Transcript PSYC 221: Applied Statistics

PSYC 221: Applied Statistics
Analysis of Variance
ANOVA
Basic Logic of the ANOVA
• Estimating population variance
– Two ways to estimate
• Within group variance
• Between group variance
Hypothesis testing with ANOVA
• If null hypothesis is true:
– Between group / Within group =1
• If null hypothesis is not true:
– Between group / Within group > 1
The F distribution
-NOT normal
-Positive skew
-Based on variance (always positive)
-Relationship to t distribution
Why not just use t?
• Expand to more than two groups
– With t each comparison p=.05
– F can test for any differences
with overall p=.05
• Expand to test more than 1 IV
• Extremely flexible
• EASY
How easy is it?
• Summary tables
Source
SS
df
MS
F
Between
Compute
Means – 1
SSB/dfB
MS Between/MS Within
Within
TOTAL
SSW/dfW
Compute
Scores-1
Let’s try it on for size
• pg 320
• SPSS
Now what?
• Interpreting an F score
– The F table (pg 669)
– Two df
• Between groups df (numerator)
• Within groups df (denominator)
– Our example
– Conclusion
Follow up testing
• F tells us that there is some significant
difference somewhere, but not exactly where
– Reject the omnibus null
• Planned comparisons (contrasts)
– Simply run a t test for each comparison
• Compare criminal record versus clean record
• Compare criminal record versus no information
• Compare clean record with no information
– p=.05 each time
Fixing the p problem
• Bonferroni correction (planned comparisons)
– Adjust p so that all comparisons to be made add
up to no more than p=.05
– Problem?
• Type 1 error
•?
A continuum of conservatism
Tukey
Sheffe