# STAT 5303 Assignment 8

## An Investigation of Socioeconomic Factors on Verbalization Skill

A study was designed to evaluate whether socioeconomic factors had an effect on verbalization skill of young children. Four socioeconomic classes were defined and 20 children under the age of six were selected from each class for the study. The research hypothesis was that the mean verbalization skills would be different for the four classes. The researchers determined that for young children there may be significant gains in verbalization skills over only a few months. Thus, they decided to record the exact age (in months) of each child. The verbalization skills (measured by testing) were determined for each child. A description of the variables appearing in the dataset along with abbreviated names is as follows.

1. Age: Age (months).
2. Verbal: Verbal skill score (higher values correspond to greater skill).
3. Class: Socioeconomic class (1=low, 2=middle, 3=upper-middle, 4=upper).

Using these data, build an ANCOVA model to compare verbal skill among the four socioeconomic classes, while controlling for age. Specifically, provide complete answers to the following questions:

• Plot verbal skill scores vs. age, using a different plotting symbol for each of the 4 socioeconomic classes. Does there seem to be a linear relationship between verbal skill and age (for each of the four classes)? If not, examine the need for transforming variables.
• Write down a linear model (ANCOVA) that allows for different slopes for each of the 4 classes. Write down a simpler model where the lines corresponding to the 4 classes are all parallel (equal slopes). Fit both models and decide (by means of an appropriate test) which model is a more appropriate fit.
• Check if there are any violations of the usual model assumptions, including potential problems like influential observations.
• Compare the verbal skill scores among the four classes using Tukey's method. Also produce a profile plot of the verbal skill main effects. Which socioeconomic class(es) has/have the highest verbal skill?

Instructions:

• Typeset your results as a report in the same style as Assignment 7.