A Two-Way Analysis of Variance Is to Be Performed Using $\quad$

question 26

Essay

A two-way analysis of variance is to be performed using the data below. Assume that the data come frompopulations that are normally distributed with the same variance. If there is a significant difference in themeans for the three levels of factor A, use Tukeyʹs test to determine which pairwise means differ using afamilywise error rate of α = 0.05. If there is a significant difference in the means for the three levels of factor B,use Tukeyʹs test to determine which pairwise means differ using a familywise error rate of α = 0.05. $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$$\text { Factor B }$
$\begin{array}{l}\begin{array} { c c c c } \hline && \text { Level 1 } & \text { Level 2 } & \text { Level 3 } \\\hline &\text { Level 1 } & 67 & 74 & 82 \\&& 71 & 73 & 76 \\&& 62 & 60 & 87\\\\ & \text { Level 2 } & 77 & 69 & 84 \\\text { Factor A }&& 81 & 75 & 80 \\ && 65 & 77 & 90 \\\\&\text { Level 3 } & 59 & 70 & 72 \\&& 67 & 58 & 68 \\&& 62 & 66 & 76\end{array}\end{array}$

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Definitions:

Dorsiflexion

The action that reduces the angle between the top part of the foot and the shin by pulling the foot upwards towards the shin.

Automatic Responses

Involuntary reactions to stimuli, not requiring conscious thought, such as reflex actions.

Subconscious Responses

Reactions that occur without conscious thought, often reflexes or actions triggered by stimuli below the level of conscious awareness.

Voluntary

Referring to actions or movements under conscious control by the individual.