One-Way ANOVA Flashcards
What is the aim of a One-Way ANOVA?
To partition variance to see if the variance due to experimental manipulation is proportionally larger than the rest of the variance (error)
What is variance?
The spread of scores around the mean
What is error variance?
Random variance AND variance due to unmeasured influences
What is treatment variance?
Systematic differences due to the IV
How is total variance partitioned in a one-way ANOVA
Into between-groups variance and within-groups variance
What is between-groups variance?
Systematic variance due to membership in difference treatment groups
What is within-groups variance?
Error variance (averaged from both samples; pooled)
What does between-groups variance measure?
The distribution of group means around the grand mean
What does within-groups variance measure?
The distribution of individual DV scores around the group mean
What is the null hypothesis for a one-way ANOVA?
µj = µ.
What is the alternate hypothesis for a one-way ANOVA?
µj ≠ µ.
for at least one group
Conceptually, what is the formula for between-groups variance?
The squared sum of the differences between groups means and the grand mean, considering the number of observations in each group
Conceptually, what is in the formula for within-groups variance?
The squared sum of the differences between individual scores and the group mean
What is the test statistic for one-way ANOVA and how is it calculated
F-ratio = MStreat/MSerror
When will the F-ratio be more than 1 (significant)?
When MStreat is bigger than MSerror
When the between-groups variance is bigger than the within-groups variance
What does MStreat represent?
The between-groups variance
What does MSerror represent?
The within-groups variance
What are the steps in a one-way ANOVA?
- Estimate between-groups variability
- Estimate within-groups variability
- Weight each estimate by the number of observations used to generate the estimate (degrees of freedom)
- Compare the ratio (MStreat/MSerror)
What is on the numerator of the F-ratio?
MStreat
What is on the denominator of the F-ratio?
MSerror
What is the df for MStreat?
no. of groups - 1
(j - 1)
What is the df of MSerror?
no. of groups * (no. of scores in each group - 1)
j (n - 1)
Conceptually, what is the structural model of a one-way ANOVA?
An individual DV score is:
The grand mean
The effect of being in the jth group (between-groups variability)
Error for i person in the jth group (within-groups variability)
What is the long range average of a statistic?
The expected value of a statistic
What are the expected mean squares?
The expected value of MStreat and MSerror
What is the expected mean square of MSerror?
The population variance
What is the long range average of MStreat?
The population variance plus the long-range average of the variance between sample means considering the number of observations in each group
What is the expected mean square of MStreat when the group means don’t vary?
The population variance/ MSerror
