Tasks 4:  Alternate Post Hoc Tests
This problem continues with the same data set presented above.

An alternative to conducting a 1-way ANOVA with 4 groups is to conduct a multiple regression where the independent variables are dummy codes for the groups.  This requires one fewer categorical variables than the number of groups, and this requires establishing a reference group.  As the researchers were interested in comparing the 4th group to the other 3 groups, run a multiple regression (the alternate format presentation of the data is already designed for this).

First, run the multiple regression.  Compare the ANOVA summary table obtained here to the ANOVA summary table from the 1st task.  Also, assess the model for statistical fit.  Finally, examine the t-ratios for the slopes for each independent variable.  Report P-values accurate to 4 decimal places and the t-ratios to 3 decimal places.

Slope for Group 1:
$\displaystyle {t}_{{1}}=$
$\displaystyle {p}=$

Slope for Group 2:
$\displaystyle {t}_{{2}}=$
$\displaystyle {p}=$

Slope for Group 3:
$\displaystyle {t}_{{3}}=$
$\displaystyle {p}=$

Based on these results, what is the conclusion regarding the groups compared to group 4?

The next step is to determine if the remaining groups’ means are statistically different or not.  The most direct way to assess this at once is to conduct an ANOVA.  Using only the first three groups, run a 1-way ANOVA.
    $\displaystyle {F}=$     (report accurate to 3 decimal places)
    $\displaystyle {p}=$     (report accurate to 4 decimal places)
What is the conclusion regarding these three groups?