One Way Analysis of Variance
(ANOVA)
Mike Arieh P. Medina
The ANOVA
• The analysis of variance compares the means
of three or more random samples and
determines whether there is a ...
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 lak...
Hypotheses
• null hypothesis, assumes that the means
are equal
• alternative hypothesis affirms that at
least one of them ...
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....
Compute SSs
6.103
15
78
5
442113 2222
bss
Compute SSs
8.1680.88.22.5wSS
Compute SSs
4.120
15
78
526
2
TSS
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...
Interpretation
• Fcomputed < Ftabular
– Accept H0
– Reject H1
• Fcomputed > Ftabular
– Reject H0
– Accept H1
Using the F-Table
df for denominator
Values
Top = 0.05
Bottom = 0.01Click to Download F-table
Now Interpret the Results
Credits: Research Methods (8th edition) by Graziano & Raulin
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One way analysis of variance (anova)

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One way analysis of variance (anova)

  1. 1. One Way Analysis of Variance (ANOVA) Mike Arieh P. Medina
  2. 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. 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. 4. Hypotheses • null hypothesis, assumes that the means are equal • alternative hypothesis affirms that at least one of them is different
  5. 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. 6. Compute SSs 6.103 15 78 5 442113 2222 bss
  7. 7. Compute SSs 8.1680.88.22.5wSS
  8. 8. Compute SSs 4.120 15 78 526 2 TSS
  9. 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. 10. Interpretation • Fcomputed < Ftabular – Accept H0 – Reject H1 • Fcomputed > Ftabular – Reject H0 – Accept H1
  11. 11. Using the F-Table df for denominator Values Top = 0.05 Bottom = 0.01Click to Download F-table
  12. 12. Now Interpret the Results Credits: Research Methods (8th edition) by Graziano & Raulin
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