ANOVA Flashcards
What is the Null Hypothesis in one-way ANOVA?
All means are equal?
What is the Alternative Hypothesis in one-way ANOVA?
The means are not equal.
What does a small F-statistic mean?
Smaller differences between means
What does a larger F-statistic mean?
Larger differences between means?
What does decreasing F do?
The within-group variances increases, so F is less likely to be significant.
How do you calculate the Grand Mean?
Take all means of Groups and Average
How do you calculate the Model Sum of Squares?
- Take the difference between each Group Mean and Grand Mean.
- Square these
- Multiply by no. in each group
- Sum.
How do you calculate the Residual Sum of Squares?
- Take difference between Group Means and Individual data points.
- Square each number
- Sum all the data points.
How do you calculate the F-statistic?
F= MSm/ MSr
What is an Omnibus Test?
Tests the overall significant of the model. A significant F states means all means differ from each other, or one does.
What sort of distribution is an F?
One-tailed, because all differences are squared and positive.
What does the F statistic tell you?
About the effects in both directions, so cannot halve the p value for one tailed test if directional prediction, because the test is already one-tailed.
What are the three ANOVA assumptions in between-subjects?
- Observations should be independent
- Variances in each condition should be similar (homogeneity of variances)
- Distributions within groups should normally distributed
How do you test the Homogeneity of Variance between conditions?
The Levene Test
How does one run the Levene Test? And why do we want it to be non-significant?
If the variances in the population are equal, differences will be equal.
If it is significant we have violated our assumption of homogeneity of variance.
We want this test to be non-significant
What does a non-significant Levene’s Test mean?
- not statistically different variances in sample.
- the variances are presumed equal and the ANOVA assumptions are met.
What is ANOVA used to assess?
Effect of a categorial IV with 3 or more levels on a continuous DV
What do you look for in an ANOVA output?
The Main Effects and the Interaction
How do you interpret the effects on a graph?
- The points are higher for one variable than the other on the graph.
- the interaction can be gleaned by the differences in the slopes of the line
What do ‘Simple Effects’ analyses do?
If there is an interaction between factors, used to understand the effect of one variable at one level of another.
What does the Higher-Order Factorial Designs
Concerns two-way or three way etc factorial designs. Looks at:
- X main effects
- X two-way interactions
- X way interaction
Steps in performing One-Way ANOVA by hand
- Calculate group and overall means and Calculate SSW
- Calculate MSS (between)
- Calculate MSS (within)
- Calculate F statistic
- Interpret the results! With F statistic.
1st step of calculating ANOVA
- Calculate mg (the addition of all numbers in a column of data)
- Calculate mG (the mg’s combined)
- Calculate mean of each column Xg
- XG = mean of mG.
- K = the number of groups.
2nd Step of calculating ANOVA
- Determine X1-Xg (squared) * X1 = column mean
- Calculate second group, X2 - Xg (squared)
- Calculate third group: X3 - Xg (squared)
- Sum up all the ( X-Xg ) columns
- Calculate SSw (within) = E (X1-Xg) + (X2 - Xg)… and then divide this number by n-k
(n being the total number data points, and k the number of groups)
3rd step of calculating ANOVA
- Calculate the MSS (between)
m1, m2, m3…. = mg (Xg - XG) (All S2)
- Sum the m’s =. E (m1 + m2 + m3)
- MSS = E. (m1+m2)
——————
k - 1
4th Step of calculating ANOVA
Calculate F. =
MSS. (within)
5th Step.
- Look up F statistic in critical value table
- Check degrees of freedom between:
- Degrees of freedom within:
- If the F stat is greater than critical value, reject the null hypothesis.
