### Beyond AP Statistics

#### Probability Basics

#### Small Samples

#### Distributions

#### Power

### Beyond AP Statistics

#### Probability Basics

#### Small Samples

#### Distributions

#### Power

# What is an Experiment?

In an experiment, a researcher manipulates one or more variables, while holding all other variables constant. By noting how the manipulated variables affect a response variable, the researcher can test whether a causal relationship exists between the manipulated variables and the response variable.

View Video Lesson## Parts of an Experiment

All experiments have independent variables, dependent variables, and experimental units.

**Independent variable**. An independent variable (also called a**factor**) is an explanatory variable manipulated by the experimenter.Each factor has two or more

**levels**(i.e., different values of the factor). Combinations of factor levels are called**treatments**. The table below shows independent variables, factors, levels, and treatments for a hypothetical experiment.Vitamin C 0 mg 250 mg 500 mg Vitamin

E0 mg Treatment

1Treatment

2Treatment

3400 mg Treatment

4Treatment

5Treatment

6/* Small screen font size for table */ @media (max-width: 500px) { table.fontsize th, table.fontsize td {font-size:8pt;} } In this hypothetical experiment, the researcher is studying the possible effects of Vitamin C and Vitamin E on health. There are two factors - dosage of Vitamin C and dosage of Vitamin E. The Vitamin C factor has three levels - 0 mg per day, 250 mg per day, and 500 mg per day. The Vitamin E factor has 2 levels - 0 mg per day and 400 mg per day. The experiment has six treatments. Treatment 1 is 0 mg of E and 0 mg of C, Treatment 2 is 0 mg of E and 250 mg of C, and so on.**Dependent variable**. In the hypothetical experiment above, the researcher is looking at the effect of vitamins on health. The dependent variable in this experiment would be some measure of health (annual doctor bills, number of colds caught in a year, number of days hospitalized, etc.).**Experimental units**. The recipients of experimental treatments are called experimental units. The experimental units in an experiment could be anything - people, plants, animals, or even inanimate objects.In the hypothetical experiment above, the experimental units would probably be people (or lab animals). But in an experiment to measure the tensile strength of string, the experimental units might be pieces of string. When the experimental units are people, they are often called participants; when the experimental units are animals, they are often called subjects.

## Characteristics of a Well-Designed Experiment

A well-designed experiment includes design features that allow researchers to eliminate extraneous variables as an explanation for the observed relationship between the independent variable(s) and the dependent variable. Some of these features are listed below.

**Control**. Control refers to steps taken to reduce the effects of extraneous variables (i.e., variables other than the independent variable and the dependent variable). These extraneous variables are called**lurking variables**.Control involves making the experiment as similar as possible for experimental units in each treatment condition. Three control strategies are control groups, placebos, and blinding.

**Control group**. A control group is a baseline group that receives no treatment or a neutral treatment. To assess treatment effects, the experimenter compares results in the treatment group to results in the control group.**Placebo**. Often, participants in an experiment respond differently after they receive a treatment, even if the treatment is neutral. A neutral treatment that has no "real" effect on the dependent variable is called a**placebo**, and a participant's positive response to a placebo is called the**placebo effect**.To control for the placebo effect, researchers often administer a neutral treatment (i.e., a placebo) to the control group. The classic example is using a sugar pill in drug research. The drug is considered effective only if participants who receive the drug have better outcomes than participants who receive the sugar pill.

**Blinding**. Of course, if participants in the control group know that they are receiving a placebo, the placebo effect will be reduced or eliminated; and the placebo will not serve its intended control purpose.Blinding is the practice of not telling participants whether they are receiving a placebo. In this way, participants in the control and treatment groups experience the placebo effect equally. Often, knowledge of which groups receive placebos is also kept from people who administer or evaluate the experiment. This practice is called

**double blinding**. It prevents the experimenter from "spilling the beans" to participants through subtle cues; and it assures that the analyst's evaluation is not tainted by awareness of actual treatment conditions.

**Randomization**. Randomization refers to the practice of using chance methods (random number tables, flipping a coin, etc.) to assign experimental units to treatments. In this way, the potential effects of lurking variables are distributed at chance levels (hopefully roughly evenly) across treatment conditions.**Replication**. Replication refers to the practice of assigning each treatment to many experimental units. In general, the more experimental units in each treatment condition, the lower the variability of the dependent measures.

## Confounding

**Confounding** occurs when the experimental controls
do not allow
the experimenter to reasonably eliminate plausible alternative
explanations for an observed relationship between independent
and dependent variables.

Consider this example. A drug manufacturer tests a new cold medicine with 200 participants - 100 men and 100 women. The men receive the drug, and the women do not. At the end of the test period, the men report fewer colds.

This experiment implements no controls! As a result, many variables are confounded, and it is impossible to say whether the drug was effective. For example, gender is confounded with drug use. Perhaps, men are less vulnerable to the particular cold virus circulating during the experiment, and the new medicine had no effect at all. Or perhaps the men experienced a placebo effect.

This experiment could be strengthened with a few controls. Women and men could be randomly assigned to treatments. One treatment group could receive a placebo, with blinding. Then, if the treatment group (i.e., the group getting the medicine) had sufficiently fewer colds than the control group, it would be reasonable to conclude that the medicine was effective in preventing colds.

## Test Your Understanding

**Problem**

Which of the following statements are true?

I. Blinding controls for the effects of confounding.

II. Randomization controls for effects of lurking variables.

III. Each factor has one treatment level.

(A) I only

(B) II only

(C) III only

(D) All of the above.

(E) None of the above.

**Solution**

The correct answer is (B). By randomly assigning experimental units to
treatment levels, randomization spreads potential effects of
lurking variables
roughly evenly across treatment levels.
Blinding
ensures that participants in control and treatment conditions
experience the
placebo effect equally, but it does not guard against
confounding. And finally, each
factor
has *two*
or more treatment levels. If a factor had only one treatment
level, each participant in the experiment would get the same treatment
on that factor. As a result, that factor would be
confounded with every other factor in the experiment.

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