Experimental Study — Definition, Formula & Examples
An experimental study is a study in which the researcher chooses which subjects get a treatment, so the effect of that treatment can be measured directly. Researchers do not just watch what happens. They make something happen on purpose and record the results.
An experimental study is a statistical study in which the investigator deliberately imposes one or more treatments (levels of an explanatory variable) on experimental units and then measures a response variable. A well-designed experiment uses comparison (usually a control group), random assignment of units to treatments, and replication. Under these conditions, a statistically significant difference in responses supports a cause-and-effect conclusion.
Worked Example
Problem: A researcher has 40 tomato plants. She randomly assigns half to receive a new fertilizer and half to receive none. After 6 weeks, the fertilized plants have a mean height of 30 cm and the unfertilized plants have a mean height of 25 cm. Identify the parts of this experimental study and find the observed treatment effect.
Step 1: Split the plants into groups. Random assignment puts half the plants in each group. The unfertilized group is the control group.
Step 2: Name the variables. The explanatory variable is fertilizer (yes or no). The response variable is plant height after 6 weeks.
Step 3: Compare the group means to find the observed difference.
Answer: The fertilized plants grew 5 cm taller on average. Because the researcher assigned the treatment at random, a hypothesis test that finds this difference significant would support the claim that the fertilizer caused the extra growth.
Why It Matters
Experimental studies are the main way to show cause and effect. Clinical drug trials and agricultural field tests rely on them. On the AP Statistics exam, you are often asked to say whether a study is an experiment or an observational study and to explain what conclusions it allows.
Common Mistakes
Mistake: Calling any study that collects data an experiment, even when researchers only survey or observe people who chose their own behavior.
Correction: A study counts as an experiment only if the researcher imposes the treatment. If subjects pick their own group, such as smokers versus non-smokers, it is an observational study. An observational study can show an association, but on its own it cannot establish causation.