Chapter 12: Analysis of Variance (ANOVA)

factor

the variable that designates the group being compared

levels

individual conditions/groups that make up a factor

one factor

one-way ANOVA

factorial design

a study that combines 2 or more factors

null hypothesis

the means of the groups do not differ

alt hypothesis

at least one mean difference between the groups

F-ratio

based on variance (variance between samples/variance within samples)

ANOVA

analyzes the overall variance to determine what is creating the variance

between treatments variance

variability results from general differences b/w conditions, differences b/w sample means (actual differences)

within treatments variance

variability within each condition, individual scores are spread out in each condition (sampling error)

null hypothesis and F-ratio

if null hypothesis is true, F is near 1.00, no evidence of systematic differences b/w groups

alt hypothesis and F-ratio

if alt hypothesis is true, F is larger than 1.00, evidence of differences b/w the groups

k

number of treatment conditions (levels, groups)

T

sum of scores for each treatment

N

total number of scores

G

grand total of all scores in study

df equations

dftotal - N-1; dfwithin - N-k; dfbetween - k-1

distribution of F-ratios

determine probability compared w/all possible f-ratios from all possible samples; table of F values is organized by 2 df -> df numerator (between) in table columns; df denominator (within) in table rows

steps of hypothesis testing

1. state hypothesis; 2. locate critical region (calculate dfs, look up critical value); 3. compute F-ratio in stages (compute SStotal, SSbetween, SSwithin -> computer MSbetween, MSwithin -> compute F); 4. make a decision

post hoc tests

follow up tests; determine exactly which mean differences are significant

relationship between ANOVA and t tests

F = t squared