11.3. The Two-Way ANOVA Test http://www.ck12.org
TABLE11.11:
Source SS d f MS F Critical Value of
F∗
Rows (gender) 14 , 832 1 14 , 832 14. 94 4. 07
Columns
(dosage)17 , 120 2 8 , 560 8. 62 3. 23
Interaction 2 , 588 2 1 , 294 1. 30 3. 23
Within-cell 41 , 685 42 992
Total 76 , 226 47∗α=. 05- What are the three hypotheses associated with the two-way ANOVA method?
- What are the three null hypotheses?
- What are the critical values for each of the three hypotheses? What do these tell us?
- Would you reject the null hypotheses? Why or why not?
- In your own words, describe what these results tell us about this experiment.
Review Answers
- Interaction
- d
- d
4.H 0 :μM.=μF., H 0 :μ 1 .=μ 2 .=μ 3 ., H 0 : all effects= 0 - Answers may vary. They could include (1)H 0 :μ 1 .=μ 2 .=...=μj., H 0 :μ 1 .=μ 2 .=...=μk.,H 0 :
all effects=0 or (2) written hypotheses that the means of the independent variable in the rows are equal
to each other, the means of the independent variable in the rows columns are equal to each other and there is
no interaction. - The three critical values are 4. 07 , 3 .23 and 3.23. These values are derived from theF-distribution. If the
calculatedF-statistic exceeds these values, we will reject the null hypothesis. - We would reject the first two null hypotheses and fail to reject the third null hypothesis.
- We can conclude that not all means in the populations are equal with regard to gender and drug dosage.
Because theF-ratio for the interaction effect (genderxdrug dosage) was not statistically significant, the
conclusion is that there is no difference in the performance of the male and female rats across the levels of
drug dosage.