1. One Way ANOVA test
Determine whether there are any statistically significant differences between the means of three or more independent groups

2. There are no significant differences between the means
Null Hypothesis
There are no significant differences between the means
A = B = C = D = E

3. Alternative Hypothesis
If you reject the null hypothesis and accept the alternative: there are at least two groups with a significant difference
Cannot pinpoint which ones are significantly different just with this test

4. Another way to look at how spread data is around the mean
ANOVA
Analysis of variance
Another way to look at how spread data is around the mean

5. Remember Standard Deviation

6. Take away the square root and you get variance-1 -1

7. Each part of the equation
∑ is sigma (sum of) x is each number
x is the mean
N is how many numbers are in the set

8. Steps to work out variance
Work out the mean
Find (x – x)2 for each value
Add the numbers together
Divide the total by the number of values minus 1

9. Daily coffee consumption
Italian
French
American
n (sample size) 70
M (mean)
4.0
3.7
3.4
S^2 (variance)
4.4
5.2
6.1
(N) Total sample size = 210

10. Null Hypothesis There are no significant differences between the means
French = Italian = American

11. Alternative Hypothesis
At least one group is different to another
French = Italian = American

12. Degrees of freedom (there are two for this test!)
BETWEEN
Total number of groups – 1
3-1
DF between = 2
(numerator DF)
WITHIN
Sum of individual degrees of freedoms for each group
French: 70 – 1 = 69
Italian: 70 – 1 = 69
American: 70 – 1 = 69
Sum = 207
(denominator DF)

13. This is what you will compare your ANOVA value to
Numerator DF = 2
Denominator DF = 207
Critical value is
This is what you will compare your ANOVA value to

14. Calculating the ANOVA Step 1: The grand mean
Sum of all individual means divided by total number of groups
( )/3
= 3.7

15. Step 2: Variance of the means
∑ is sigma (sum of) x is each number
x is the mean
N is how many numbers are in the set

16. Step 2: Variance of means
(4.0 – 3.7)2 + (3.7 – 3.7)2 + (3.4 – 3.7)2
(3 – 1)

17. Step 2: Variance of means
(4.0 – 3.7)2 + (3.7 – 3.7)2 + (3.4 – 3.7)2
(3 – 1)
= 0.09

18. Step 3: Calculate variance BETWEEN groups
Variance of means x n
(n is the sample size for each group)
0.09 x 70 = 6.3
s^2BETWEEN

19. Step 4: Calculate variance WITHIN groups
(Sum of variances of each group)/number of groups 3
5.233
s^2WITHIN

20. F = s^BETWEEN/s^WITHIN
Step 5: ANOVA value (F)
F = s^BETWEEN/s^WITHIN
= 6.3/5.233
= 1.20

21. Step 6: compare F value with critical value
Reject the null hypothesis if F>critical value
What do we do?

22. Step 6: compare F value with critical value
Accept the null as F value is lower than critical value
Cannot say with confidence there is a difference between how French, Italian and American people drink coffee