Individuals / units

Most data sets consist of one or more values that are recorded from each of a set of individuals (or plants, plots of land, repetitions of an experiment or other 'units'). These individuals will vary in many ways other than the variables that are recorded.

There are two different ways in which data can be collected from these units.

Observational studies

Data are collected in an observational study if we passively record (observe) values from each unit.

Most observational studies are conducted by sampling units from some population.

Heights of fathers and sons

The scatterplot below describes the heights (inches) of a randomly selected group of 60 men at age 18 and their fathers' heights at the same age.

Click Take sample a few times to see the heights of other fathers and sons. Observe that both variables vary from data set to data set since the data are observational.

Experiments

In an experiment, the researcher actively changes some characteristics of the units before the data are collected. The values of some variables are therefore under the control of the experimenter. In other words, the experimenter is able to choose each individual's values for some variables.

Type of experiment Possible controlled variables
Agriculture Fertiliser applied to plot of land
Irrigation applied to plot
Time of planting seeds
Psychology Time allowed to memorise text
Type of stimulus in reaction-time test
Industrial Temperature of chemical reaction
Quality of raw materials for a process

Lathe experiment

A mechanical engineer is investigating the surface finish of metal parts produced on a lathe and its relationship to the speed (in RPM) of the lathe. The engineer measures the finish of 4 parts produced at each of 8 lathe speeds, and the resulting data are displayed below.

This is experimental data since the engineer can control the lathe speed (the explanatory variable).

Click Take sample a few times to repeat the experiment and observe that the distribution of lathe speed remains the same — only the response (surface finish) changes in repetitions of the experiment.