Tasks 4:  ANOVAs with and without the Outliers
This problem continues with the same data set presented above.  This task also requires information from the previous task about those data points flagged as possible outliers.

Here, you will first run the ANOVA with the data as is.  Next, you will (temporarily) drop the data points that are possible outliers from each group and rerun the ANOVA.  Finally, you will make a conclusion about the similarity (or differences) between the groups' means.  Continue using a significance level of $\displaystyle \alpha={0.05}$.

ANOVA with the complete data sets:
Run the one-way fixed-effects ANOVA with the groups as the levels of the factor.  Report the P-value to 4 decimal places; report all other statistics accurate to 3 decimal places.
$\displaystyle {F}=$
$\displaystyle {p}=$
$\displaystyle \omega^{{2}}=$
Conclusion from this test:

ANOVA with the outliers removed from the data sets:
Run the one-way fixed-effects ANOVA with the groups as the levels of the factor.  Report the P-value to 4 decimal places; report all other statistics accurate to 3 decimal places.
$\displaystyle {F}=$
$\displaystyle {p}=$
$\displaystyle \omega^{{2}}=$
Conclusion from this test:

Do the results from the 2 ANOVAs agree?

Do the outliers have an impact on the analysis?

Questions for Reflection:  First, if the ANOVAs result in the same conclusion, how would you report the findings?  In particular, which of the ANOVAs would you report and why?  Next, what additional information should you report if you do decide to drop the outliers?  Finally, how would you assess the effect size for these ANOVAs?  If the effect sizes were different, which is the more appropriate value to report in a journal article and why?