Psychology 304: Exam 4
The Two-Group Design: Correlated Assignment
- A method of assigning research participants to groups so that there is a relationship between small number of participants - These small groups are then randomly assigned to treatment conditions (paired or matched assignment).
Interpretation of Data
- Statistics are a tool to help you understand the data from your experiment - Statistics are useless if you do not know how to interpret them
Beyond two-group design
Allows for more complicated and interesting questions
Understanding Interactions: Pt 2
- A significant interaction means that the effects of the various IV's are not straightforward and simple - For this reason, we virtually ignore our IV main effects when we find a significant interaction - Sometimes interactions are difficult to interpret, particularly when we have more than two IV's or many levels of an IV
Factorial Design
Gives the power we need to devise an investigation of several factors (IVs) in a single experiment
Independent Variable and Dependent Variable
IV: the thing you are manipulating DV: outcome variable; depends on the IV
Nonrandom Assignment to Groups: Difficulty
Matched Pairs or Sets: Difficult Natural Pairs or Sets: Very Difficult Repeated Measures: Difficult or impossible to conduct an experiment with repeated measures on multiple IV's
Number of Groups
- A multiple-group design compares three or more levels or amounts of an IV. -A multiple group design can have a control group and two or more experimental groups *Compare 3,4,5, or more levels of IV -Multiple group design does NOT have a control group
Understanding Interactions: Pt 5
- A strategy that often helps us make of an interaction is to graph it - By graphing your DV on the y axis and one IV on the x axis, you can depict your other IV with lines on the graph - Can usually deduce what happened to cause a significant interaction
Understanding Interactions: Pt 3
- A strategy that often helps us to make sense of an interaction is to graph it. - By graphing your DV on the y axis and one IV on the x axis, you can depict your other IV with lines on the graph - We can deduce what happened to cause a significant interactions *Intersection or Convergence on graph means there is an interaction
The Two-Group Design: Confounded Experiment
- An experiment in which an extraneous variable varies systematically with the IV - Confounding makes drawing a cause and effect relation impossible - Confounding may occur if participants are not equal before the start of the variable
Advantages of Correlated Group Designs
- Control Issues: The three methods for creating correlated - groups designs give us greater certainty of group equality. - Statistical Issues: Correlated - groups design can help reduce error variation - Error Variability: Variability in DV scores that is due to factors other than IV = individual differences, measurement error, and extraneous variation statistic = between - groups variability / error variability
Analyzing two-group designs
- For a two-independent group design: t test to analyze data
Experimental Design and Statistics
- For a two-independent groups design, use a t test for independent samples to analyze your data - For a two-correlated groups design, analyze your data with a t test for correlated samples (paired t test or within groups t test).
Comparing Two-Group Design TO Multiple-Group Design: Control Issues
- Multiple-independent groups design uses the control technique of randomly assigning participants to groups - Multiple- correlated groups design use the control techniques of matching, repeated measures, or natural pairs to assure equality of groups and to reduce error variability
Practical Considerations: Independent Group Design
- Must take into account the large number of participants you will need to make random assignment feasible and to fill the multiple groups
The Two-Group Design: Natural Pairs
- Pairs of participants are created from naturally occurring pairs *Biological or Socially related
The Two-Group Design: Choosing Two-Group Design
- Random assignment should equate your groups adequately (assuming large group) - 20 or more participants: randomization will work - 5 or fewer: randomization won't work
The Two-Group Design: Nonrandom Assignment
- Random assignment tends to create equal groups in the long run - As groups get larger, we can place more confidence in random assignment achieving what we want it to - If we are faced with a situation in which we have few potential research participants and we are worried that random assignment may not create equal groups
The Two-Group Design: Within-Subject Comparison
- Refers to a contrast groups of participants who were assigned groups through matched pairs, natural pairs, or repeated measures - we are comparing within the same participants (subjects) - Direct comparison is literally true only for repeated measures designs, participants in matched or natural pairs are the same with regard to the matching variable
The Two-Group Design: Matched Pairs
- Research participants in a two group design who are measured and equaled on some variable before the experiment - Typically we measure a variable that could result in confounding if not controlled - After we have measured this variable, we create pairs of participants that are equal on this variable - After we have created our matched pairs, we then randomly assign participants from these pairs to different treatment conditions
Understanding Interactions: Pt 4
- Significant interaction: will notice that the lines of the graph cross and converge - Pattern is a visual indication that the effects of one IV change as
Two-Way ANOVA for Independent Samples: Pt 2
- Source Table: A significant interaction renders the main effects moot because those main effects are qualified by the interaction and are not straightforward -Crossing lines, in conjunction with the low probability of chance for the interaction term, denote a significant interaction -explanation of an interaction effect must include a reference to both IV's in order to make sense
One-way ANOVA for Independent Samples
- Source Table: A table that contains the results of ANOVA. Source refers to the source of the different types of variation -Sum of Squares: The amount of variability in the DV attributable to each source. -Mean Square: the "averaged" variability for each source. The mean square is computed by dividing each source's sum of squares by its degree of freedom - Variance: A single number that represents the total amount of variation in the distribution. The square of the standard deviation F = mean square between groups/mean square within groups
One-way ANOVA for correlated samples
- The probability of a statistic is never 0.000 no matter how large the statistic gets - In light of this problem, we advise you to list p < 0.001 if you ever have such a result on your computer print out.
The Two-Group Design: Repeated Measures
- The same participants are tested in both treatment conditions of our experiment - The matched pairs are perfectly equal because they consist of the same people or animals tested across the entire experiment - No extraneous variables should be able to confound this situation because any difference between the participants' performance in the two treatment conditions is due to the IV - In this type of experiment, participants serve as their own controls
Two-Way ANOVA for Correlated Samples
- The two-way ANOVA for correlated samples requires that we have two IVs with correlated groups for both IVs - Most often these correlated groups would be formed by matching or by using repeated measures *Correlated = one group sees all conditions
Two-Way ANOVA for Independent Samples
- The two-way ANOVA for independent samples requires that we have two IV's with independent groups -Create this design we would use four different randomly assigned groups of salesclerks -DV scores represent clerks' response times in waiting on customers
Two-Way ANOVA for Mixed Samples
- The two-way ANOVA for mixed samples requires that we have two IV's with independent groups for one IV and correlated groups for the second IV - Example: Clothing-customer sex experiment - use different randomly assigned group of saleclerks for each customer sex
The Two-Group Design: True Experiment + Ex Post facto research
- True experiment: An experiment in which the experimenter directly manipulates the IV - Ex post facto research: A research approach in which the experimenter cannot directly manipulate the IV but can only classify, categorize, or measure the IV because it is predetermined in the participants
Using Measured IVs
- Using a measured rather than a manipulated IV results in ex post facto research - A research approach in which the experimenter cannot directly manipulate the IV but can only classify, categorize, or measure the IV because it is predetermined in the participants -Without the control that comes from directly causing an IV to vary, we must exercise extreme caution in drawing conclusions from such studies -We can develop an experiment that uses one manipulated IV and one measured IV at the same time
Variations of Multiple-Group Design
- We already know that a particular IV has an effect, then we can use a multiple-group design to help us define the limits of that effect - Important to add control in order to account for possible placebo effect -Placebo Effect: experimental effect that is due to expectation or suggestion rather than IV - Ex post facto research deals with measured rather than manipulated IV's
Control Issues
- We need to consider independent versus correlated groups in factorial designs - A complicating factor for factorial designs is that we need to make this decision (independent vs. correlated groups) for each IV we include in an experiment
Understanding Interactions
- When two variables interact, their joint effect may not be obvious or predictable from examining their separate effects - Combinations of drugs, in particular, are likely to have synergistic effects so that a joint effect occurs that is not predictable from either drug alone *The effects are greater than what is individually possible.
Rationale of Factorial ANOVA
- With factorial designs, the sources of treatment variability increase - Instead of having one IV as the sole source of treatment variability, factorial designs have multiple IVs and their interactions as sources of treatment variability
Understanding Interactions: Pt 6
-A significant interaction = will notice that the lines of the graph cross or converge -This pattern is a visual indication that the effects of one IV change as the second IV is varied - Nonsignificant interactions typically show lines that are close to parallel *An interaction is present when the effects of one IV depends on the specific level of the other IV
Practical Considerations: Correlated Groups Designs
-Matched Sets: must consider the difficulty of finding three or more participants to match on the extraneous variable you choose -Natural Sets: May be limited by size of the natural sets you intend to study -Repeated Measures: Each participant must be measured at least three times
Correlated Groups
-Matched sets: participants are matched on a variable that will affect their performance on the DV (matching variable). -Repeated Measures: Each participant must participate in all of the treatment conditions -Natural sets: Analogous to using natural pairs except that sets must include more than two research participants. Many researchers use litter mates as natural sets
Analyzing Multiple-Groups Designs
-Multiple-groups designs are measured with the analysis of variance (ANOVA) *The ANOVA procedure used to analyze a multiple-group design with one IV is known as a one-way ANOVA *A one-way ANOVA for independent groups is known as completely randomized ANOVA *A one-way ANOVA for correlated groups is known as a repeated - measures ANOVA
The Two-Group Design: Groups
-One IV, but at least two groups -Simplest Design: Compare some research participants who receive IV to some others that do not receive IV. -If those groups differ, and we are assured that we controlled potential extraneous variables, then we conclude that the IV caused the participants to differ
The Two-Group Design: Levels
-The most common manner of creating two groups is when the presence of the IV is contrasted with the absence of the IV. -These differing levels of the IV are referred to as the levels (treatment conditions) of the IV.
Experimental Questions
-The number of questions we can ask in a factorial experiment -When we ask additional questions, we must make certain that the questions coordinate w/ each other experimental questions should not clash
One-way ANOVA for independent samples: Statistical Significance
-Where the significance lies in a multiple-group experiment, we must do additional statistical tests known as post hoc comparisons *Post hoc comparisons: Statistical comparisons made between group means after finding a significant F ratio.
Research Problem: Logical steps (Independent Sample)
1) Test only one IV 2) Tested three different levels of IV 3) Used random assignment and one-way ANOVA
Research Problem: Logical steps (Correlated Sample)
1) Use repeated measures 2)multiple-within-group and a one-way ANOVA
Research Problem
1. Reviewing relevant research literature: choose IV 2. Decide to test one IV 3. Choose levels of IV 4. same size determines type of test 5. Interpretation of Data
Three Types of ANOVA
1. Two-way ANOVA for independent samples 2. Two-way ANOVA for correlated samples 3. Two-way ANOVA for mixed samples
Simplest Factorial Design
2x2 Design -The number of numbers tells us how many IV's there are -The value of each number tells us how many levels each IV has
Mixed Assignment
A factorial design that has a mixture of independent groups for one IV and correlated groups for another IV
Assigning Participants to Groups: Independent or Correlated
All participants assigned randomly or in a correlated fashion, or we could have one IV with independent groups and one IV with correlated groups. This is referred to as mixed assignment
Final Note
Assuming that a significant main effect is not qualified by an interaction, you need to calculate a set of post hoc tests to determine exactly where the significance of that IV occurred.
Rationale of ANOVA
Between-group variability: variability in DV scores that is due to the effects of the IV. Error Variability (within-group variability): variability in DV scores that is due to factors other than the IV (individual differences, measurement error, and extraneous variation). *The notion has evolved for the ANOVA is that we are comparing the ratio of between-groups variability to within-group variability
Nonrandom Assignment to Groups
Completely within-groups (or within-subjects) designs. Participant groups for all IV's have been formed through nonrandom assignment
Independent vs. Dependent T test Output
Dependent: mean difference AND corr. indicate dependent Independent: t= AND equal variance assumed.
Planning the Statistical Analysis
Designed a 2 x 2 experiment in which the two IVs - use ANOVA to divide the variability into two sources (treatment variability and error variability).
Dealing with more than Two IVs
Designing an experiment with more than two IVs is probably the most important variation of the factorial design. The simplest possible factorial design with three IV's (often referred to as a three-way design) has three IV's, each with two levels. This design represents a 2 X 2 X 2 experiment. This design would require eight different groups if it is planned as a completely between-groups design.
Experimental Group Control Group
Experimental Group: Group of participants that receives the IV Control Group: Group of participants that does not receive the IV
F
F = variability due to IV + Error variability/ error variability - When the IV has a significant effect on the DV, the F ratio will be large - When the IV has no effect or only a small effect, the F ratio will be small (near 1). F = between-groups variability/within-groups variability
Assigning Participants to Groups
Independent or Correlated Groups
What does a factorial design look at?
Look at combinations of IVs at the same time, similar to the real world.
Mixed Assignment to Groups
Mixed Assignment designs involve a combination of random and nonrandom assignment, with at least one IV using each type of assignment to groups - A two-IV factorial design, mixed assignment involves one IV with random assignment and one IV with nonrandom assignment - The use of repeated measures is probably more likely than other types of nonrandom assignment -Mixed designs combine the advantages of the two types of designs -The conservation of participants through the use of repeated measures for a between-subjects variable makes for a popular and powerful design
Independent Groups
Random Assignment serves as an important control procedure -Helps to ensure that potential extraneous variables are controlled
The Two-Group Design: Random Assignment
Random Assignment: independent groups * Each participant has an equal chance of being in any group. * Between-subject comparisons: compare the performance of participants in these independent groups
Interpretation of Data: Computer Statistical Output
T Test for Independent Samples - Homogenity of Variance: the assumption that the variances are equal for two groups you plan to compare statistically - Heterogenity of Variance: occurs when we do not have homogenity of variance. This means that our two or more groups' variances are not equivalent
Interpretation of Data: Computer Statistical Output: translation
T test for independent samples -If two equal groups began the experiment and they are now unequal. - If our controls have been adequate, our only choice is to assume that the difference between the groups is due to the IV
Interpretation of Data: Computer Statistical Output : Robust
T test for independent samples -generally speaking t tests are robust with regard to the assumption of homogeneity -a robust test is one that can tolerate violations of its assumptions and still provide accurate answers
POWER
T-test: power of 0.95, and alpha level of 0.05, effect size of 0.50, and a t value of 1.65 ANOVA: power of 0.95, alpha level of 0.05, effective size of 0.25, critical t value of 3.03
Experimental Design
The general plan for selecting participants, assigning participants to experimental conditions, controlling extraneous variables, and gathering data
Factors designated by letters
The levels within a factor are often designated by the letter that corresponds to the factor and a number to differentiate the different levels -Main Effect: A main effect refers to the sole effect of one in a factorial design -Interaction: Joint simultaneous effect on the DV of more than one IV
Comparing Two-Group Design TO Multiple-Group Design
Two Group Design: 2 IV levels. Can tell whether your IV has an effect. Multiple-Group Design: More than 2 IV levels. Appropriate when you find the answer to your basic question and wish to go further. *First consideration should be experimental question. Decide whether to use independent or correlated groups.
