Dr Green Conducted an ANCOVA to Determine Whether Hearing-Impaired Children $\alpha$

Essay

Dr. Green conducted an ANCOVA to determine whether hearing-impaired children who were taught sign language early on would develop better language skills compared to those who did not learn sign language. The data set contains two independent random samples (children who learned sign language and those who did not) of paired values on the covariate (X; child's hearing) and the dependent variable (Y; language skills measured when the child was three years old). Dr. Green also examined the data to see if the assumptions of ANCOVA were met. The following table and figures are the selected output from Dr. Green's analysis ( $\alpha$ = .05):

Tests of Between-Subjects Effects
Dependent Variable: Language

$\begin{array}{cccccc}\hline\text { Source } & \text { Type III Sum of Squares } & d f & \text { Mean Square } & F & \text { Sig. } \\\hline \text { Sign } & 22681.088 & 1 & 22681.088 & 5.963 & .020 \\\text { Hearing } & 3084.607 & 1 & 3084.607 & .811 & .374 \\\text { Sign*Hearing } & 23130.912 & 1 & 23130.912 & 6.082 & .019 \\\text { Error } & 136920.190 & 36 & 3803.339 & & \\\text { Corrected Total } & 162488.375 & 39 & & & \\\hline\end{array}$



a. What assumption is being evaluated here?
b. Was this assumption satisfied? If not, what effect might it have on the results of ANCOVA?