Psychology Statistics

One Sample Z-Test

-used to compare a sample mean to a population mean

-z-test is hard because we don't usually know the population standard deviation (use t-test instead)

Test Statistic

-a statistic whose value helps determine whether a null hypothesis should be rejected

T-Test

-a statistical test used to evaluate the size and significance of the difference between two means

-do not require knowledge of variability statistics in the population

General Form of t-test

t= (sample statisticpopulation - parameterestimated) / standard error of statistic

Effect Size

-A measure of how different two groups are from one another(or a measure of the magnitude of treatment)

-Represented by Cohen's d

Small Effect Size Range

0 - .2

Medium Effect Size Range

.2 - .5

Large Effect Size Range

above .5

independent samples t-test/Between Subjects Design

-a hypothesis test used to compare two means for a between-groups design, a situation in which each participant is assigned to only one condition

-Only tested once

Example of Independent Sample t-test

-Do exercise classes (i.e., in a group context) improve people's moods more than solo exercise (i.e., working out alone)?

-Null hypothesis : μclasses=μsolo (no difference working out alone or in group)

-Alternative Hypothesis: μclasses ≠ μsolo (there is a difference between working out alone or in a group)

homogeneity of variance

-situation in which the dependent variables do not differ significantly between or among groups

-variance in population for our groups is equal

dependent samples t-test/within subjects

-an inferential statistical analysis used when comparing two samples of data in either a matched groups design or a repeated-measures design

-compare same group against themselves

-Investigate whether some treatment made an effect compared to a baseline within the same individual(s)

-asks whether the mean difference between each subject's pair of observed values is significantly different from 0

self-efficacy

an individual's belief or confidence in his or her ability to achieve goals

Example experiment of dependent sample t-test

-Does watching a TED Talk affect students' perceived self- efficacy?

Outline of experiment

-Population --> measure self efficacy (baseline)--> watch TED Talk--> Measure self efficacy (post treatment)

How to get the difference of subjects in dependent sample t-test

Difference = baseline - post treatment

One-Way ANOVA

-To be able to measures differences along some dimension among subjects in more than two groups

-Only one factor w/ many levels

-Investigates whether any of the population means of our groups differ

-Omnibus Test

-Doesn't tell which group is different

ANOVA

-ANalysis Of VAriance

-Use F

Factor(s)

-Independent variable(s) in the study

Level(s)

-Groups within each independent variable

Response

-The dependent variable in the study

Example of factor, level, and response

-Factor: Political Affiliation

-Levels: Green party, Constitution party, Republican, democrat, libertarian, modern wing

Omnibus test

Tests whether there are any differences among groups

Why can't we just keep doing multiple t-tests?

Increases rate of Type 1 Error

Null and Alternative Hypothesis for One-Way ANOVA

-Null: μ1=μ2=μ3=...=μk (p=a)

-Alternative: The means are not all equal = there is a difference

General F-Statistic Formula

F= Variance due to group difference/ variance due to random chance (Error)

When will variance between groups be small?

-If there are no "treatment effects," or differences between groups, leading to a small F statistic

When will variance between groups be large?

-if there are "treatment effects," or differences between groups, leading to a large F statistic

What is the Effect Size of ANOVA represented by?

-represented by Eta n^2

Two-Way (Factorial) ANOVA

-To compare whether differences exist between multiple factors, as well as in interactions between the levels of different factors

Example experiment of two way ANOVA

-Factor A: Commute type

-Level A-1: Walking & Light Rail

-Level A-2: Drive

-Factor B: Time of Day

-Level B-1: 6:30AM

-Level B-2: 8AM

-Response: Comute Time

-Possible test #1: effect of commute type

-Possible test #2: effect of time of day

-Possible test #3: effect of time and commute combined

Factorial Plot

-see all possibilities

An Interaction

-describes the degree to which the effect of one factor depends on the level of the other factor

Review Correlation

-Either +, -, or zero

-Positive means one variable changes and the other variable changes the same direction

-Negative means as one variable changes the other variable changes in the opposite direction

-Zero means no relationship

-Correlations are between -1.0 & +1.0

-The closer to +-1 the stronger the relationship

-The closer to 0 the weaker the relationship

-Rxy

-Descriptive Statistics

Correlation with Inferential Statistics

-able to determine whether an observed correlation coefficient is significantly different from 0 or not

Coefficient of determination

-The percentage of variance in one variable that is accounted for by the variance in the other variable

r^2

For ANOVAS what type do the variables need to be?

-Nominal or Ordinal

What type of variables do Regression Models allow you to have?

-Ratio and interval

Problem with Regression Models

there are errors

Example of Regression Model

-Predict total cost based on # of drinks you buy

-Problem: if drinks cost different amounts

Regression

-A statistical technique for finding the best-fitting line for a set of data

-Be able to model the quantitative relationship between 2 variables, allowing us to make predictions about one on the basis of the other

General formula for Regression

Y'= bX + a

Mean structure models

-we seek to explain mean differences between groups or treatment conditions

Least Squares

an approach to fitting a model to data where the sum of the squared distances to the data is minimized

Multiple regression

be able to model the quantitative relationship between more than 2 variables, allowing us to make predictions about one on the basis of several others

Multiple regression formula

Y'= b1X1 + b2X2 + ... + bnXn + a

-Each variable has its own slope and there is still a point that hits y-axis