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One way analysis of variance (anova)
One way analysis of variance (anova)
One way analysis of variance (anova)
One way analysis of variance (anova)
One way analysis of variance (anova)
One way analysis of variance (anova)
One way analysis of variance (anova)
One way analysis of variance (anova)
One way analysis of variance (anova)
One way analysis of variance (anova)
One way analysis of variance (anova)
One way analysis of variance (anova)
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One way analysis of variance (anova)

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  • 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

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