MA19.A2.28

Mathematics (2019) Grade(s): 09-12 - Algebra II with Statistics

MA19.A2.28
Describe differences between randomly selecting samples and randomly assigning subjects to experimental treatment groups in terms of inferences drawn regarding a population versus regarding cause and effect.

Unpacked Content

Knowledge

Students know:

Techniques for selecting random samples from a population.
Techniques for randomly assigning subjects to experimental treatment groups.

Skills

Students are able to:

Recognize if a sample is random.
Reach accurate conclusions regarding the population from the sample.
Reach accurate conclusions regarding the cause and effect of an experimental treatment.

Understanding

Students understand that:

Random selection is essential to external validity, or the extent to which the researcher can generalize the results of the study to the larger population.
Random assignment is central to internal validity, which allows the researcher to make causal claims about the effect of the treatment.

Vocabulary

Randomly
Non-randomized
Inference
Treatments
Cause and effect

COS Examples

Example: Data from a group of plants randomly selected from a field allows inference regarding the rest of the plants in the field, while randomly assigning each plant to one of two treatments allows inference regarding differences in the effects of the two treatments. If the plants were both randomly selected and randomly assigned, we can infer that the difference in effects of the two treatments would also be observed when applied to the rest of the plants in the field.

MA19.A2.28 Describe differences between randomly selecting samples and randomly assigning subjects to experimental treatment groups in terms of inferences drawn regarding a population versus regarding cause and effect.