Statistics Final Exam Review

Final Exam Information

• The final exam is on Saturday, December 7th, from 8:30 AM to 10:30 AM.
• Multiple locations are available in BA. Refer to the Exam Information document for specific locations.
• The exam is 2 hours long.
• The exam is worth 100 points.
• 80 points are multiple choice.
• 20 points are short answer (10 questions, 2 points each).
• The format of the short answer questions is similar to the midterm format.
• No aids are permitted, including calculators.
• Material covered includes lecture weeks 1–14, chapters 1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 12, 13 (pages 401–418), chapter 14, and the statistics module (pages 467–479). Chapter 3 from the price text is also included (PDF version in the course information folder).
• The exam emphasizes material covered after the midterm, which accounts for approximately 60% of the exam. This corresponds to lecture weeks 9-14 and text chapters 9-14.
• Approximately 80% of the lecture and text shared material will be covered on the exam.
• Approximately 10% of the lecture-only material will be tested.
• Approximately 10% of the textbook-only material will be tested (by multiple-choice questions).
• Approximately 2% of the lab-only material will be tested (by multiple-choice questions).

Week 1 Outline

• Simple vs. more complex hypotheses and designs
• Testing interaction hypotheses
• Factorial designs
• Describing features of factorial designs (Terminology: variables, levels, conditions) Independent-groups, within-groups, mixed
• Manipulated IVs vs. Participant Variables
• Interpreting results of a 2 x 2 factorial design
• Example experiment
• Types of effects: main effects, interaction
• A note on statistical significance
• The possible patterns of results
• Identifying effects in tables and graphs
• Extensions and variations
• Increasing the number of levels of an IV
• Increasing the number of IVs

Week 1 Outline (Continued)

• More on interpreting main effects and interactions
• Follow-up tests
• Interaction effects are more important
• Describing in words
• Combining IVs and PVs
• Uses of IV x PV designs
• Cautions in interpreting results
• Assignment to conditions in factorial design
• Independent-groups designs (between)
• Within-groups designs (within)
• Mixed designs (between-within)
• Advantages and uses of factorial designs
• Advantages of factorial designs compared to one-way designs
• Uses of factorial designs
• Identifying factorial designs in your reading

Simple Causal Hypotheses

• State the effect that one IV will have on a dependent variable (DV).
• Tested in "one-way" designs with one IV.
• Conclusions are "general" or "unqualified."
• Prompts research to specify conditions under which the effect disappears or grows stronger.
• Boundary conditions

More Complex Causal Hypotheses

• State how two (or more) IVs affect a DV.
• Called "interaction hypotheses" because they specify how independent variables "interact" to influence a dependent variable.
• Can lead to more "qualified" conclusions about behavior

Interaction Hypothesis: Example (Examples of different hypothesis tests)

• The effect that X has on Y depends on Z.
• The effect that anxiety has on performance depends on task difficulty.
• When tasks are easy, increases in anxiety produce increases in performance.
• When tasks are difficult, increases in anxiety produce decreases in performance.
• The effect that violent media has on children's aggression depends on their parents' reactions.
• When parents react favorably, more violence watched, the more aggressive the child will be.
• When parents react unfavorably, more violence watched, the less aggressive the child will be.

Interaction Hypotheses: Testing for Moderators

• A moderator is a variable that changes the strength of association between two other variables.
• In experiments, a moderator is an independent variable that changes the strength of the effect another IV has on the DV.
  • The effect that anxiety has on performance is moderated by task difficulty.
  • The effect that media violence has on aggression is moderated by the parents' reactions.

Describing Factorial Designs

• A research design that tests the effect of two or more factors (IVs) simultaneously.
• Each factor is "crossed" with each other factor, creating all possible combination.
• The number of conditions (or "cells") is the product of the number of levels of each factor.

2 x 2 Factorial Design

• See tables in document.

2 x 4 Factorial Design

• See table in document.

2 x 3 Design, example #1 and #2

• See tables in document.

3 x 3 Design Example

• See table in document.

2 x 4 Design Example

• See table in document.

2 x 2 x 2 Design Example

• See table in document.

Interpreting Higher Order Factorial Designs

• With three factors, there are three main effects (performance level, task importance, presence of others), three two-way interactions (performance level x task importance, performance level x presence of others, task importance x others), and one three-way interaction (performance level x task importance x others).

Examining 2-way Interactions in a Higher Order Design

• Examine each 2-way interaction by ignoring or "collapsing across" the remaining factors.

Examining the 3-way Interaction in a 3-way Design

• A 3-way design can provide information about the combined effects of all three factors.
• There will be a 3-way interaction if a two-way interaction between two factors differs depending on the other remaining factor.
• Ask: Does a two-way interaction differ across the levels of the remaining factor?
• Examine the two-way interaction pattern at each level of the remaining factor.

Follow-Up Tests

• If the IV has only two levels, no further tests are needed.
• If the IV has more than two levels, further tests are needed to interpret the findings.
  • Called "post hoc tests" or "multiple comparisons"
• Want to determine precisely which of the marginal means differ significantly from each other

Post Hoc Tests

• See tables in document.

Describing Main Effects and Interactions in Words

• Main effects (without an interaction)
• Main effects (with an interaction)
• Interaction effects

Example: One Main Effect without an Interaction

• There was no significant main effect of task importance.
• There was a significant main effect of performance level
• The interaction between performance level and task importance was not significant.

Example: One Main Effect with an Interaction

• There was no significant main effect of task importance
• There was a significant main effect of performance level
• The effect of performance level was qualified by a significant interaction between performance level and task importance.

Interactions are More Important than Main Effects

• When a study shows both a main effect and an interaction, the interaction is almost always more important.
• This interaction qualifies the main effect.
• There may be real differences in marginal means, but the more interesting part is the interaction.

Describing an Interaction: Generic Templates

• The interaction between factor A and factor B indicates the effect of factor A differs depending on the levels of factor B.
• For example, when first level B is present, increases in factor A result in higher scores in DV, and in the contrast, when second level B is present, increases in factor A result in lower scores in DV.

Pattern #6b – Alternate Example

• See table in document.

Description of Interactions in Words: Textbook Examples

• Describe the interactions.

Recall: Interaction Hypothesis Example

• The effect of X on Y depends on Z.
• The effect of anxiety on performance depends on task difficulty.
• When tasks are easy, increases in anxiety increase performance.
• When tasks are difficult, increases in anxiety decrease performance.
• The effect that violent media has on children's aggression depends on their parents' reactions.
• When parents react favorably, more violence watched, the more aggressive the child will be.
• When parents react unfavorably, more violence watched, the less aggressive the child will be.

Combining IVs and PVs

• Sometimes called IV x PV designs
• Use to test the generality of an IV's effect on the DV for different kinds of people.
• Use to test the association between a participant variable (PV) and the DV in different situations
• Cautions in interpreting results: cannot draw causal conclusions for effects involving the participant variable; Participant variable might moderate the effect of the IV; participant variable can be called a moderator if there is an interaction. Given examples with Depression diagnosis and Experience with Task (2 variables to the participant).

Assignment to Conditions and Orders

• Independent Groups (Between-subjects)
• Within-Groups (Repeated Measures)
• Mixed-factorial design

Independent-Groups Design

• Random assignment of participants to conditions. For example, 2 x 3 design will have 6 different conditions.

Within-Groups Design

• Each participant is in each factorial condition. For example, conditions were arranged as a sequence or order, that is measured or assessed across time.

Mixed-Factorial Designs (Between-Within)

• A study with at least one independent-groups and one within-groups factor.

Tests of Simple Effects

• Simple effects of A at B1
• Simple effects of A at B2
• Simple effect of B at A1
• Simple effect of B at A2

Identifying Factorial Designs in Your Readings

• The method section will describe the design of the study (including factorial notation).
• The results section will examine whether main effects and interactions were significant.
• Look for “it depends” or “only when” to highlight an interaction.
• Look for participant variables (age, gender, ethnicity).