Statistics

Ways to Gain Information

Empiricism, Faith/Intuition, Tenacity, Authority, Observe, Tradition, Rational/Logical

Empiricism

Research Based

Faith/Intuition

Gut, No Source, Can not separate accurate v. inaccurate

Tenacity

Superstitions, "Lucky Charm

Authority

Experts in the field, Bias, Wrong, Subjective

Tradition

Info accepted as true/ Always have; "Can't teach dogs new tricks

Rational/Logical

Assumptions/Wrong

Observe

See it, but cannot observe all situations

Inductive

Start specific move toward generalizabilty

Deductive

General topic narrowed down to specific topics

Research Hypothesis

Have a topic not yet confirmed; educated guess for the outcome; Design an experiment to test the assumption (Must be Testable)

Null Hypothesis

Ho (No Change)

Alternative Hypothesis

Ha (Modify IV (Intervention))

Independent Variable

IV; The variable being tested/observed

Dependent Variable

DV; Outcome

Operational Definition

Specific & Observable Definitions of Variables

Positive Correlation

1 thing goes up; other thing goes up; (Same Direction); EX: Pressure on Gas, Speed Increases

Negative Correlation

One thing goes up, other thing goes down (Opposite directions); Pressure on breaks; Car slows down

Correlation

Cause & Effect Relationship

Types of Correlation

Temporal Order, Correlation/Co-variation, No Alternative Explanations

Temporal Order

1st thing comes before something less

Correlation/Co-variation

1 thing to move in relation to another

No Alternative Explanations

(! Ha); ex: Ice cream sales, heat & crime)

Validity

Internal & External

Internal Validity

Internal Relationship

External Validity

Generalizability

Prevent Internal Validity Threats

Random Assignment

Prevent External Validity Threats

Replication

Construct

Umbrella that holds everything about/goes into the experiment

Types of Constructs

Face Validity, Concurrent Validity, Convergent Validity

Face Validity

If experiment looks like it's measures what it is supposed to measure (right); checked with experts in field

Concurrent Validity

Comparing results to other similar research; Measuring something in generally the same way

Convergent Validity

Same stimulus/Using same set of data; Come to same conclusion

Reliability Measures

Regression to the Mean, Interrater, Intra-rater

Regression to the Mean

Math test today vs. Math test Tomorrow (Test; Retest)

Interrater Reliability

Different people rating the same thing

Intra-rater Reliability

Same person rating the same thing

Range

Upper limit of highest number to Lower limit of lowest number; Highest number to Lowest number + Class Interval; Interval

Scientific Method

(1) Observe,
(2) Hypothesize,
(3) Use hypothesis to Generate Testable Prediction,
(4) Evaluate Prediction by making Systematic, Planned Observations,
(5) Use Observations to support, refute, or refine hypothesis.

Bias

Error, Deviate, Residuals (Average = Expected Value)

How to reduce Bias

Bigger sample; Way present Information; Standardize

Demand Characteristics

How people behave in Study; Help or harm you/the experiment

Hawthorne Effect

Change behavior when know you're being watched

Good Participant

Know what you want to heard & give it to you

Bad Participant

Make up data; Know what you want; gives you bad data

Institutional Review Board (IRB)

Make sure experiments do not harm any human beings (Informed Consent, Confidentiality, Deception)

Probability Sampling

Random, Stratified Random, Cluster, Proportionate

Simple Random

Equal chance to be selected; Choice of 1 doesn't affect others

Stratified Random

Define groups (left out); Try to get equal numbers for the groups; can oversample groups; EX: Age groups (18-25, 25-30)

Cluster

Large sample; Not representative; Random unbias size unknown; main equal chance to be selected; EX: neighborhood

Proportionate

Divide population calculate probability of all groups; Reflect correct proportions of groups (Underrepresented)

Non-Probability Sampling

Convenient, Quota, Purpose, Snowball

Convenient

Voluntary (selected, available, have to (for a grade); Bias

Quota

Identify subgroups, but take all available people; Fill the spots/#'s; 50 men & women (or whoever is available)

Purpose

Select people - certain characteristics; Extreme groups; (EX: Top 5% vs Bottom 5%)

Snowball

Not random; Only way to get unlikely participants; Hard to generalize; Population that would not volunteer [EX: Addicts, Prostitutes]

Fraud

Fudging your information; Filling in any answer; Explicit effort to falsify/ manipulate data

True Experiments

...

Non-Experiment

No control group; pre-experiment

Correlational Study

2 independent studies to see if they correlate; Ex: anxiety & depression (Not Causation)

Quasi-Experiment

Missing Randomization; Analyzing; No IV/DV

Greek

Population (Parameters); Constant; (u, o)

Latin

Statistic; Variable; (x, s)

Population

N; All possible options for people (Whole population)

Sample

n; People you collect for your research

Occam's Razor

Simplest Solution tends to be the best one"; Ex of Parsimony

Scales of Measurement

Nominal, Ordinal, Interval, Ratio

Nominal

Categories with no relation to others; (EX: Hair color; Sports jerseys)

Ordinal

Categories grouped; Order Matters; Groups do not have to be equal; (Silver, Bronze)

Interval

Categories are increments are the same; Zero: no meaning; absence; (Temperature)

Ratio

Categories with intervals and an absolute zero; Absent zero; (Distance Traveled)

Kurtosis

Measures thickness of the tails*; not center mass; (Variance)

Leptokurtic

Tales very narrow; Scores closer to mean

Mesokurtic

(Normal) Baseline to compare other examples

Platykurtic

Incredible difference; (EX: Height of circus performer)

Positive Skew

Tail in + direction away from 0 (Zero)

Negative Skew

Tail in - Direction toward 0 (Zero)

Normal Standard Deviation

Mean, Median. Mode = 0 (Perfectly Standardized); Measure in Z Scores; Percentile - Closer to 0; Closer to percentile points

The Standard Deviation

Principles of Science

Empirical, Public, Objective

Empirical

Structured; Observations; Support/ Reject Hypothesis

Public

Available for others to Replicate* it

Objective

Not Skewed/Bias

Pseudoscience

Hypothesis not refutable/ testable

Types of Psychological Research

Qualitative & Quantitative

Qualitative

Numbers, Scores, Statistical Analysis; Interpret Results

Quantitative

Observation, Understanding something (ex. Behavior)

How to Find Research Topics

(1) Interests
(2) Observations/Practical Issues
(3) Theories
(4) Previous Research

2 Types of Variables:

(1) Well-Defined
(2) Constructs

Well-Defined

Easily measurable (Height, Weight)

Constructs

Intangible/Abstract; Hypothetical entities that predicts behavior

Validity.

Measure what it is supposed to measure

Reliability

Able to be replicated; Generalized; Consistency

No Correlation

Constructs

Scores from measurements behave same as construct measured

Types of Constructs

Convergent & Divergent

Convergent

Measure correlates with similar constructs; Different scales/tests that measure the same answer

Divergent

Does not correlate with different constructs; EX: Happiness test measures with Depression

Factor Analysis

Structure of Scale; Support that sub-domains exist; Verbal Comprehensions (Dimension Scales; Sub-scores)

Content

Items on measure/Test; Items represent Sample/ Content/Construct (Educational)

Criterion

Measure persons standing; (Psych Boards; Intervention)

Types of Criterion Validity

Predictive; Concurrent; Incremental

Predictive

The test & future criterion; GPA+SAT=College Exam

Concurrent

Same point in time

Incremental

Increased value when adding multiple factors

True Score Theory

Every score has true level of knowledge & some error; (X = T + E)
Observed Score = True Score + Error

Test & Retest

Success of Measurements; Problem: Learned from first test (Parallel tests, Change wording)

Interrater

Simultaneous evaluation; Agreement btw 2 or more people who rate/grade sessions

Internal Consistency

Split & Cronbach's Alpha

Split Half

Split down the middle; Compare one half to the other; EX: 100 Question test - Compare 50? To other 50?

Cronbach's Alpha

Average of all split half correlations; Remove bias; (EX: .9 or higher = Good); High stakes tests

Modalities of Measurement

Self-Report; Physiological; Behavioral

Self-Report

Direct Questions (Pain level)

Physiological

Objective, Expensive; May not provide valid measure of construct; (EX: Blood pressure, heart rate, MRI)

Behavioral

State vs. Trait; Behaviors are NOT stable; (Scales, Words Recalled, IQ) (EX: IQ vs. Hunger)

4 Ethical Issues:

(1) Do NOT Harm
(2) Informed Consent
(3) Confidentiality
(4) Deception

Do NOT Harm

Ex: Prison Studies (Guards vs. Prisoners); Milgrim Study (Electric Shock)

Informed Consent

Know all information about a study to make rational decisions;
(1) To be apart of the study or not
(2) To cancel or quit at any time
(3) Understand what is expected of them in the study

Confidentiality

Everything Protected & Safe & Secure; All Demographics, Responses and other information are secure

Deception

Could Modify Behaviors of Participants if they knew true reason for the study;Behavior Modification

Debriefing

Informing the participants of the true purpose of the study AFTER the study is over.

2 Types of Deception

Passive & Active

Passive

Withhold Information (Test on Memory)

Active

False or Misleading Information (Confederate)

Confederate

Use of actors in studies
(Ex: Ashe Study: Match the lines; All actors with 1 participant)

Plagarism

Using someone else's work & publish as their own; Unethical representation of someone else's work as their own

Types of Bias

(1) Parsomony
(2) Plausible Rival Hythothesis
(3) Findings VS. Conclusions

Parsomony

Occum's Razor to Research

Plausible Rival Hythothesis

Results of any simple experiment may be result of influences other than IV; *Eliminate All Other Factors; Demonstrate effect multiple times to be true; (Ex: Significant findings could be due to chance or bias)
Demonstrate effect multiple times to be true

Findings

Descriptive feature of study; (What you got from the study)

Conclusions

Hypothesis (Expansions of Content)

Single Blind Study

Participant unaware of Study

Double Blind Study

Participant & Experimenter Unaware of Study

4 Elements of Experiments

(1) Manipulation
(2) Measurement
(3) Comparison
(4)

Manipulation

Researcher manipulates IV to change the value; Levels of the Independent Variable

Measurement

(Dependent) measure effects of change; Cause

Comparison

Scores/Treatment condition compared to another;
(a) Experiment:
(b) Control:

Experiment

Receive treatment or different level of treatment

Control

Do not receive treatment/ Placebo

Control

IV & DV; Control all other Variable Separate from IV & DV; Extraneous/ Confounding Variables (Do not affect IV & DV)

Control for Confounding Variables

(1) Match Design
(2) Random Assignment
(3) Confound

Match Design

(Stratified Sample) Match so both groups are equal

Random Assignment

Randomly assigned to 1 group/ other (Divide group evenly)

Confound

2 Variables are related to another unknown variable (Random, Manipulation, & Comparison )

Pre-test

Determine pre-existing knowledge before the study; When cannot control for experiment (Quasi-experiment)

Control Group

Something to compare the experimental group against

Random Sample

How you drew the people/population to study

Stem & Leaf Plot

Group Scores; Know the Information; Weakness: Do not know exact #'s (Lost Info)

Interpolation

Group Frequency Table; Weakness: Lose Specificity

Histogram

Interval/Ratio Data (Continuous); Real Limits

Bar Graph

Ordinal; Nominal

Probability Density Function

Normal Distribution; At mouth of the curve of Histogram -- With More Score Points; (For All Score Points)

Mean

Add all scores (divide) by Sample Size; Ordinal; Ratio/Interval (No Nominal); Most representation not always suitable

Median

Middle; 50% (Percentile)

Mode

Most Frequent Numbers

Symmetrical Distribution

Mean, Median are the same; 2 Different Modes

Uniform Distribution

Mean, Median are the Same; No Mode; No Peak; Random Sampling

Intercortical Range

Between 75% & 25% (percentile); Closer to Middle (Middle 50% - percentile)

Semi-Intercortical Range

Take intercortical (75% -25%) & Divided by 2

Variance

Average (squared)2 difference from mean

Standard Deviation

Average Distance from Mean; Most scores within Range (Mean)

Degrees of Freedom

# of Scores in observation; Not all options are free to Vary (cannot change)

Z Scores

Relative standing in the group; Score in Standard deviation units; Positive above the mean, Negative below the mean

Standardizing of Z Scores

Negative Numbers (Half positive, Half negative); Difficult to interpret negative score (May not be correct interpretation)

Unit Normal Table

3 ways to look up probability; Proportion in body, tail; Z Score greater than 1

Distribution of Sample Means

Collection of Sample Means of ALL possible random samples for a particular size; Normally distributed - Because Normal (same method for individuals)

Standard Error of the Mean

R O X O
R O O
Difference is the X; Treatment Made a Difference

History

Specific (global) events occurring btw 1st & 2nd measurement

Maturation

Respondents are function of passage of time
(a) Change over time
(b) Growing older, hungrier, more tired, etc.

Testing

Effects of taking a test upon the scores of the 2nd test; Only introducing testing threat (EX: Pre-test vs. Post-test)

Instrumentation

Changes in measurements due to changes in calibration of measuring instrument or in observers/scorers (Different rater & rater style; Change measures from Pre-test to Post-test)

Statistical Regression

Groups selected on basis of extreme scores; Extremes natural rush toward means (Regression toward the mean)

Selection

Biases of respondents for comparison groups; 2 Groups - Not equivalent before study begins

Experimental Mortality

Differential loss of respondents from comparison group; Die or Drop out of the study/ experiment

Selection-Maturation Interaction

Multiple-group quasi-experimental designs is confounded w/mistaken for the effect of experimental variable; Not equivalent before study; 1 group matures quicker than the other

Reactive/Interaction Effect of Testing

Pretest might increase or decrease the respondent's sensitivity or responsiveness to experimental variable; Know what study is about/ other group present; Cannot generalize to the population

Interaction Effect of Selection /(Treatment) Experimental Variable

Groups not equivalent prior to study; Respond to treatment differently; Hard to recruit sample

Reactive Effects of Experimental Arrangements

Conditions of study different from real world; People know in study and React differently (Being Watched)

Multiple Treatments Interference

Multiple treatments are applied to same respondent; Prior treatments are not erasable; Repeated measures design (ABAB); Because repeated (measure if works) OR Different treatment unsure which one worked

Temporal Sequence

Intervention first then measurement (Cause than Effect)

Reactivity

Modify natural behaviors to natural settings

Good Subject Role

Aware of purpose of study & try to support hypothesis (Ex: Respond in unnatural ways)

Apprehensive Subject Role

Overly concerned about being evaluated; Worried about answers & how they respond; Dishonest because uncomfortable

Negative Subject Role

Not Nice; Know study and want to be oppositional/ disprove the study or hypothesis

Faithful Subject Role

Know hypothesis, but avoid acting on it; Do not want to screw up the study; Honest, apathetic & Not affected

Inferential

Generalizing from sample to population; How general public will react based on sample

Effect Size

Size of the difference rather than confounding with sample size

Hypothesis Testing

4 Steps:
(1) State Hypothesis
(2) Set alpha level & criteria for decision
(3) Parametric Test (Assumptions)
(4) Make Decision

State Hypothesis

Ho (Null Hypothesis)
H1: Alternate Hypthesis

Null Hypothesis

(Ho) No Effect = IV had no affect over DV

Alternate Hypothese

(H1) IV does have affect over DV

Set alpha level & criteria for decision

Alpha Level

Alpha

What would warrant rejection of Ho; Define probability value for what is unlikely

Alpha Level

To confidence or error probability; Not always failure of treatment (by chance)

1 Tail Test

ex: 5% chance on 1 end (all on 1 side)

2 Tail Test

split on either side of region; examines positive and negative effects (Critical region in tails)

Parametric Test

Assumptions:
(1) Normality
(2) Homogeneity
(3)Interval/Ratio
(4) IV Observations
(5) Random Sample

Normality

Sample or Hypothesis are normally distributed

Homogeneity of Variance

Multiple groups; Pulled Variance (Same Population)

Independent Observations

Each person is responding independently; Other participants do not influence another

Random Sampling

Infer from sample to population (Must be Representative)

Make Decision

(1) Reject Null
(2) Fail to Reject the Null

Reject the Null

Support the Hypothesis; If sample statistics falls in critical region; Parsimony

Fail to Reject the Null

May be left out some portion; Always Alternate Evidence

Parsimony

Without further evidence, No effect

Decision Accuracy Table

Z-Test

Standard area with fixed (same area) = fixed parameter; (Find Z - See if it falls in/out of the tails)

Critical Region

Single T-Test

Approximate population variance with sample variance

T Statistic

t(df) = (t-value), p<(p-value)

Between Samples

(Independent Variable) Same population; Control Groups [Ex: Male vs. Female; Treatment vs. Control]

Within Samples

(Dependent Variables) Same participants; Change for sample group; [Measure Anxiety , then Hypnosis]; Measure Impact of Treatment

Matched Subject Design

(Equivalent Groups) Same Qualities; [1 treatment, 1 control group; People that compare in characteristics]

Independent T-Test

Ho = u1 - u2 = 0;
(1) Find df
(2) Find Sp
(3) Find t Value
(4) Define Critical Region
(5) Reject/Fail to Reject

Dependent T-Test

Evaluate 2 set of scores (Impact of treatment);
(1) Ho = u = 0
(2) Find df
(3) Find Sx
(4) Find T Value
(5) Define Critical Region
(6) Reject/Fail to Reject

ANOVA (1 Way)

Evaluate mean difference between 2 populations; Purpose: Split different types of variance

1-Way Anova Steps

Ho= u1 = u2 = ... = u15
(1) Level of Significance & Critical Level
(2) Complete Source Table
(3) Reject/Fail Null
[F(df1,df2) = F, p (>,<) .05/.01, R2 = (value)

Anova Source Table

Correlation Statistics

Relationship between 2 variables; No Causal; [Greek - p; Latin - r]; (For validity & reliability)

3 Characteristics of Correlation

(1) Form (Linear)
(2) Direction of Relationship (Positive/Negative)
(3) Degree of Relationship (Strength)

Correlation - Degree of Relationship

Closer to 0 (bad; no relationships); Closer to 1 (stronger relationship)

Pearson Correlation

Linear relationships; Interval/Ratio; Quantifies relationship between 2 variables in a scatterplot

Regression

Finding best-fitting straight line for set of data ("Fit Line"); Predict "y" when only know "x" value; Higher the correlation, higher the prediction

Residual

Left over" [Same as the deviate from the mean]

Restriction of Range

Do not know the full extent of the relationship; Make predictions, Do not have all the information;
(Limits the correlation; Do not go the full range)

Outlier

Extreme score compared to average data; Remove it - Mess up data