ANOVAANOVAUsed to test difference of means Used to test difference of means

between 3 or more groups.between 3 or more groups.

Assumptions:Assumptions:Independent samplesIndependent samplesNormal distribution Normal distribution Equal VarianceEqual Variance

HypothesisHypothesis

Hr: At least one group mean is not equal to Hr: At least one group mean is not equal to at least one other group mean. at least one other group mean.

Ho: Ho: μμ1 = 1 = μμ2 = 2 = μμ33

Conceptualizing ANOVAConceptualizing ANOVA

Does the IV (i.e., belonging to a group (religion, Does the IV (i.e., belonging to a group (religion, social class, race) explain variation (differences) in social class, race) explain variation (differences) in the DV.the DV.

Example:Example:Research Question: Research Question: Does the average IQ differ Does the average IQ differ

among working, middle, and among working, middle, and lower class individuals?lower class individuals?

Hr:Hr: The average IQ for at least one social class is The average IQ for at least one social class is different from one or more of the other social different from one or more of the other social classes.classes.

Anova uses an F test to test the relationship Anova uses an F test to test the relationship between the IV and DV when we have three or between the IV and DV when we have three or more groups.more groups.

A significant F value:A significant F value:

Reject Ho Reject Ho At least one group mean is significantly At least one group mean is significantly

different from the other group means. different from the other group means.

A Closer Look at the F TestA Closer Look at the F Test

Compares variation within groups to variation Compares variation within groups to variation between groups .between groups .

Variation between groups is the deviation of Variation between groups is the deviation of each group mean from every other group each group mean from every other group mean.mean.

Variation within groups is the deviation of the Variation within groups is the deviation of the raw scores from each group mean.raw scores from each group mean.

Calculating ANOVACalculating ANOVA

F = MS (mean square) Between/ MS WithinF = MS (mean square) Between/ MS Within

MS is derived from SS (Sum of Squares) MS is derived from SS (Sum of Squares) (3 components SS total, SS within, SS between)(3 components SS total, SS within, SS between)

See Social Class & IQ example on overheadSee Social Class & IQ example on overhead

ANOVA in SPSSANOVA in SPSS

Hr:Hr: The average age for first kid born for at The average age for first kid born for at least one group is least one group is different from one or more of different from one or more of the other group means.the other group means.

See SPSS overheadSee SPSS overheadRemember F = MS between / MS withinRemember F = MS between / MS within

SPSS outputSPSS outputMS between = SS between / df betweenMS between = SS between / df between

df between = k (# of groups –1) = 4-1=3df between = k (# of groups –1) = 4-1=3MS between = 1382.697/3= 460.90MS between = 1382.697/3= 460.90

MS within = SS within / df withinMS within = SS within / df withindf within = N (total N) – K (# of groups)df within = N (total N) – K (# of groups)df = 1960- 4 = 1956df = 1960- 4 = 1956MS within = 53296.40/1956 = 27.25MS within = 53296.40/1956 = 27.25

F = 460.90/27.25 = 16.91F = 460.90/27.25 = 16.91

DecisionDecision

What is the significance level of for a What is the significance level of for a calculated F of 16.91?calculated F of 16.91?

Do we reject the HoDo we reject the Ho

How would you write up this result?How would you write up this result?

How often would we make a type I error?How often would we make a type I error?