Final Material Flashcards
A distribution may be positively skewed (to the right), symmetrical, or negatively skewed (to the left). Note where mean, median, and mode are.
Product of the Binomial, or Gaussian Distribution: The area under the normal curve
In statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is. Normal distribution.
Kurtosis
Positive kurtosis indicates heavier tails and a more peaked distribution, while negative kurtosis suggests lighter tails and a flatter distribution. Kurtosis helps in analyzing the characteristics and outliers of a dataset. The measure of Kurtosis refers to the tailedness of a distribution
- Leptokurtic (thin)
- Mesokurtic
- Platykurtic (flat)
Algebra
y = mx + b
y = (slope times x ) plus the y intercept
Monotonic & Nonmonotonic Functions
Quadratic Equation
y= x^2 + x + b
Cubic Equation
y = x^3 + x^2 + x + b
Positive & Negative Accelerated Increasing and Decreasing Function
Scatterplots
Visually show correlations
- careful not to confuse correlation with slopeSS
Different ways to analyze data
- one-sample t-test
- independent samples t-test
- dependent (or repeated measures, or correlated) samples t-test
- one way ANOVA
- two way ANOVA
- chi-square
- regression
Three tests relevant to “single-factor design”
- independent samples t-test
- dependent (or repeated measures, or correlated) samples t-test
- one way ANOVA
Single Factor Experimental Design
single factor experimental design- two levels
- between-subjects
- within-subjects
single factor- more than two levels
- between-subjects
- within-subjects
Factors, Levels, Cells (or Treatments)
- factors is the thing we compare
- levels looks at treatments
- each cell represents an amount of people
- 1 by 2
- 1 by 4
- 2 by 4
Between subjects vs within-subjects
Between-subjects:
- Different levels of the IV are administered to different groups of participants (each participant is administered only one level)
- Each participant has only one score on the DV so scores cannot vary “within” each participant, they can only vary between participants
Within-subjects:
- Different (multiple) levels of the IV are administered to each participant (each participant usually receives every level)
- Each participant has as many scores on the DV as there are two or more levels so scores can vary “within” each participant
- Scores (average across all levels) can also vary between participants
Different statistical tests correspond to different experimental designs
Tests associated with “Single Factor–Two Levels” design:
Independent Samples t-test
Dependent Samples t-test
Independent Samples t-test
- Corresponds to “single factor—two levels, between-subject” design
- Use this when you have two separate groups of participants and you want to compare means from these groups
- Goodwin makes distinction between “independent groups design” (with random assignment) and “nonequivalent groups design” (quasi experiments where random assignment is not possible).
- Find the two means, find the difference between these means, and see if this difference is “significantly” greater than zero
Example of a nonequivalent group design
Sex Aggression
male 23
male 12
male 10
male 7
female 18
female 49
female 31
female 25
Dependent Samples t-test
- Corresponds to “single factor—two levels, within-subject” design
- Use this when you have one group of participants being tested 2 times and you want to compare means at the 2 different times (“within-subjects design”)
- And use it with “matched groups”
- Find the mean of each participant’s or pair’s “difference score” and see if this is “significantly” greater than zero
- Counterbalancing…
Tests associated with “single Factor-More Than Two Levels” design
One-Way ANOVAs
Factor, Levels, Cells (or Treatments)
One-Way ANOVAs
Regular One-Way ANOVA
One Way ANOVA Example
Repeated Measures One-Way ANOVA
Repeated Measures One-Way ANOVA Example
Control Groups
Chi Square
Chi-Square Example
Kasser & Sheldon Article (2000)
OF WEALTH AND DEATH:
MATERIALISM, MORTALITY SALIENCE, AND CONSUMPTION BEHAVIOR (2002)
Author Name: Kasser & Sheldon
Background:
- humantisitc & terror-management theories of materialism
- terror management theory: “in order to cope with the overwhelming anxiety resulting from the realization of one’s inevitable demise, people believe in cultural worldviews that help them feel that they have meaningful lives and are worthy members of their culture”
Hypothesis: They predicted that those who wrote about death would be more materialistic. They thought that those people experience more anxiety so they consume more resources in an attempt to have a more meaningful life.
Main Structure:
- Study 1: Participants were asked to either write about death or a neutral condition (music) to inflict “anxiety” and then asked to describe their financial expectations for themselves within the next 15 years.
- Study 2: Had a similar construct in terms of what the participants were asked to write about. But the assessment included having participants participate in a forest-management game to measure fear and greed.
Methods:
- 60 undergraduate students (21 male and 39 female) were offered extra credit to complete a survey packet.
- Subjects wrote down 6 personal strivings they were focused on and used a 9-point scale to rate how those strivings might help them get to 6 possible futures: self-acceptance/personal growth, affiliation, community feeling, (3 intrinsic) an attractive appearance, social recognition, and financial success (3 extrinsic).
- A relative extrinsic orientation score was computed for each subject by subtracting the ratings for the three intrinsic possible futures from the ratings of the three extrinsic possible futures.” Higher scores indicated greater material focus.
IV: topic of the writing (death or neutral)
DV: future financial expectations and consumption ratings
Results: showed that the feelings of insecurity produced by thoughts of death can produce materialistic behavior, but that there is only correlational evidence for this.
- Those in study 1 who wrote about more neutral conditions were found to have higher expectations for themselves in 15 years
- Those in study 2 who wrote about death were more “greedy” in their consumption ratings.
Critiques:
* see image
Factorial Design Basics
- more than one independent variable
a. not just more than one level of one IV) - use this notion
a. 2 x 3 Factorial Matrix
b. Read Two by Three”
c. Use ANOVA to look for significant differences - can’t use t-tests because
Type of Factorial Design?
How do we sketch a 2x2x2x3 design?
How do we sketch a 2 x 2 x 2 x 3 x 4 design?
Factorial Design Basics
Suppose we want to see how males and females differ on measures of aggression/fear when presented with stimuli of various kinds/levels of threat. This is useful on Halloween!
- DV: Level of aggression/fear
- IV1: Gender (male, female – subject variable, see 2nd part of lecture)
- IV2: Imagery (control, somewhat threatening, very threatening)
This 2 x 3 matrix has 6 possible conditions (notice 2 x 3 = 6)
- A 4 x 2 x 3 matrix would have 24 conditions
- Each IV is called a factor with x number of levels
Vocab is Important
In summary, a 2 x 3 factorial matrix has
2 independent variables AKA factors
- Factor A has two levels
- Factor B has three levels
Combined, there are 6 possible conditions
Interpreting Results
Looking for main effects
Interpreting the results
- Main effects - when the row means or column means are not equal (could be both, could be neither, could be either one)
- ANOVA needed to test for significant differences
Main Effects
- Column means: 10.67, 8.67
Main effect for GENDER –> column means are not equal. Men & women differ on their average scores.
- Row means: 4, 10, 15
Main effect for THREAT LEVEL –> row means are not equal. Scores differ by condition.
- Both factors contain a main effect
Interactions
Main Effects & Interactions
Two Significant main effects, no interaction
One significant main effect & significant interaction
Significant interaction, no main effects
What is the purpose of interactions?
Types of factorial Designs
Mixed Factorial Designs
Counterbalancing
Different Types of Factorials
P x E designs
Subject variables
Interpreting Subject Variables
The “E” Variable
Examples of the P x E design
Notes on Factorial Designs
This can get complicated quickly!
Making sense of interactions more complex than three-way interactions can be daunting!
Significant Differences
Significance
Setlle, Ball, & Runk (1997)
Listening to Mozart Does Not Enhance Backwards Digit Span Performance (1997)
Author Name: Setlle, Ball, & Runk
Background: Rauscher, Shaw, and Ky (1993) reported that participants in the study increased their mean spatial reasoning scores by 8 or 9 IQ points after listening to Mozart’s music for 10 minutes.
- This was labeled the “Mozart Effect,” and was found to be temporary, only lasting for 10-15 minutes.
- Attempts by Kenealy and Monsef(1994), Newman et al.(1995), Stough et al.(1994), and Carstens et al.(1995) were all unsuccessful in replicating the original findings.
- Rauscher, Shaw, and Ky (1995) reported a replication of the Mozart effect, specifying that an appropriate task should involve spatial recognition, as well as incorporating spatial and temporal transfusions.
Hypothesis: examine whether a Mozart effect would be produced following the procedure of Rauscher et al. (1993).
Main Structure:
- Used backwards digit span performance as the dependent variable, adhering to Rauscher’s specification that the task should involve spatial and temporal transformations.
- The study consisted of a within-subjects design with 2 independent variables and a control condition.
Methods
- Thirty-six Euro-American university students (28 Women and 8 men) from a psychology course who volunteered and received course credit for participating.
- Two stimulus tapes of a 10 minute duration were used:
–> Mozart Sonata for Two Pianos in D Major (K448)
–> Recording of a gentle rainstorm (“Spring Showers”)
- Sequences of digits were recorded on separate tapes for the digit span task.
- Participants were told the experiment concerned the effect of relaxation on recall and were sat in a comfortable recliner chair.
- All participants listened to the Mozart tape, the rainstorm tape, and sat quietly after being told to “relax,” with the order of each stimulus being counterbalanced using a Latin square design.
- After exposure to the stimulus condition participants listened to three nine-digit sequences and attempted to repeat the sequence in reverse order after each one.
- Correct recall was defined as the correct digit in the correct serial location.
IV: Type of music listed to (Mozart or spring showers)
DV: the sum of number of digits correctly recalled in reverse order.
Results
- No difference overall in mean recall as a function of preceding stimulus condition.
- Lack of differences not due to unsystematic variability.
- Clear practice effect was observed.
- Mean recall improved by additional experience with the task.
- no significant differences among treatments
- Exposure to Mozart’s music was not followed by an enhancement in performance on the backwards digit span task.
Critiques
*see image
Keltner, Ellsworth & Edwards (1993)
Beyond Simple Pessimism: Effects of Sadness and Anger on Social Perception (1993)
Author Name: Keltner, Ellsworth & Edwards
Background:
- General positive and negative moods shown to influence various judgments.
- (see Forgas & Bower 1987)
–> Personal Efficacy
–> TAT Scores
–> Social Performance
- However, not much research on specific effects that diff. emotions have on judgments
Hypothesis Overall:
- Empirical Question: Do different negative emotions influence judgments in more specific ways than creating a general pessimism?
- Hypothesis: Sadness and anger will exert different influences on causal judgments.
Effects of Sadness & Anger on Judgements of the Probability of Future Events
- Experiment #1: Sad participants will perceive situationally caused events as more likely than angry participants. Angry participants will perceive events caused by humans as more likely than sad participants.
Effects of Sadness & Anger on Judgements on Causal Judgments of an Ambiguous Situation
- Experiment #2:
Sad participants will emphasize the situation as being the cause of an ambiguous situation.
Angry participants will emphasize other people’s actions as being the cause of an ambiguous event.
Sad participants will perceive an ambiguous situation as hopeless.
Angry participants will perceive others’ actions as unfair in an ambiguous situation.
Main Structure
- 48 college students from intro psych class at Stanford
- 2x2 Factorial Design
Students were randomly assigned to 1 of 4 conditions
Methods
- experiment #1:
–> Participant Instructions: the survey will investigate the way people imagine hypothetical scenarios.
–> Emotion Induction (sadness or anger)
–> Life Events Questionnaire
- experiment #2:
–> Same false instructions as Exp. #1
–> Emotion Induction - same as Exp #1**
–> Target Situation
–> Questionnaire (rating on 1-9 scale)
a. Target situation’s causes
b. Situation’s hopelessness
c. Fairness of others’ actions
d. Your emotions (sad, angry, guilty, contemptuous, happy, proud)
IV: were induced sadness and induced anger
DV: Rated probability 1-10 of life events
Results
- statistically significant differences
- 3 way interaction between Emotion, Agency of Judgement & Form Type was significant (partially confirms hypothesis)
- Emotion and Judgement Interaction = Not significant (doesn’t support hypothesis)
- Sad participants were more likely than angry participants to attribute the mishap to situational forces. Angry participants were more likely than sad ones to attribute it to other people.
- Sad participants perceived the situation to be more hopeless than angry participants. Angry participants perceived other people as less fair than angry participants.
Overall:
- Researchers found that different negative emotions would result in different interpretations of events.
- Sadness → More situational agency
Anger → More human agency
Used different manipulations & measures to confirm this
Sadness and anger BOTH influence judgments of…
- Probability of future events caused by humans or situational forces
- Responsibility for an embarrassing social situation
- The sources of one’s own life circumstances and future problems.
In real life..
- Emotions are more salient → have greater effect (most likely)
*experiments #3-5 replicated results of experiment 1 while adjusting certain conditions and the results supported the original hypothesis
Critiques see image
Main effects and Interactions
One main effect or
Two main effects or
No main effects
And
Interaction or
No interaction
Color vs Black & White
What kind of effect is this?
One main effect: color vs Black & White
If one is always higher than the other, this is one main effect AND no interaction (parallel)
- you don’t say it depends (doesn’t depend)