Introduction to Experiments (College Board AP® Statistics): Revision Note

Introduction to experiments

What is an experiment?

• An experiment is a type of study where certain conditions (treatments) are applied to items or individuals (experimental units) to see if it causes a response

  • When experimental units are people they can also be called subjects

• For example, if 10 swimmers from a club are given a new type of swim cap to see if it improves the time it takes to swim one lap, then:

  • an experimental unit is 'a swimmer from the club'

  • the treatment is 'being given a new type of swim cap'

What are explanatory and response variables in experiments?

• The explanatory variable is the quantity or property that you want to change to see if it causes a response

  • The treatment is a change in this explanatory variable

    • (or sometimes the combined change of multiple explanatory variables)

  • An explanatory variable is also referred to as a factor

  • The different categories or specific values of this explanatory variable that are imposed on the experimental units are called its levels

• The response variable is the response shown by the experimental units after the treatment has been applied

  • This can often be measured on a scale

• For the swimming example above:

  • the explanatory variable is 'the type of swim hat'

  • the response variable is 'the time it takes to swim one lap'

• The key question in an experiment is

  • "Does a change in the explanatory variable cause a change in the response variable?

What is an observational study?

• An observational study is a way of finding out information from a sample by simply recording what you observe naturally

  • e.g. filling in a tally chart or a sending out a questionnaire (sample survey)

• They can be either

  • retrospective, where data is collected then analyzed

    • e.g. sample surveys

  • or prospective, where a sample is observed for a period of time into the future

    • e.g. following the behavior of a class of students over two years

How is an experiment different to an observational study?

• In an observational study, you do not influence or change the individuals

  • You simply observe them

• However, in experiments you do influence the individuals because you impose a treatment on them to see if it causes a response