Chapter 11 Textbook Notes PDF

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Chapter 11 Textbook Notes...

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Chapter 11: Factorial Designs: 11.1: Introduction to Factorial Designs:  In real-life situations, variables rarely exist in isolation. There is often a variety of variables acting and interacting simultaneously. - Factorial designs: research studies that include more than one independent variable (quasi-independent variable); used to examine more complex, real-life situations. - 2 factors can act together, creating unique conditions, different from either factor alone  Experimental studies: involve manipulation of two or more independent variables - It is possible for factorial designs to involve variables such as gender & age, that are not manipulated and are therefore quasi-independent variables  Factorial designs have: 2 independent variables; 2 x 2 matrix shows 4 different combinations of the variables, producing 4 treatment conditions to be examined.  Factors: term for the independent variables when 2 or more independent variables are combined in a single study; denoted by letters (A,B,C…)  Factorial Design: study including two or more factors  Two-Factor Design: design described the number of its factors  Single-Factor Design: design with only one independent variable  Levels: number of values EX: 2 levels for one factor, 2 levels for the other factor = 2 x 2 (two by two) EX: 2 x 3 = 2 factorial design with 2 levels of first factor & 3 levels of second factor = 6 treatment conditions EX: 2 x 3 x 2 = three-factor design with 2, 3, & 2 levels of each of the factors for a total of 12 treatment conditions  Advantage of factorial designs: creates a more realistic situation which can be obtained by examining a single factor in isolation 11.2: Main Effects & Interactions:  Structure of a two-factor design can be represented by a matrix in which levels of one factor determine columns and levels of the second factor determine the rows; then the mean differences among the rows define the main effects for 1 factor, and the mean differences among the columns define the main effect for the 2nd factor.  Each cell in matrix = specific combination of the factors (separate treatment condition) Main Effects:  Main effect: difference between the 2 column means; mean differences among the columns determine the main effect for one factor.  Statistical test determines whether mean difference is significant. The Interaction Between Factors:  Some situations where effects of one factor are completely independent of the levels of the second factor. - Neither factor has a direct influence on the other  Some situations where one factor does have a direct influence on the effect of a second factor = Interaction between factors (interaction): 2 factors, acting together, produce mean differences that are not explained by the main effects of the 2 factors. If the main effect for either factor applies equally across all levels of the 2nd factor, then the 2 factors are independent & there is no interaction.

Alternative Views of the Interactions between Factors:  Different perspective on the concept of an interaction focuses on the notion of independence, as opposed to dependence, between the factors.  Interaction: when the effects of one factor depend on the different levels of a second factor  When two factor study results are graphed, lines that cross or converge (nonparallel) are an interaction. Constant distance between lines = no interaction Identifying Interactions:  Do this by comparing the mean differences in any individual row (column) with the mean differences in other rows or columns.  If size & direction of differences in 1 row/column are the same as corresponding differences in other rows/columns, then there is no interaction. Differences = interaction Interpreting Main Effects & Interactions:  Mean differences between columns & rows = main effects in 2 factor study  Extra mean differences between cells = interaction- must be evaluated by statistical hypothesis before they can be considered significant  If analysis results in significant interaction, then main effects, whether significant or not, may present distorted view of the actual outcome  Because each main effect is an average, it may not accurately represent any of indiv. effects used to compute average. Independence of Main Effects & Interactions:  Two factor study allows researchers to evaluate 3 separate sets of mean differences; mean differences from main effect of factor A, then from factor B, then from the interaction between factors; all three are separate & completely independent. 11.3: Types of Factorial Designs & Analysis Between-Subjects and Within-Subjects Designs:  Between-subjects: separate group of participants for each of the treatment conditions]  Disadvantages of Between-subjects: can require a large number of participants; individual differences (characteristics that differ from one participant to another) can become confounding variables and can increase variance of the scores  Advantages of Between-Subjects: completely avoids any problem from order effects because each score is completely independent of every other score  Between-subjects is best suited to situations with a lot of participants, small individual differences, order effects are likely.  Within-subjects: a single group of indiv. participates in all of the separate treatment conditions  Disadvantages of Within-subjects: many treatment conditions mean participants might get tired and walk away before finishing (participant attrition); many treatment effects mean including potential for testing effects (fatigue, practice effects) which make it more difficult to counterbalance the design to control for order effects.  Advantages of Within-Subjects: require only 1 group of participants; eliminate or greatly reduce problem w/individual differences  Within-subjects is best suited for situation where individual difference is relatively large & little reason to expect order effects to be large & disruptive Mixed Designs: Within Subjects & Between Subjects:

Mixed study: factorial study that combines two different research designs. Common example is factorial study with one between-subjects factor and one within-subjects factor. Experimental & Nonexperimental or Quasi-Experimental Research Strategies:  It is possible to construct factorial study that is purely experimental research design- both factors are true independent variables that are manipulated by the researcher  It is also possible to construct a factorial study in which all factors are nonmanipulated, quasi-independent variables Combined Strategies: Experimental & Quasi-Experimental or Nonexperimental:  Combined strategy: uses two diff research strategies in the same factorial design- one factor is true independent variable (experimental strategy) and one factor is quasiindependent variable (nonexperimental or quasi-experimental strategy)  The second factor may be preexisting participant characteristic (age/gender) or factor may be time and how the diff treatment effects persist over time Pretest-Posttest Control Group Designs:  Pretest-posttest design: involves 2 separate groups of participants with one group measured before & after receiving treatment & second group is also measured twice before/after treatment but does not receive any treatment between the 2 measurements Higher-Order Factorial Designs:  More complex designs involving three or more factors; researcher evaluates main effects for each of the three factors as well as a set of two-way interactions ( AxB, BxC, AxC & then AxBxC as potential for three way interaction) Statistical Analysis of Factorial Designs:  Depends whether the factors are between-subjects, within-subjects, or a mixture.  Compute the mean for each treatment condition (cell) & use an analysis of variance (ANOVA) to evaluate the statistical significance of the mean diff  Two-factor ANOVA: conducts three separate hypothesis tests: one each to evaluate the two main effects & one to evaluate the interaction.  ANOVA conducted using a statistical computer program such as SPSS - Two between subjects factors = independent-measures two-factor ANOVA - Only one of factors is between-subjects = specify which it is & use mixed-design two-factor ANOVA - Two within-subjects factors = use repeated-measures two-factor ANOVA 

11.4: Applications of Factorial Designs: Expanding & Replicating a Previous Study:  Often, factorial designs are developed when researchers plan studies that are intended to build on previous research results.  In a single study, researcher can replicate/expand on previous research Reducing Variance in BS Designs:  Individual differences can result in large variance for the score within a treatment condition  Solution is to use the specific variable as a second factor, creating a two-factor study.  Reduce variance without sacrificing external validity Evaluating Order Effects in WS Designs:

Order effects can be serious problem in within-subjects; confounding variable that should be eliminated  It is possible that treatments occur early in the order may influence a participants scores for treatments that occur later in the order. Using Order of Treatments as a Second Factor:  Measure & evaluate order effects using counterbalancing which requires separate groups of participants with each group going through a set of treatments in a different order  Counterbalance = half participants beginning with treatment I & then move to II; other half of participants begin with treatment II & then move to I.  3 possible outcomes that can occur: 1. No order effects: does not matter if a treatment is presented first or second; data shows a pattern w/no interaction- mean is the same in either case 2. Symmetrical order effects: in this situation, size of the treatment effect (I vs. II) depends on the order of treatments – the effect of 1 factor depends on the other factor; symmetrical = symmetrical interaction in data 3. Nonsymmetrical order effects: for example, diff treatment conditions may produce diff levels of fatigue or practice; in data, lines do not intersect at their midpoints and difference between groups in treatment I is much smaller than difference in treatment II. Nonsymmetrical produce lopsided (nonsymmetrical) interaction between treatments & orders. ...