One Way ANOVA

One Way ANOVA

analysis from when you have more than two groups

omnibus test

assesses the equality of all the mean simultaneously

if omnibus test if significant follow up with

post-hoc-test

Factor

the independent variable that designates the group being compared

level

the different conditions or values that make up a factor

fixed effects

the levels that the research is interested in are included in the design and analysis for the study ; generalization can only be made about levels of the IV that are actually selected

ANOVA compares two sets of estimates of population variance

1- variability between sample means

2- variability within samples

null hypothesis of ANOVA

all groups are random samples from the same population having a mean u and a variance (same)

total sum of squares

variability there is between scores

between treatment sum of squares

how much variability can be explained by the model we fit to the data — variability due to the experimental manipulation

within treatment sum of squares

how much cannot be explained; variability due to individual differences

test the significance of the model

use an f-statistic; similar to multiple linear regression

when null hypothesis is true F-ratio

is near 1; treatment group effect is near zero

if alternative hypothesis is true, F-ratio

is larger than 1; treatment group effect more than zero

F-Ratio Equation

(SSb/dfB) / (SSw/dfw)

SSTotal equation

individual scores - grand mean; dfT=N-1

SSw equation

score-group mean; add all group sum of squares together; dfw = N-k

SSb equation

Sum(n*(mean groupi - GM)² - dfB = k-1

Effect size n²

proportion of total variance explained by the indicated source (R² or r² ) based on the sample

instead of using n² because its biased used

omega ²

what does the omnibus test indicate

F-ratio indicates that at least one difference in means is statistically significant; BUT it does not indicate which means differ significant from each other

Post-hoc test

not planned - no hypothesis and compare all pairs of means

3 post hoc test

bonferroni

scheffe’s test

tukeys honesty significant difference

bonferroni’s solution

use stricter alpha, divide alpha by number of comparisons

Scheffe’s test

an F-statistic but the MSB'; only contains the two groups being compared