1. One Way Analysis of Variance
(ANOVA)
Mike Arieh P. Medina

2. The ANOVA
• The analysis of variance compares the means
of three or more random samples and
determines whether there is a significant
difference between the populations from
which the samples are taken.

3. Problem:
Lake
Osian
Lake
Cee
Lake
Koy
3 4 9
1 3 7
3 5 8
2 5 11
4 4 9
Is there a significant difference in the BOD of 3 lakes at 0.01?

4. Hypotheses
• null hypothesis, assumes that the means
are equal
• alternative hypothesis affirms that at
least one of them is different

5. Summary Statistics
Lake Osian Lake Cee Lake Koy Totals
Sum of X 13 21 44 78
Sum of X2 39 91 396 526
n 5 5 5 15
Mean 2.6 4.2 8.8
SS 5.2 2.8 8.8

6. Compute SSs
6.103
15
78
5
442113 2222
bss

7. Compute SSs
8.1680.88.22.5wSS

8. Compute SSs
4.120
15
78
526
2
TSS

9. Fill in the Summary Table
Source of
Variation
df SS MS F
Between 2 103.6 51.8 37.00
Within 12 16.8 1.4
Total 14 120. 4
dfb = no. of groups (k) – 1
dfw = total no. of observations – no. of groups (N-K)
MS = SS/df
F = MSb/MSw

10. Interpretation
• Fcomputed < Ftabular
– Accept H0
– Reject H1
• Fcomputed > Ftabular
– Reject H0
– Accept H1

11. Using the F-Table
df for denominator
Values
Top = 0.05
Bottom = 0.01Click to Download F-table

12. Now Interpret the Results
Credits: Research Methods (8th edition) by Graziano & Raulin