Presentation is loading. Please wait.

Presentation is loading. Please wait.

2x2 ANOVA BG & MG Models Kinds of Factorial Designs ANOVA for BG, MG & WG designs Causal Interpretation of Factorial Results.

Published by Modified over 8 years ago

Similar presentations

Presentation on theme: "2x2 ANOVA BG & MG Models Kinds of Factorial Designs ANOVA for BG, MG & WG designs Causal Interpretation of Factorial Results."— Presentation transcript:

1 2x2 ANOVA BG & MG Models Kinds of Factorial Designs ANOVA for BG, MG & WG designs Causal Interpretation of Factorial Results

2 When working with factorial designs we will consider two major types of IVs… those that are investigated using a between groups comparison different participants in the conditions of the IV (BG) those that are investigated using a within-groups comparison the same participants are in all conditions of the IV (WG) Thus, there are three “kinds” of 2-way factorial designs: All three kinds of these designs can involve any combination of manipulated IVs and/or selected IVs All three kinds of these factorial ANOVA models have 3 F-tests one for each of two Main Effects and one for the Interaction

3 BETWEEN GROUPS FACTORIAL DESIGN: both of the IVs use between groups comparison each participant completes only one condition of the design WITHIN-GROUPS FACTORIAL DESIGN: both of the IVs use within-groups comparison each participant completes all conditions of the design MIXED FACTORIAL DESIGN: one of the IVs uses a between groups comparison and one of the IVs uses a within-groups comparison. each participant completes both conditions of the within- groups IV, but completes only one condition of the between groups IV. it is important to specify which IV uses a between groups comparison and which IV uses a within-groups comparison

4 Between groups factorial design -- Each participant is in only one condition, having a particular combination of Initial Diagnosis and Type of Treatment. Type of Treatment Initial Diagnosis Individual Group Therapy Therapy Clients diagnosed Clients diagnosed Depression as depressed who as depressed who are treated with are treated with individual therapy group therapy Clients diagnosed Clients diagnosed Social Anxiety with social anxiety with social anxiety who are treated with who are treated with individual therapy group therapy

5 Mixed group factorial design Species was a between groups IV (a turtle can only be a member of one species). Each turtle participated in both the mid-morming & dusk conditions of the Time of Day IV. Species of Turtle Time of Day Snapping Turtle Painted Turtle Each snapping turtle Each painted turtle Mid-morning completed a trial completed a trial during mid-morning during mid-morning Each snapping turtle Each painted turtle Evening completed a trial completed a trial during the evening during the evening

6 Within-groups factorial design -- Each participant completed four trials, one of each combination of Retention Interval and Word Type. Retention Interval Word Type Immediate Test Delayed Test The test was given The test was given Familiar immediately after the 5 minutes after the study of a list of study of a list of 40 familiar words. 40 familiar words. The test was given The test was given Unfamiliar immediately after the 5 minutes after the study of a list of study of a list of 40 unfamiliar words. 40 unfamiliar words.

7 Practice Identifying Types of Factorial Designs - answers next page The purpose of the study was to examine the possible influence of two variables upon maze-learning by rats, length of the maze (either 10 feet or 30 feet) and the size of the reward (either 1sugar pellet or 5 sugar pellets). Here are three “versions” of the study tell which is BG, WG & MG a. Each rat completed one trial. Each was assigned to either the longer or the shorter maze, and also assigned to receive either 1 or 5 sugar pellets upon completing the maze. b. Each rat completed two trials in either the longer or the shorter maze. Following one trial in the assigned maze, each received 1 pellet reward, after the other trial they received the 5 pellets. c. Each rat completed four trials, two in the shorter maze and two in the longer maze. Each received 1 pellet after one of the short-maze trials and 5 pellets after the other, and also 1 pellet after one of the long-maze trials and 5 pellets after the other. BG MG WG

8 Another Example -- 3 versions of the same study The researcher wanted to investigate infants’ startle responses to loud sounds. The two variables of interest were the Position of the Sound (in front of versus behind the infant) and the Type of Sound (a hand-clap versus deep male voice saying "Hey"). Here are three “versions” of the study tell which is BG, WG & MG a. Each infant completed trials all involving a hand-clap or all involving the voice saying "Hey". During some of the trials, the appropriate type of sound was made in front of the infant. During other trials, the appropriate type of sound was made behind the infant. b. Each infant had some trials during which the sound was made in front of them and some during which the sound was made behind them. Some of the sounds were the hand-clap and the others were the voice saying "Hey". c. Each infant always heard either the hand-clap or the “Hey”, and whatever sound they heard was always played either in front of them or behind them. BG MG WG

9 Remember about the causal interpretation of effects of a factorial design Start by assessing the causal interpretability of each main effect Remember, in order to causally interpret an interaction, you must be able to casually interpret BOTH main effects. For each of the following: Tell the IVs and tell what effects could be causally interpreted (assuming proper RA, IV manip. and confound control were used): 1. Male and female participants who were African American, Mexican American, or European American were asked to complete a questionnaire about satisfaction with their Senators. 2. Children played with either a toy gun, a toy car or a puzzle, some while their parents were in the room and some not. The DV was the amount of aggressive behavior they exhibited. 3. Participants played with either a simple puzzle or a complex puzzle in pairs made up of two boys, two girls or one boy & one girl. zilcho-causo Puzzle type only. All three !

10 Statistical Analysis of a 2x2 Design Task Presentation (a) SE of Presentation Paper Computer for Easy Tasks Task Difficulty (b) Easy 90 70 80 Hard 40 60 50 65 65 SE for Presentation for Hard Tasks Presentation Difficulty Interaction Main Effect Main Effect Effect SS Presentation SS Dificulty SS Interaction 65 vs. 65 80 vs. 50 SE Easy vs. SE Hard F Presentation ME F Difficulty ME F Presentation X Diffuclty Interaction

11 In a 2x2 Design, the Main effects are sufficient to tell us about the relationship of each IV to the DV… since each main effect involves the comparison of two marginal means -- the corresponding significance test tells us what we need to know… whether or not those two marginal means are “significantly different” Don’t forget to examine the means to see if a significant difference is in the hypothesized direction !!! Statistical Analyses Necessary to Describe Main Effects of a 2x2 Design

12 However, the F-test of the interaction only tells us whether or not there is a “statistically significant” interaction… it does not tell us the pattern of that interaction to determine the pattern of the interaction we have to compare the simple effects to describe each simple effect, we must be able to compare the cell means we need to know how much of a cell mean difference is “statistically significant” Statistical Analyses Necessary to Describe the Interaction of a 2x2 Design

13 Using the Pairwise Computator & LSDmmd to Compare cell means to describe the simple effects of a 2x2 Factorial design n = N/4 = 20/4 = 5 k = 4 conditions For a 2x2 BG Factorial Design

14 Using the Pairwise Computator & LSDmmd to Compare cell means to describe the simple effects of a 2x2 Factorial design n = N = 20 k = 4 conditions For a 2x2 MG Factorial Design

15 Applying mmd lsd to Simple Effects Describing the Interaction Task Presentation F int = 13.21, p =.012 Paper Computer LSDmmd = 14 Task Difficulty Easy 90 70 Hard 40 60 for the following, tell the size of the effect and apply the mmd lsd Simple effect of Task Presentation SE Task Presentation for Easy Tasks SE Task Presentation for Hard Tasks Simple effects of Task Difficulty SE of Task Difficulty for Paper Pres. SE of Task Difficulty for Comp. Pres. 20 > - 20 < 50 > 10 =

16 Applying mmd lsd to Simple Effects Checking if Main effects are Descriptive/Misleading - 1 Task Presentation F dif = 1.21, p =.72 Paper Computer LSDmmd = 14 Task Difficulty Easy 90 70 Hard 40 60 Main effect of Task Presentation marginal mean for Paper marginal mean for Computer Simple effects of Task Presentation SE of Task Presentation for Hard SE of Task Presentation for Easy Main effect of Task Presentation is …. 65 20 > -20 < misleading

17 Applying mmd lsd to Simple Effects Checking if Main effects are Descriptive/Misleading - 2 Task Presentation F dif = 7.83, p =.027 Paper Computer LSDmmd = 14 Task Difficulty Easy 90 70 Hard 40 60 Main effect of Task Difficulty marginal mean for Easy marginal mean for Hard Simple effects of Task Difficulty SE of Task Difficulty for Paper Pres. SE of Task Difficulty for Comp. Pres. Main effect of Difficulty is …. 80 50 > 10 = misleading

Download ppt "2x2 ANOVA BG & MG Models Kinds of Factorial Designs ANOVA for BG, MG & WG designs Causal Interpretation of Factorial Results."

Similar presentations

Complex Experimental Designs

Complex Experimental Designs
Survey of Major Correlational Models/Questions Still the first & most important is picking the correct model… Simple correlation questions simple correlation.

Survey of Major Correlational Models/Questions Still the first & most important is picking the correct model… Simple correlation questions simple correlation.
ANCOVA Workings of ANOVA & ANCOVA ANCOVA, Semi-Partial correlations, statistical control Using model plotting to think about ANCOVA & Statistical control.

ANCOVA Workings of ANOVA & ANCOVA ANCOVA, Semi-Partial correlations, statistical control Using model plotting to think about ANCOVA & Statistical control.
Factorial Designs Passer Chapter 9

Factorial Designs Passer Chapter 9
Kxk BG Factorial Designs expanding the 2x2 design reasons for larger designs statistical analysis of kxk BG factorial designs using LSD for kxk factorial.

Kxk BG Factorial Designs expanding the 2x2 design reasons for larger designs statistical analysis of kxk BG factorial designs using LSD for kxk factorial.
Research Methods in Psychology Complex Designs.  Experiments that involve two or more independent variables studies simultaneously at least one dependent.

Research Methods in Psychology Complex Designs.  Experiments that involve two or more independent variables studies simultaneously at least one dependent.
Factorial Hypotheses Some review & practice Identifying main effect and interaction RH: Explicit factorial RH: “Blending” interaction and main effect RH:

Factorial Hypotheses Some review & practice Identifying main effect and interaction RH: Explicit factorial RH: “Blending” interaction and main effect RH:
3-way Factorial Designs Expanding factorial designs Effects in a 3-way design Causal Interpretations of 3-way factorial effects Defining a 3-way interaction.

3-way Factorial Designs Expanding factorial designs Effects in a 3-way design Causal Interpretations of 3-way factorial effects Defining a 3-way interaction.
Analytic Comparisons & Trend Analyses Analytic Comparisons –Simple comparisons –Complex comparisons –Trend Analyses Errors & Confusions when interpreting.

Analytic Comparisons & Trend Analyses Analytic Comparisons –Simple comparisons –Complex comparisons –Trend Analyses Errors & Confusions when interpreting.
Chapter 9 – Factorial Designs Factorial Design -- definition –Two or more IVs –every level of one IV combined with every level of other IV –IVs -- called.

Chapter 9 – Factorial Designs Factorial Design -- definition –Two or more IVs –every level of one IV combined with every level of other IV –IVs -- called.
11. Experimental Research: Factorial Design What are factorial experimental designs, and what advantages do they have over one-way experiments? What is.

11. Experimental Research: Factorial Design What are factorial experimental designs, and what advantages do they have over one-way experiments? What is.
Two Factor ANOVA.

Two Factor ANOVA.
Multiple Group X² Designs & Follow-up Analyses X² for multiple condition designs Pairwise comparisons & RH Testing Alpha inflation Effect sizes for k-group.

Multiple Group X² Designs & Follow-up Analyses X² for multiple condition designs Pairwise comparisons & RH Testing Alpha inflation Effect sizes for k-group.
Design Conditions & Variables Explicating Design Variables Kinds of “IVs” Identifying potential confounds Why control “on the average” is sufficient Characteristics.

Design Conditions & Variables Explicating Design Variables Kinds of “IVs” Identifying potential confounds Why control “on the average” is sufficient Characteristics.
Factorial Designs: Research Hypotheses & Describing Results Research Hypotheses of Factorial Designs Inspecting tables to describe factorial data patterns.

Factorial Designs: Research Hypotheses & Describing Results Research Hypotheses of Factorial Designs Inspecting tables to describe factorial data patterns.
Multiple Group X² Designs & Follow-up Analyses X² for multiple condition designs Pairwise comparisons & RH Testing Alpha inflation Effect sizes for k-group.

Multiple Group X² Designs & Follow-up Analyses X² for multiple condition designs Pairwise comparisons & RH Testing Alpha inflation Effect sizes for k-group.
ANCOVA Workings of ANOVA & ANCOVA ANCOVA, Semi-Partial correlations, statistical control Using model plotting to think about ANCOVA & Statistical control.

ANCOVA Workings of ANOVA & ANCOVA ANCOVA, Semi-Partial correlations, statistical control Using model plotting to think about ANCOVA & Statistical control.
Describing Factorial Effects Kinds of means & kinds of effects Inspecting tables to describe factorial data patterns Inspecting line graphs to describe.

Describing Factorial Effects Kinds of means & kinds of effects Inspecting tables to describe factorial data patterns Inspecting line graphs to describe.
Statistical Analysis of Factorial Designs z Review of Interactions z Kinds of Factorial Designs z Causal Interpretability of Factorial Designs z The F-tests.

Statistical Analysis of Factorial Designs z Review of Interactions z Kinds of Factorial Designs z Causal Interpretability of Factorial Designs z The F-tests.
Multivariate Analyses & Programmatic Research Re-introduction to Programmatic research Factorial designs  “It Depends” Examples of Factorial Designs Selecting.

Multivariate Analyses & Programmatic Research Re-introduction to Programmatic research Factorial designs  “It Depends” Examples of Factorial Designs Selecting.

Similar presentations

Ads by Google