Chapter 11

Structure of a Two-Factor Experiment

The levels of one factor determine the columns and the levels of the second factor determine the rows

Factorial Design Facts

-A two-factor design has two IVs -A single-factor design has one IV -2 x 3 x 2 design is a three-factor design with a total of 12 conditions

Two-factor design

-Can be represented by a matrix Each cell corresponds to a separate treatment condition (i.e., a specific combination of the factors) -Data provide three separate and distinct sets of information Describes how the two factors independently and jointly affect behavior

Advantages to a factorial design

-Creates a more realistic situation than examining a single factor in isolation -Can see how individual factors as well as the group of factors, acting together, influence behavior

Identifying Interactions

-Graphing the results of a two-factor study -Nonparallel lines (lines that cross or converge) indicate an interaction between the two factors -Note: A statistical test is needed to determine whether the interaction is significant

Interaction Between Factors

-One factor has a direct influence on the effect of a second factor -An example drug interaction: one drug modifying the effect of another drug One drug can exaggerate the effects of another One drug may minimize or completely block the effects of another -Independent factors have no interaction

Two0factor design main effects

-The mean differences among the levels of one factor -A two-factor study has two main effects; one for each factor

Identifying an Interaction in a Data Matrix

1. Compare the mean differences in any individual row with the mean differences in other rows (applies to columns also) -The size and the direction of the differences in one row are the same as the corresponding differences in other rows ►no interaction -Differences change from one row to another ► evidence of an interaction -A statistical test is necessary to determine whether the interaction is significant

Interpreting Main Effects and Interactions

1. Significant effects indicated by a statistical analysis ► be careful about interpreting the outcome -Main effects may present a distorted view of the actual outcome •Each main effect is an average it may not accurately represent any of the individual effects that were used to compute the average

Independence of Main Effects and Interactions

1. The two-factor study allows researchers to evaluate three separate sets of mean differences: -The mean differences from the main effect of factor A -The mean differences from the main effect of factor B -The mean differences from the interaction between factors

Experimental and Nonexperimental or Quasi-Experimental Research Strategies

A factorial study that is a purely experimental research design -Both factors are true independent variables that are manipulated by the researcher •A factorial study for which all the factors are non-manipulated, quasi-independent variables -Note: the non-manipulated variables are still called factors

A mixed design

A mixed design: a factorial study that combines two different research designs •Used when one factor is expected to produce large order effects -A common example of a mixed design is a factorial study with one between-subjects factor and one within-subjects factor

Factorial design

A research design that includes two or more factors (IVs)

In a factorial design experiment, the number of factors is the number of what variables? a. independent b. dependent c. extraneous d. confounding

A. independent

Which of the following is a correct description for a research study comparing problem-solving obtained under three different levels of temperature? a. single factor design b. two-factor design c. three factor- design d. factorial design

A. single factor design

Factor

An independent variable (IV) in an experiment, especially those that include two or more IVs

Which of the following correctly describes a research study comparing problem- solving ability for girls versus boys under three different levels of temperature? a. 2 X 2 design b. 2 X 3 design c. 2 X 2 X 3 design d. none of the above

B. 2 X 3 design

A researcher is trying to determine the best time of day for patients to take a cholesterol medication. A sample of men who have high cholesterol is divided into six groups. One group takes the medication every morning, a second group takes the medication at mid-day, and a third group takes the medication each night. There are also three control groups that receive a placebo instead of the real medication, one in the morning, one at mid-day, and one at night. If the results of the study show a 50-point main effect for the medication (men taking the medicine average 50 points lower cholesterol than men taking the placebo) and also show a significant interaction between medication and time of day, then what can the researcher conclude about the effect of the medication? a. The medication lowers cholesterol by around 50 points and it does not matter time of day it is taken. b. Although the average effect of the medication is to lower cholesterol by 50 points, the exact effect depends on what time of day it is taken. c. Because there is an interaction, you cannot conclude that the medication has any effect on cholesterol. d. None of the other options is an appropriate conclusion.

B. Although the average effect of the medication is to lower cholesterol by 50 points, the exact effect depends on what time of day it is taken.

The following data represent the means for each treatment condition in a two-factor experiment. What pattern of results is shown in the data? A1 A2 B1 M= 20 M= 40 B2 M= 30 M= 50 a. Main effects for both factors and an interaction b. Main effects for both factors and no interaction c. A main effect for factor A, no main effect for factor B, and no interaction. d. A main effect for factor A, an interaction, but no main effect for factor B.

B. Main effects for both factors and no interaction

In a two-factor ANOVA, what is the implication of a significant A X B interaction? a. At least one of the main effects must also be significant. b. Both of the main effects must also be significant. c. Neither of the two main effects can be significant. d. The significance of the interaction has no implications for the main effects.

D. The significance of the interaction has no implications for the main effects.

Statistical Analysis of Factorial Designs

Depends partly on whether the factors are: -Between-subjects -Within-subjects -Some mixture of between- and within-subjects •The standard practice includes: -Computing the mean for each treatment condition (cell) and -Using ANOVA to evaluate the statistical significance of the mean differences

Using the Order of Treatments as a Second Factor

Makes it possible to evaluate any order effects that exist in the data •There are three possible outcomes that can occur: -No order effects -Symmetrical order effects -Nonsymmetrical order effect

Using a Participant Variable as a Second Factor

Purpose is to reduce the variance within groups by using the specific variable as a second factor ►creates a two-factor study -Greatly reduces individual differences within each group -Does not sacrifice external validity

Expanding and replicating a previous study

Replication: repeating the previous study by using the same factor or IV exactly as it was used in the earlier study -Expansion: adding a second factor in the form of new conditions or new participant characteristics •Ascertain whether previously reported effects can be generalized to new situations / new populations

Experimental factorial design

Two or more IVs (factors) are manipulated May involve quasi-independent variables (e.g., age, gender) that are not manipulated

Combined Strategies

Uses two different research strategies in the same factorial design -One factor is a true IV (experimental strategy) -The second factor is a quasi-independent variable (nonexperimental or quasi-experimental strategy) •Falls into one of the following categories: a preexisting participant characteristic or tim

How many participants would be needed for a two-factor experiment with two levels of Factor A and three levels of Factor B if both factors are within subjects and there are five scores in each treatment condition? a. 50 b. 10 c. 15 d. 30

a. 50

Which of the following would allow a researcher to determine whether the treatment effects observed in a single-factor study would also be obtained with older participants? a. Add additional treatments to the original study b. add age as a second factor to the original study c. counterbalance the order in which different age groups are tested. d. limit the range of ages of participants to reduce the variance.

b. add age as a second factor to the original study

How many different hypothesis tests (F-ratios) are contained in a two-factor ANOVA? a. 1 b. 2 c. 3 d. More than 3. The exact number depends on the number of levels or each factor.

c. More than 3. The exact number depends on the number of levels or each factor.

Order effects can be measured and evaluated with a a. counterbalanced single-factor within-subjects design b. factorial design using a participant variable (such as age) as a second factor. c. factorial design using the order of treatments as a second factor d. the other three choices can be used to assess order effects

c. factorial design using the order of treatments as a second factor

Which of the following is an advantage of using gender as a second factor in a study comparing two treatment conditions instead of using a mixed group of males and females in each treatment? a. the two-factor study would show how the treatments affect males and females separately b. the two-factor study would determine whether the treatment effect depends on gender. c. the two-factor study could reduce variance if the scores for males are consistently higher or lower than the scores for females. d. all of the other options are advantage of the two-factor study.

d. all of the other options are advantage of the two-factor study.

A factorial study that measures depression before and after treatment for a treatment group and a control group is an example of? a. between-subjects design b. within-subjects design c. repeated measures design d. mixed design

d. mixed design

The pretest-posttest control group design is an example of a. between-subjects design b. within-subjects design c. repeated measures design d. mixed design

d. mixed design