ANOVA

True or false The Calculated F (for a one-way ANOVA) is analagous to t-test and critical t

True

What is the F statistic or F ratio?

variance BETWEEN groups / variance WITHIN groups (error)

What is the Alternative (one way) hypothesis?

μ1≠ μ2≠ μ3≠ μ4 (There is at least ONE difference between groups)

What does a SIGNIFICANT INTERACTION tell us?

This tells us that any main effects may be MISLEADING or MEANINGLESS

What are the # of levels? Ex: You want to know how gait speed varies based on age and gender. Define IV, DV, and levels.

# of groups within each independent variable DV: Gait speed IV: Age and Gender 3 levels (groups) for age 2 levels (groups) for gender

How to calculate the degrees of freedom: 3 groups, 10 subjects per group, measured ONCE What is the TOTAL df?

# of observations - 1 30-1=29

Testing differences in gait velocity with 3 groups -Group 1: 50-59 year olds (n=10) -Group 2: 60-69 (n=10) -Group 3: 70-79 (n=10) What kind of ANOVA is this? Why?

1-way ANOVA There is ONE independent variable (age)

What thigns do you need in order to analyze an ANOVA for significance?

1. Calculated F statistic (ratio) 2. TWO different degrees of freedom values 3. Critical F (from table A.3)

What is a 2 way ANOVA?

2 independent variables

Testing differences in gait velocity with 3 groups -Group 1: 50-59 year olds (n=10) -Group 2: 60-69 (n=10) - Group 3: 70-79 (n=10) How many levels are there?

3 levels levels= groups 1-way ANOVA with 3 levels

What is calculated F used for?

4. ANOVA compares calculated F to critical F to test for a significant difference between ANY TWO MEANS

What is the assumption of an ANOVA?

NORMAL DISTRIBUTION for each group (just like the t-test)

What is the null hypothesis?

All means are equal μ1 = μ2 = μ3 = μ4

What is the error in the F statistic/ F ratio?

Any variation NOT due to the INDEPENDENT VARIABLE

What is the 2nd step when considering an ANOVA?

Assess the ANOVA summary table!

What do main effect and interaction effect have in common?

Assessing effect of the IV

You want to test for sex differences in gait velocity among 3 age groups used earlier. What is the "main effect"?

Average effect for each independent variable. Main effect for sex (combing all ages) "What is the effect of sex on gait speed? Is there a difference in gait speed if you're male versus female? Do men and women have different gaits speeds?" Main effect for age (combining both genders)? "Does gait speed depend on age?"

You want to test for sex differences in gait velocity among 3 age groups used earlier. What is the DV? How many IVs? How many levels?

DV: gait speed IVs: Age and sex Levels: 3 levels for age, 2 levels for sex

You want to test for sex differences in gait velocity among 3 age groups used earlier. What is the interaction asking?

Does the effect of gender (on gait speed) DEPEND on how old you are? Does the effect of age (on gait speed) DEPEND on sex? or: For gait speed, is there a different trend of increasing age for women versus men?

How to calculate the degrees of freedom: 3 groups, 10 subjects per group, measured ONCE What is the denominator df?

Error df = denominator df = (Total df) - (group df) Total df: # of observations - 1= 30 Group df: # groups -1 (numerator df) = 2 30-2=27

Testing differences in gait velocity with 3 groups -Group 1: 50-59 year olds (n=10) -Group 2: 60-69 (n=10) - Group 3: 70-79 (n=10) What is the dependent variable?

Gait velocity

What happens to critical F as the # of groups increases?

Gets smaller

What happens to critical F as the # of subjects increases?

Gets smaller

Internet What is the Sum of Squares?

How much the scores vary from the mean within a group Variability within the group

You want to know how gait speed varies based on age and gender. What are the IVs? DVs?

IV: Age and gender DV: Gait speed

Testing differences in gait velocity with 3 groups -Group 1: 50-59 year olds (n=10) -Group 2: 60-69 (n=10) - Group 3: 70-79 (n=10) What is the Independent Variable?

Independent variable = Age (grouping variable)

How to calculate the degrees of freedom: 3 groups, 10 subjects per group, measured ONCE What is the NUMERATOR df?

Independent variable = numerator df # groups -1 3-1=2

What is the 3rd step in assessing an ANOVA?

Inspect the group means! (Means and standard error section) Ex: Group 1 ---- Mean: 1.3, SE:.04 Group 2 -----Mean: 1.4, SE:.04 Group 3 -----Mean: 1.1, SE:.05

What is the fourth step?

Inspect the plot data to compare means

What is the interaction ?

Is there an interaction BETWEEN the independent variables? Analyze all subgroups for significant differences

What is MS between and MS error?

MS between: ANOVA compares avg variable between/among groups to MS error: avg variability between subjects WITHIN a group

Internet What is the mean square formula?

Mean Square= Sum of Squares divided by its degrees of freedom In ANOVA, mean squares are used to determine whether factors (treatments) are significant. Represents the variation between the sample means.

What is another way to re-state the formula for the F statistic?

Mean square BETWEEN groups/ Mean square WITHIN groups (error)

How to calculate the degrees of freedom: 3 groups, 10 subjects per group, measured ONCE How do you calculate critical F?

Numerator df (2) Denominator df (27) F critical (2, 27) = 3.35

When do you look at post-hoc tests?

ONLY IF overall F value is significant

You want to test for sex differences in gait velocity among 3 age groups used earlier. What is the null hypothesis for each main effect? What is the null for the interaction?

One null for each main effect: Age: μ1 = μ2 = μ3 Sex: μ males = μ females One null for the interaction: μ1 males = μ1 females = μ2 males = μ2 females = μ3 males = μ3 females

What is an ANOVA?

Parametric statistic that tests for differences among 2 or more MEANS

What is the FINAL check for an ANOVA?

Post-hoc tests

What is the purpose of a post-hoc test?

Purpose: Discover which pairs of scores are significantly different -Preserves FAMILY-WISE PROTECTION against Type I error

What is the first step in assessing an ANOVA?

Test for Normality Assumption: Skewness Normality of residuals

If you are assessing a graph for an interaction, what is the key?

The lines are NOT PARALLEL Means there is an interaction

What is error variance?

Variability among subjects in the SAME GROUP is considered error/error variance All variance WITHIN a group that is unexplained by the IV (in denominator of f-statistic?)