Lec 20 - ANOVA, Post Hoc, Chi Square

ANOVA

technique used to examine differences between two or more groups

ANOVA outcome

a numerical value for the F-statistic

one-way ANOVA

used to analyze data in studies with one independent and one dependent variable

repeated-measures ANOVA

used to analyze data from studies where the same variables are repeatedly measured over time on a group or group of subjects; change over time

ANOVA assumptions (5)

1. the populations from which the samples were drawn (or the random samples) are normally distributed

2. the groups must be mutually exclusive

3. the groups must have equal variance (homogeneity)

4. the observations are independent

5. the dependent variable is measured at the interval or ratio level

post hoc

used to determine where the differences lie

Newman-Keuls

compares all possible pairs of means and is the most liberal (a is not as severely decreased)

Tukey HSD

computes one value with which all means within the data set are computed

Scheffe

most conservative test - with a decrease in the type I error there is an increase in the type II error

Dunnett

requires a control group - experimental groups are compared with the control group without a decrease in a

active independent variable

refers to an intervention, treatment, or program

attributional independent variable

characteristic of the participant (gender, diagnosis, ethnicity)

ANOVA formula

F = mean square between groups / mean square within groups

mean square

variance

between groups variance

differences between the groups/conditions being compared

-df = # of groups - 1

within groups variance

differences among/within each group’s data

-df = n - # of groups

ANOVA calculation steps (5)

1. compute the correction term - C

2. compute the total sum of squares and subtract C

3. compute between groups sum of squares

4. compute within groups sum of squares (subtract the between groups sum of squares (step 3) from total sum of squares (step 2)

5. create ANOVA summary table

pearson chi-square (x²)

inferential statistical test calculated to examine differences among groups with nominal level variables

chi-square assumptions (3)

1. the data are nominal level or frequency data

2. the sample size is adequate

3. the measures are independent of each other or that a subject’s data only fit into one category

chi-square df

based on the number of categories in the analysis

eq: df = (R-1)(C-1)

-R = rows

-C = columns

one-way chi square

statistic that compares different levels of one variable only

two-way chi square

statistic that tests whether proportions in levels of one nominal variable are significantly different from proportions of the second nominal variable

eq: x² = n[(A)(D)-(B)(C)]² / (A+B)(C+D)(A+C)(B+D)