AP Stats 1.10: Data Collection

The three components of an investigative question

Topic 1.10 returns to the investigative question and connects it to how you collect data, and a well-formed investigative question has three components. The first guides data collection and is phrased in terms of the variable(s) of interest. The second guides the analysis: for a hypothesis test it names the parameter and the direction of the alternative (not equal, greater than, less than, association, or not independent), and for a confidence interval it names the parameter and the goal of estimating it within a range. The third indicates the type of conclusion, including the population the conclusions apply to, and, for an experiment that uses random assignment, whether a cause-and-effect conclusion is allowed.

Ways to collect data

The CED names several study types.

• A census records information from every item or individual in the population.
• An experiment is a study in which a researcher assigns conditions, or treatments, to experimental units. The experimental unit is the unit a treatment is assigned to (people are called subjects or participants), the explanatory variable or factor has levels that become the treatments, and the response variable is the outcome measured after treatment.
• An observational study records variables without imposing treatments. A prospective study follows units forward in time, a retrospective study looks at past data, and a survey collects data from people using a standard set of questions.

Only an experiment imposes treatments, which is the line between the two study types; see experiments vs observational studies.

Confounding and generalizing

A confounding variable offers an alternative explanation for a relationship between the explanatory and response variables. To confound, a variable must be associated with both, which is why observational studies rarely support cause-and-effect claims; see correlation vs causation.

Who is in the sample decides how far your conclusions reach. A sample is random when every unit is selected by a random mechanism such as a random number generator, and random selection lets you generalize to the whole population. A sample is not random when units are deliberately chosen or volunteer themselves, and then you may generalize only to a population similar to those studied.