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.
- Age: Age (months).
- Verbal: Verbal skill score (higher values correspond to greater skill).
- 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.