2Simple designsComposed 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 functionHypothesis: 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)
3Factorial 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 varThe simplest type of factorial design is a 2 X 2—has two indep var, each having two levels.
4Example: 2 X 2 Indep var 1: difficulty of the task—easy or hard Indep var 2: attitude of the confederate—helpful or mockingDep var: performance on a cognitive task
6Interpretation of Factorial Designs Main Effect The impact of each indep var on the dep variable:InteractionThe effect of any combination of two or more indep vars on the dep var.The effect that an indep var has on the dep var depends on the level of the other indep var.
7Example: 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 variableHypothesis: IV one: Irritating noise: loud vs softIV two: predictable vs. non predicableDV: Number of attempts at difficult puzzle during different noise levels
8Noise intensity vs. Predictability LoudSoftPredictableGroup 1Group 2UnpredictableGroup 3Group 4
9Noise intensity vs. Predictability LoudSoftPredictable78Unpredictable35
10Calculating Main Effects: Comparing Row and Column Means Column Means: Loud= 5Soft = 6.5Row Means: Predictable = 7.5Unpredictable = 4
11Interpretation of Main Effects A reliable difference in the column means would indicate an effect of noise intensity, independent of noise predictabilityA reliable difference in the row means would indicate an effect of noise predictability, independent of noise intensity
12InteractionsNumber 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
14Factorial Designs With Manipulated and Nonmanipulated Variables: IV X PV Designs allow researchers to investigate how different types of individuals respond to the same manipulated variableE.g., of Participant variables – gender, age, ethnic group, personality characteristicsThe simplest IV X PV design includes one manipulated independent variable with at least two levels and one Participant variable with at least two levelsE.g., Participant variable – two different age groups; or males vs. females
15IV 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 introvertedManipulated var—distractionSubject var—extroversion or introversionMeasured var—reading comprehensionA repeated measures design was used college students read material in silence and within hearing range of a TV program
16ResultsOverall, students had higher comprehension scores when they studied in silenceInteraction between extraversion and distractionWithout a distraction, the performance of extraverts and introverts was the sameHowever, extraverts performed better than introverts when the TV was on.
17Further 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 femalesCould then look at the main effects and interactions within each of these 2 x 2s )(three main effects)genderlecture vs. discussionclass size (small=10; large= 40)
18Interactions in a 2 X 2 X 2Could also look at the interaction in the 2 x 2 x 2 design—have the possibility of 3 simple interactionsInstruction method and class sizeInstruction method and genderClass size and genderCould 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 variableThree-way interactions are complicated and hard to interpret
19F-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.
20F test is the ratio of two types of variance: 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 variabilityF 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 increaseError variance: the deviation of the individual scores in each group from their respective group mean.
21F-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.