Behavioral ResearchChapter 10

Complex Experimental Designs

Simple designs • Composed of one indep var that is

manipulated with two levels and one dep var which is measured.– Example: IV: Stress vs. no stress (control)

• Both measured by a test of cognitive function• Hypothesis: The affects of stress impair cognitive

function stress as well as cognitive function would have to be operationally defined as to what was used as a stressor (IV) and what measurement did one use to measure cognitive function (DV)

Factorial design

• Designs with more than one indep var or factor .– all levels of each indep var are combined with

all levels of the other indep var– The simplest type of factorial design is a 2 X 2

—has two indep var, each having two levels.

Example: 2 X 2– Indep var 1: difficulty of the task—easy or

hard– Indep var 2: attitude of the confederate—

helpful or mocking– Dep var: performance on a cognitive task

Four Experimental Conditions for 2 X 2 Factorial Design– Easy task – helpful confederate– Easy task – mocking confederate– Hard task – helpful confederate– Hard task – mocking confederate

Interpretation of Factorial Designs

• Main Effect The impact of each IV on the DV.

-The number of main effects depends on the number of Independent Variables.

• InteractionThe effect of any combination of two or more IV. on the D.V..

– The effect that an independent variable has on the dependent variable depends on the level of the other independent variable.

Example: Factorial design

Examining the after-effects of exposure to an irritating noise on several behavioral measures as a measure of frustration: Two levels of each independent variable

• Hypothesis: IV one: Irritating noise: loud vs. soft IV two: Predictability: predictable vs. non

predicable DV: Number of attempts at difficult puzzle during different noise levels

Noise intensity vs. Predictability

Loud Soft

Predictable Group 1 Group 2

Unpredictable Group 3 Group 4

Noise intensity vs. Predictability

Loud Soft

Predictable 7 8

Unpredictable 3 5

Calculating Main Effects: Comparing Row and Column

MeansColumn Means: Loud= 5 Soft = 6.5

Row Means: Predictable = 7.5 Unpredictable = 4

Interpretation of Main Effects– A reliable difference in the column means

would indicate an effect of noise intensity, independent of noise predictability

– A reliable difference in the row means would indicate an effect of noise predictability, independent of noise intensity

Interactions

• Number of attempts to solve the difficult puzzle was greater when the noise was soft than when it was loud.

• However, this relationship was dependent on whether the noise was unpredictable

Effects of Predictable vs. Unpredictable Loud vs. Soft Noise on Puzzle Attempts

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Loud VS. Soft

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Predictable

Unpredictable

Factorial Designs With Manipulated and Nonmanipulated Variables: IV X PV Designs

– allow researchers to investigate how different types of individuals respond to the same manipulated variable

– E.g., of Participant variables – gender, age, ethnic group, personality characteristics

– The simplest IV X PV design includes one manipulated independent variable with at least two levels and one Participant variable with at least two levels

– E.g., Participant variable – two different age groups; or males vs. females

IV X PV design, Furnham, Gunter, Peterson (1994)

– Showed that the ability to study with a distracting task in the room is affected by whether you are more extraverted or introverted

– Manipulated var—distraction– Subject var—extroversion or introversion– Measured var—reading comprehension– A repeated measures design was used college

students read material in silence and within hearing range of a TV program

Results– Overall, students had higher comprehension

scores when they studied in silence– Interaction between extraversion and

distraction– Without a distraction, the performance of

extraverts and introverts was the same– However, extraverts performed better than

introverts when the TV was on.

Further Considerations in Factorial Designs

• If you were to have a 2 x 2 x 2 factorial design, you could look at it as two 2 x 2 designs.– E.g., 2 (instruction method: lecture or discussion) x

2 (class size: 10 or 40) x 2 (gender) – Divide 2 x 2s by gender—2x2 for males and 2x2 for

females– Could then look at the main effects and interactions

within each of these 2 x 2s )(three main effects)– gender– lecture vs. discussion– class size (small=10; large= 40)

Interactions in a 2 X 2 X 2– Could also look at the interaction in the 2 x 2 x

2 design—have the possibility of 3 simple interactions

– Instruction method and class size– Instruction method and gender– Class size and gender

» Could also have a three-way interaction, where the effect of the interaction b/t two of the variables differs depending on the particular level of the third variable

» Three-way interactions are complicated and hard to interpret

F-Statistic• Used in Factorial Designs• Is an extension of the t-test. • It is an analysis of variance that is a more general

procedure than the t-test. • When a study has only one independent variable and only

two groups using an F or a t makes no difference.• However analysis of variance (ANOVA) is conducted when

there are more than two levels of an independent variable and when a factorial design with two or more independent variables is used.

• Therefore, the f-test is appropriate for the simplest experimental design as well as more complex.

• T-test demonstrates the relationship between two groups and the within group variability

• F test is the ratio of two types of variance:– Sytematic variance: deviation of the group means from

the grand man which is the mean score of all individuals in all groups. (Grand mean-5.75: Loud=5, Soft = 6.5)• Is small when the differences between group means is small and

increases as the group mean differences increase– Error variance: the deviation of the individual scores in

each group from their respective group mean.

F-Significance• Ratio of Systematic variance over Error

Variance.• Therefore you want systematic variance

(difference between groups as shown by comparing grand mean to group means) to be high.

• Error variance to be low (comparison of individual scores against the group mean)

• Low error variance indicates homogeneity within your groups which will increase your F statistic and be more likely to show significant results.