The Logic of Statistical Analysis

Lesson 2

Population A Population B

Sample 1 Sample 2

OR

Mysteries of Life

We have questions Why do people behave that way? Is global warming occurring? Will my cancer come back?

To get answers, we need… Information Data Explanation analysis & interpretation ~

Theories & Statistical Models

Theories Describe, explain, & predict real-

world events/objects Models

Replicas of real-world events/objects

Can test predictions ~

Models & Fit Model not exact replica

Smaller, simulated Sample

Model of population Introduces error

Fit How well does model represent population? Amount of error in model Good fit more useful ~

Models in Psychology

My research model Domestic chicks Effects of pre-/postnatal drug use Addiction & its consequences

Who/What do most psychologists study? Rats, pigeons, intro. psych. students

External validity Good fit with real-world populations? ~

The General Linear Model Relationship b/n predictor & outcome

variables form straight line Correlation, regression, analysis of

variance Other more complex models ~

Populations & Samples

Population The whole group of interest parameter population mean =

Samples A portion of population statistic sample mean =~X

Populations & Samples

Research goals Learn about population Characteristics that widely apply Impossible/impractical to directly study

Research methods Study representative sample Introduce sampling error ~ X

Analyzing Data

Descriptive Statistics Quantitative descriptions of

characteristics Mean & standard error

Inferential Statistics Statistical tests Use sample descriptive statistics Draw conclusions about population

parameters ~

Hypothesis Testing

Hypotheses testable assumptions About groups

Same From same populations Null hypothesis

Different From different populations Alternative hypothesis ~

Population A Population B

Sample 1 Sample 2

OR

This or That?

Hypothesis Test: General Form

sindividualbetween difference

groupsbetween difference statistictest

21

21

XXs

XXt

Logic of the Hypothesis Test Difference between groups

Caused by independent variable Difference between individuals

Due to individual differences Average difference between

individuals chosen randomly Chance/error (or natural variability) ~

Variability & Variance Characteristics are variable

People are different Variance

Numerical measure of variability Expected differences between

individuals Statistics

Help sift through natural variability Help determine if same or different ~

Logic of the Hypothesis Test Groups the same

Or too similar Difference between groups =

difference between individuals Test statistic ≤ 1

Groups different Difference between groups bigger than

difference between individuals Test statistic >> 1 ~

Rosenthal & Jacobsen (1968)

Inferential statistics Hypothesis testing

Reporting results Descriptive statistics for each group Summary of results of statistical test

Bloomers (M=16.5, SD=19.4) had a statistically significant greater increase in IQ scores than Non-bloomers (M=7.0, SD=10.1), t(57)=2.36, p=.022.