A Researcher Was Interested in Determining the Effectiveness of Humanistic

A researcher was interested in determining the effectiveness of humanistic therapy for alleviating depression. He administered a depression inventory to a sample of clients with depression on three occasions: before therapy started, two months after therapy began, and four months into therapy. Depression scores could range from 1 (not at all depressed) to 15 (extremely depressed).
$\begin{array}{ccccc}\text { GROUP } & \mathrm{N} & \text { MEAN } & \text { STD DEV } & \text { STD ERROR } \\1 \text { (Time 1) } & 10 & 13.50 & 1.58 & 0.50 \\2 \text { (Time 2) } & 10 & 9.40 & 2.88 & 0.91 \\3 \text { (Time 3) } & 10 & 7.30 & 4.06 & 1.28\end{array}$

$\text { ONEWAY ANOVA: DEPRESSION by TIME (CORR SAMP) }$

$\begin{array}{lrrrrr} & \text { SUM OF } && {\text { MEAN }} \\\text { SOURCE } & \text { SQUARES } & \text { DF } & \text { SQUARES } & \text { F RATIO } & \text { PROB. } \\\text { TIME } & 198.87 & 2 & 99.43 & 18.43 & .000 \\\text { SUBJECTS } & 147.88 & 9 & 16.43 & 185.04 & .000 \\\text { WITHIN CELLS } & 97.13 & 18 & 5.40 & & \\\text { TOTAL } & 443.88 & 29 & & &\end{array}$

POST HOC TEST: Tukey-HSD with significance level .05
* Indicates significant differences shown for pairings

$\begin{array}{lll}G & G & G \\r & r & r \\p & p & p \\1 & 2 & 3\end{array}$


$\begin{array}{ll}\text { Mean}&\text { TIME }\\13.50 & \text { Grp } 1 \\9.40 & \text { Grp 2 } \\7.30 & \text { Grp 3 }\end{array}$

-Why is a probability value of .000 slightly misleading?