A Scientist Was Interested in the Success of a Newly $\quad$

question 15

Multiple Choice

A scientist was interested in the success of a newly developed sleep aid called 'Night Owl' on time taken to fall asleep and quality of sleep. She recruited 30 participants who were randomly allocated to receive either a dose of Night Owl or a placebo. The scientist measured the mean time taken for each participant to fall asleep (minutes) and the quality of their sleep (measured on a scale of 1 (poorest quality) to 10 (best possible quality) ) over the course of one week.
-What does the output below show?
$\quad$$\quad$ Box's Test of Equality
$\quad$$\quad$$\quad$ of Covariance
$\quad$$\quad$$\quad$$\quad$ Matrices ${ } ^ { a }$
$\begin{array}{|l|r|}\hline \text { Box's M } & .229 \\\text { F } & .070 \\\text { df1 } & 3 \\\text { df2 } & 141120.000 \\\text { Sig. } & .976\\\hline\end{array}$
Tests the null hypothesis that the observed covariance matrices of the dependent variables are equal across groups.

a. Design:
Intercept + Drug Bartlett's Test of Sphericity ${ } ^ { a }$
$\begin{array}{|l|r|}\hline \text { Likelihood Ratio } & .000 \\\text { Approx. Chi-Square } & 101.046 \\\text { df } & 2 \\\text { Sig. } & .000\\\hline\end{array}$

Tests the null hypothesis that the residual covariance matrix is proportional to an identity matrix.
a. Design: Intercept + Drug

• A)The assumption of equality of covariance matrices has been violated.
• B)The assumption of sphericity has been met.
• C)The covariance matrices are not significantly equal.
• D)The covariance matrices are roughly equal as assumed.

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