Hello, I'd like to ask how to interpret the results of Dunnett's test and Games-Howell test in R studio.(I attached result files of them.) I checked whether the data has equal variances among groups or not; however; it doesn't. Therefore, I used Welch's test and then employed the post-hoc methods, Dunnett's test and Games-Howell test. Also, I would like to say that '1-2' group is not the control. I wanted to do one-way ANOVA among 6 groups at the first time, and compare 6 groups whether they are significant different groups. I think the results might be similar to Duncan's test, but they didn't.
1. I attached result captures on Dunnett's test and Games-Howell test in R.
2. I guess that the difference between 1-2 and 3-6 is the smallest according to Dunnett's test, and also it proves through Games-Howell test. How can I compare 6 groups like Duncan's multiple range test? I looked up Tukey's test, too. By the way, my data doesn't have equal variances by groups. I have no idea how to explain the results. ;-(
3. Here's my R codes.
install.packages("multcomp")
library(multcomp)
dunnett_model1
Seulki,
Your first image shows the overall result of your ANOVA model. Report as follows F(5, 20463) = 178.6, p < .001, R2 = .04, Adjusted R2 = .04. This means that your overall model rejected the null hypothesis (p-value), and that the independent variable explained about 4% of the variance in the model (R2/Adj. R2). This would be considered to be a small to medium effect. This information is acquired at the bottom of the "dunnetresult" image.
The second image just compares each group via the post hoc test. For example, line 1 compares the "3-6" group with the "1-2" group. the "diff" column is the difference between the means of the groups (962-760). The 2nd and 3rd columns show the boundaries of the confidence interval. The 4th column is the t-statistic, the 5th is degrees of freedom, and lastly the p-value for the comparison. So the null hypothesis for the difference between the means of "3-6", and "1-2" has been rejected, and may be reported as such: t(1064) = 10, p < .01, 95% CI: 144, 260. Note that this result is similar for all of your comparisons except for "13-19" and "7-12", and ">65" and"7-12" groups.
Lastly, It looks as though the larger groups have the larger variances in this dataset. You may usually ignore the violation of the assumption of equality of variances in this case, and this is compounded by the fact that the dataset is large. This quality alone results in rejection of null hypotheses for p-value driven tests, which include that of your ANOVA, and also tests for assumptions of homogeneity.
That said, being cautious of bias is always wise. Choosing the Games-Howell, Dunnet's C, or Dunnet's T3 are wise choices for a post hoc test if your groups have unequal variances. The Dunnet's choices are better if you want to keep tight control of Type I error. Games-Howell is more powerful, but accurate for unequal variances, as long as your sample sizes are large enough (which is not an issue here). I would choose only one though.
I hope these answers help; good luck!
Keston
Seulki,
Your first image shows the overall result of your ANOVA model. Report as follows F(5, 20463) = 178.6, p < .001, R2 = .04, Adjusted R2 = .04. This means that your overall model rejected the null hypothesis (p-value), and that the independent variable explained about 4% of the variance in the model (R2/Adj. R2). This would be considered to be a small to medium effect. This information is acquired at the bottom of the "dunnetresult" image.
The second image just compares each group via the post hoc test. For example, line 1 compares the "3-6" group with the "1-2" group. the "diff" column is the difference between the means of the groups (962-760). The 2nd and 3rd columns show the boundaries of the confidence interval. The 4th column is the t-statistic, the 5th is degrees of freedom, and lastly the p-value for the comparison. So the null hypothesis for the difference between the means of "3-6", and "1-2" has been rejected, and may be reported as such: t(1064) = 10, p < .01, 95% CI: 144, 260. Note that this result is similar for all of your comparisons except for "13-19" and "7-12", and ">65" and"7-12" groups.
Lastly, It looks as though the larger groups have the larger variances in this dataset. You may usually ignore the violation of the assumption of equality of variances in this case, and this is compounded by the fact that the dataset is large. This quality alone results in rejection of null hypotheses for p-value driven tests, which include that of your ANOVA, and also tests for assumptions of homogeneity.
That said, being cautious of bias is always wise. Choosing the Games-Howell, Dunnet's C, or Dunnet's T3 are wise choices for a post hoc test if your groups have unequal variances. The Dunnet's choices are better if you want to keep tight control of Type I error. Games-Howell is more powerful, but accurate for unequal variances, as long as your sample sizes are large enough (which is not an issue here). I would choose only one though.
I hope these answers help; good luck!
Keston
I appreciate that you save me. Your explanations are clear and wonderful. Thanks a lot!!!! :-)
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