1. The ANOVA, Easy
Statistics

2. Why an ANOVA? Greater power! Utilizes variance instead of the means.
F = MSb/MSw
Analyses multiple independent variables and levels
Provides interaction analyses

3. Interactions?
When one independent variable changes as the result of another independent variable’s activity
How I killed my grandmother’s plants

4. What the F is That Ratio?
Essentially, this is a measure of the variance between groups as compared to the variance within the groups.
The greater variance between and the less variance within, the higher the ratio
Significance is determined along an F distribution (roughly similar to a t distribution) utilizing degrees of freedom.

5. Making Assumptions Linearity Normality Homogeneity of Variance
Interval level data

6. The F Ratio in Eight Simple Steps
SSb = [(SX1)2/n1 +(SX2)2/n2…] – (SXall scores)2/N
SSw = SXall scores2 - [(SX1)2/n1 +(SX2)2/n2…]
SSTOT = SXall scores2 - (SXall scores)2/N
dfw = N – k (k = number of groups)
dfb = k – 1
MSb = SSb / dfb
MSw = SSw / dfw
F = MSb / MSw

7. Easiest if it Starts With a TableX1 2 3 7 6
X12 X2 10 8 7 5
X22 X3 10 3 14 13 15
X32 4
100
100 9 64 9 49 49
196 4 25
169 36
100
225
S = 20
102 40
338 65
859
S all scoresX2 = 1299
Sall scores X = 125

8. Step 1: SSb SSb = [(SX1)2/n1 +(SX2)2/n2…] – (SXall scores)2/N
=[202/ / /5] – 1252/15
= –

9. Step 2: SSw SSw = SXall scores2 - [(SX1)2/n1 +(SX2)2/n2…]
= 1299 – [202/ / /5] =
= 54

10. Step 3: SSTOT SXall scores2 - (SXall scores)2/N 1299 – (1252/15)
SSTOT = SSw + SSb
= =

11. Steps 4 and 5: Degrees of Fredom
dfw = N – k (k = number of groups)
= 15 – 3 = 12
dfb = k – 1
= 3 – 1 = 2

12. Steps 6 and 7: The Means Squared
MSb = SSb / dfb
= /2 =
MSw = SSw / dfw
= 54/12
= 4.5

13. Step 8: Calculate F F = MSb / MSw = 101.667/4.5 = 22.59
…but is it significant?
F crit = 3.88 (p = 0.05)
(F(2, 12) = 22.59, p ≤ 0.05)

14. After the Fact So, what does this mean?
That one of these three groups is different from another one of these groups.
Useless? Not quite, but will need a post hoc test to sort it out:
Tukey’s HSD
Fisher’s LSD

15. It is Soooo Much Easier With a Computer
To demonstrate, let’s use SPSS on the provided data set and interpret the results.

16. The F ratio is best described as
The ratio of variance between groups and the variance within groups
The largest gap between the means of two groups
The difference between means and the total standard deviation
The difference between expected and observed frequencies
The ratio of variance between groups and the variance within groups

17. An interaction is best described as:
The significant difference between means
The interaction between one dependent and one independent variables.
When change on the dependent variable, which is attributed to one independent variable changes based on another independent variable.
When a significant correlation between the dependent and independent variables is noted.
That really long one

18. Questions? Thoughts?