1.10 The Investigative Question Revisited and Data Collection

Determine the components of an investigative question within a statistical study.

• The first component of an investigative question should guide the data collection process and should be phrased in terms of the variable(s) of interest in the study.
• The second component of an investigative question should guide the data analysis choice.
  • i. In the case of a hypothesis test, the investigative question should make clear the parameter and the direction of the alternative hypothesis (i.e., not equal, greater than, less than, association, not independent).
  • ii. In the case of a confidence interval, the investigative question should make clear the parameter and the goal of estimation of that parameter within a range of potential values.
• The third component of an investigative question should indicate the type(s) of conclusion(s) applicable from the study. The investigative question should provide the population to which the conclusions will be applicable and, in the case of an experiment that uses random assignment, a cause-and-effect conclusion.

Identify a census.

• A census consists of recording information from all items or individuals in a population.

Identify an experiment.

• An experiment is a study in which a researcher assigns conditions, or treatments, to experimental units to explore an investigative question of interest about the population.
• The experimental unit is the observational unit to which the treatment is assigned. When experimental units consist of people, they are sometimes referred to as subjects or participants.
• An explanatory variable, or factor, is a variable whose different categories, or levels, are imposed on the experimental units. The different categories, or levels, of the explanatory variable are called treatments. When there is more than one explanatory variable, the combinations of the categories, or levels, of the explanatory variables are called treatments.
• A response variable is an outcome measured on each experimental unit after the treatment has been administered.

Identify an observational study.

• An observational study is a study where treatments are not imposed. The researcher records the values of the variables of interest in order to explore an investigative question of interest.
• A prospective study is one in which the observational units of study are selected at a point in time, and data are gathered both at that time and into the future.
• A retrospective study is one in which the observational units of study are selected at a point in time and data from the past are gathered.
• A survey is an observational study in which the data are collected from humans using a standard set of questions.
• A confounding variable in an observational study provides an alternative explanation for the observed relationship between the explanatory and response variables determined in the study, thereby reducing the possibility of concluding a causal relationship between the explanatory and response variables of interest. To be a confounding variable, a variable must be associated with both the explanatory variable and the response variable.

Justify the appropriateness of generalizations for a statistical study.

• A sample is considered random when all observational units in the sample are selected from the population using some type of random mechanism, such as a random number generator.
• When observational units, or experimental units, in a sample are randomly selected from a population, it is appropriate to make generalizations about the entire population of individuals from which the sample was selected.
• A sample is not randomly selected when observational units are deliberately chosen or volunteer themselves to be in the sample.
• When observational units, or experimental units, in a sample are not randomly selected from a population, it is appropriate to make generalizations only about a population of individuals that are similar to those used in the study.