AP Statistics - Section 3C: Experiments

Comprehensive practice flashcards for AP Statistics Section 3C: Experiments, covering confounding, the four principles of experimental design, completely randomized designs, randomized block designs, matched pairs, statistical significance, scope of inference, and data ethics.

What is the difference between a response variable and an explanatory variable?

A response variable measures an outcome of a study, while an explanatory variable may help explain or predict changes in a response variable.

In statistics, when does confounding occur?

Confounding occurs when two variables are associated in such a way that their effects on a response variable cannot be distinguished from each other.

According to the AP Exam Tip, what two relationships must you explain when identifying a potential confounding variable?

You are expected to explain how the variable you choose (1) is associated with the explanatory variable and (2) is associated with the response variable.

What is a treatment in an experiment?

A treatment is a specific condition applied to the individuals in an experiment. If an experiment has several explanatory variables, a treatment is a combination of specific values of these variables.

What is an experimental unit, and what are human experimental units called?

An experimental unit is the object to which a treatment is randomly assigned. When experimental units are human beings, they are often called subjects.

What is a placebo?

A placebo is a treatment that has no active ingredient but is otherwise like other treatments.

In an experiment, what is a factor and what are its levels?

A factor is an explanatory variable that is manipulated and may cause a change in the response variable. The different values of a factor are called levels.

In the Rutgers five-second rule experiment testing $4$ surfaces, $4$ lengths of time, and $2$ bacteria preparations, how many treatments were formed?

There were $32$ treatments formed by combining every possible level ($4 \times 4 \times 2 = 32$).

What is the purpose of a control group in an experiment?

A control group is used to provide a baseline for comparing the effects of other treatments.

What is the placebo effect?

The placebo effect describes the fact that some subjects in an experiment will respond favorably to any treatment, even an inactive treatment.

What distinguishes a double-blind experiment from a single-blind experiment?

In a double-blind experiment, neither the subjects nor those who interact with them and measure the response variable know which treatment a subject is receiving. In a single-blind experiment, only one of these groups does not know.

What is random assignment, and what is its primary purpose in an experiment?

Random assignment means treatments are assigned to experimental units using a chance process. Its purpose is to create roughly equivalent groups of experimental units by balancing the effects of other variables among the treatment groups.

What defines a completely randomized design?

A design in which the experimental units are assigned to the treatments completely at random.

What type of experimental design is displayed in this diagram?

A completely randomized design.

Why does flipping a coin until one treatment group fills up to an equal size violate the principles of a completely randomized design?

Continuing coin flips until one group fills forces the remaining subjects into the other group, making the last subjects very likely to end up in the same group instead of maintaining an independent $50\%$ chance.

What does replication mean in statistics?

Replication means giving each treatment to enough experimental units so that a difference in the effects of the treatments can be distinguished from chance variation due to the random assignment.

What does the principle of control mean in an experiment, and why is it used?

Control means keeping other variables constant for all experimental units. It helps avoid confounding and reduces variability in the response variable.

What are the four principles of experimental design?

1. Comparison
2. Random assignment
3. Replication
4. Control

What is a block in an experiment?

A block is a group of experimental units that are known before the experiment to be similar in some way that is expected to affect the response to the treatments.

What is a randomized block design?

An experimental design in which the random assignment of experimental units to treatments is carried out separately within each block.

What type of experimental design is illustrated in this diagram?

A randomized block design.

What rule of thumb describes the relationship between control, blocking, and randomization?

Control what you can, block on what you cannot control, and randomize to create comparable groups.

What is a matched pairs design?

A common experimental design for comparing two treatments that uses blocks of size $2$. Either two very similar experimental units are paired and randomly assigned different treatments, or each unit receives both treatments in a random order.

Why is it important to randomize the order of treatments when each subject receives both treatments in a matched pairs design?

Randomizing the order prevents confounding from extraneous variables that change over time (such as room temperature changes or order-of-testing fatigue).

When are the results of an experiment considered statistically significant?

When an observed difference in responses between groups is so large that it is unlikely to be explained by chance variation in the random assignment (typically occurring in less than $5\%$ of simulated random assignments by chance alone).

Based on the provided table, what is the difference ($\text{Passenger} - \text{Cell phone}$) in the proportion of drivers who stopped at the rest area?

The difference is $0.375$, calculated as $\frac{21}{24} - \frac{12}{24} = 0.875 - 0.500 = 0.375$.

What specific inferences are justified by random selection versus random assignment?

Random selection of individuals justifies inference about the population from which they were chosen. Random assignment of individuals to groups in an experiment with statistically significant results justifies inference about cause and effect.

What are the three basic principles of data ethics for studies gathering data from human subjects?

1. All planned studies must be reviewed in advance by an institutional review board (IRB).
2. All subjects must give informed consent before data are collected.
3. All individual data must be kept confidential.