Question

A 1993 study showed that college students temporarily gained up to 9 IQ points after listening to a Mozart piano sonata. This conclusion, dubbed the Mozart effect, has since been criticized by a number of researchers who have been unable to confirm the result in similar studies. Suppose that you wanted to see whether there is a Mozart effect for students at your school. a. Describe how you might design an experiment for this purpose. b. Does your experimental design include direct control of any extraneous variables? Explain. c. Does your experimental design use blocking? Explain why you did or did not include blocking in your design. d. What role does randomization play in your design?

Short answer

An experiment can be designed by selecting a group of students and dividing them into two groups where one listens to Mozart's music. Direct control of extraneous variables is included by keeping variables like testing time and environment constant. Blocking isn't used as it's unnecessary in this case. Randomization plays a key role in preventing bias.

Step-by-step solution

Experiment Design

To design an experiment, start by defining a clear hypothesis to test if listening to a Mozart piano sonata has any effect on student's IQ. Then, select a representative sample of students from the school. Divide them into two groups randomly: a control group that will carry on their normal activities without any interference, and an experimental group that will listen to a Mozart piano sonata before taking an IQ test.

Direct Control of Extraneous Variables

The experiment design does include direct control of extraneous variables. An extraneous variable that could affect the IQ results, such as the time of day the test is taken or the environment in the testing room, are kept constant for all participants to avoid biased results. All students take the test under the same condition at the same time of day.

Use of Blocking

The experimental design does not include blocking. This is because there is only one treatment being tested (listening to Mozart) and it would be sufficient to control for extraneous variables without requiring to block the participants into subgroups based on any characteristic, such as sex, age group etc.

Role of Randomization

Randomization plays a role in this design by preventing bias in the selection of participants and allocation of treatments. Students are randomly selected from different classes to ensure no particular group (like high achievers) is overrepresented. Assigning students randomly to control and treatment groups also ensures that the effects measured can be attributed to the treatment (listening to Mozart's sonata) and not to some other uncontrolled variable.

Key concepts

Experiment Design in Statistics

When designing an experiment in statistics, the main goal is to structure the process in such a way that it highlights the relationship between the independent variable, which is manipulated, and the dependent variable, the outcome being studied. It is crucial to start with a clearly defined hypothesis. For example, if you're studying the so-called Mozart effect, your hypothesis might be that listening to a Mozart piano sonata enhances a student's IQ.

Once the hypothesis is set, a representative sample needs to be selected, which can provide insights that are applicable to the larger population. In the case of the Mozart effect, that would be a cross-section of students from the school. Then, these students ought to be divided into two groups: the control group, who do not listen to the sonata, and the experimental group, who do. This allows for a comparison to determine the effect of the independent variable.

The experimenter must also decide on the treatment procedures. For students, this would entail when and how they listen to the sonata before taking an IQ test. Ensuring the credibility of the outcome necessitates a meticulous approach to every aspect of the experiment's design.

Control of Extraneous Variables

The validity of an experimental outcome hinges on the control of extraneous variables—those which are not the independent variable being studied but could influence the results. In the context of determining the Mozart effect, any factor other than the sonata itself that could impact IQ scores qualifies as an extraneous variable.

It is vital to control for such factors to mitigate the risk of a false association between the treatment and the outcome. You would ensure that all participants, regardless of the group they are in, take the IQ test in the same environment and at the same time of day. By maintaining consistency in these conditions, you are effectively neutralizing the influence of potential confounders. Sometimes, it is impossible to control all extraneous variables, and this is where randomization becomes a key component.

Randomization in Experiments

Randomization is a cornerstone principle in experimental design that involves assigning subjects or test units to different conditions or treatments based on chance rather than choice. This method is essential in ensuring that the experiment is as fair and unbiased as possible.

By randomizing the assignment of students to either the control group or the experimental group, you reduce the impact of extraneous variables that have not been controlled directly. This randomization process ensures each student has an equal chance of being allocated to any condition, thus balancing out known and unknown factors that could affect the results across groups. Such a method also aids in the creation of statistically valid inferences, allowing for the more reliable generalization of the results to the larger population.

Blocking in Experimental Design

Blocking is an experimental design technique used to group subjects with similar attributes together, and then performing the experiment within these blocks. By doing so, it aims to remove sources of variability related to those attributes.

However, in our exercise concerning the Mozart effect, blocking was deemed unnecessary since only one treatment (listening to Mozart) was tested, and the extraneous variables were considered controllable. In cases where there are more treatments or the influence of specific subject characteristics (like age or previous knowledge of music) is suspected to interact with the treatment, blocking would be integral to the experimental design. It would allow for more precise estimates of the treatment effect by controlling the within-block variation, which could be substantial.