identifying and explaining bias. They will describe how "bad" sampling (like convenience or voluntary response) leads to results that don't represent the population. They will also demonstrate the mechanics of "good" sampling, such as Simple Random Samples, Stratified Samples (to ensure group representation), and Cluster Samples (for efficiency).

Finally, students will demonstrate their skills by evaluating the scope of inference. They will explain whether a study's results can be generalized to a larger population (based on random selection) or if a treatment truly caused an effect (based on random assignment). They will prove they can identify confounding variables—hidden factors that might confuse the results—and suggest ways to control them through blinding or placebos.