TYPES OF ANOVA.pptx

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1. TYPES OF ANOVA

2. ONE WAY ANOVA: compares the means of two or more independent groups in order to determine whether there is statistical evidence that the associated population means are significantly different   One-Way ANOVA is a parametric test This test is also known as: One-Factor ANOVA

3. FUNCTION: The one-way analysis of variance (ANOVA) is used to determine whether there are any statistically significant differences between the means of three or more independent (unrelated) groups TWO HYPOTHESES: The null hypothesis (H0) is that there is no difference between the groups and equality between means (walruses weigh the same in different months). The alternative hypothesis (H1) is that there is a difference between the means and groups (walruses have different weights in different months) .

4. TWO WAY ANOVA: A two-way ANOVA is designed to assess the interrelationship of two independent variables on a dependent variable  compares the mean differences between groups that have been split on two independent variables (called factors ).

5. EXAMPLE: You are researching which type of fertilizer and planting density produces the greatest crop yield in a field experiment. You assign different plots in a field to a combination of fertilizer type (1, 2, or 3) and planting density (1=low density, 2=high density), and measure the final crop yield in per acre LAND at harvest time. You can use a two-way ANOVA to find out if fertilizer type and planting density have an  effect  on average crop yield.

6. EXAMPLE: A pharmacology research laboratory is testing the effect of four drug candidates on the concentration of nitric oxide (NO) in rat plasma (n = 12). The data for the quantification of NO, in µ mol /L, is displayed below. Determine if the treatments result in a significant change to the concentration of NO in rat plasma. (α = 0.05)

7. STEP 1: TABULATE THE DATA ON EXCEL SPREAD SHEET

8. STEP 2:  “Data” tab > Click “Data Analysis” > Click “ Anova : Single Factor” > Press OK

9. STEP 3: Highlight your data

10. STEP 4: Click the highlighted box

11. STEP 5: SET THE SIGNIFICANCE LEVEL

12. STEP 6 : SELECT THE CIRCLE TO THE LEFT OF “OUTPUT RANGE:

13. STEP 7: CLICK THE HIGHLIGHTED BOX TO THE RIGHT OF “OUTPUT RANGE:”

14. STEP 8: CHOOSE AN EMPTY CELL ON YOUR SPREADSHEET .

15. STEP 9: CHOOSE AN EMPTY CELL ON YOUR SPREADSHEET.

16. STEP 10: CLICK THE HIGHLIGHTED BOX

17. STEP 11: Press “OK”

18. RESULT: EXCEL SHOULD GENERATE THE TABLE SHOWN BELOW

19. INTERPRETATION OF THE RESULT (PROBLEM 1) WE performed the test at a significance level (α) of 0.05. If you obtain a p-value greater than 0.05, that means there is no statistically significant difference between the means due to a factor. However, in the example shown above, we obtained a  p-value of 0.00281 , which is  lower than 0.05 , meaning  there is a statistically significant difference  (we reject H !).

20. Since p ≤ 0.05, we have strong statistical evidence that the factor (treatment) has an effect (concentration of NO in rat plasma) that is likely not due to chance and we may reject H . We may also state that since p ≤ 0.05, there is a statistically significant difference in the mean concentrations of NO in rat plasma due to the drug treatments (we accept H 1 !).