Assignment on Statistical Analysis, Coursework Example

The assignment consists of two parts, Part A and Part B.

Part A

Clients at a Diabetic Education Program were randomly assigned to one of two learning programs.

Group A participants attended a three-day, in-class set of lectures, discussions and demonstrations.

Group B participants accessed an online program that allowed them to complete the material on their own time over a two-week period.

At the end of each program, participants completed the same multiple-choice test of knowledge and skills. The test was scored out of 100

 Questions

• Identify the dependent and independent variables.

The dependent variable is the participants’ test scores. The independent variable is the group where the participant belonged.

• If you wanted to determine which of the two learning programs made the bigger difference in the participant’s knowledge and skills, what statistical tests would you perform? What assumptions would the test have to meet before you proceed? How would you determine these assumptions?
  NOTE: you do not actually have to do the statistics, only answer the questions posed.

I would need to make use of an independent t-test. This test would assume that the participants were randomly selected and grouped, and that the data is normally distributed (Boneau, 1960). This test also assumes that the variances of the scores in the two groups do not differ significantly (Boneau, 1960). For the first assumption, it is given in the problem that the clients were randomly assigned. Thus, the assumption is met. For the second assumption of normality, I can plot the histograms of the data to see if they resemble a normal distribution which is bell-shaped (McPherson, 1990). I can also conduct a test for normality such as the Jarque-Berra test (Jarque & Bera, 1987). For the third assumption, I can compute the sample variances and compare them with one another. To make sure, I can conduct a test for equality of variances such as Levene’s test (Levene, 1960).

Part B

Suppose you are reading the results of a research report; the research question is:

“What factors are associated with psychological distress on family caregivers of persons with Alzheimer’s?”

The researchers used instruments to measure the variables: age of the family caregiver; the caregiver’s perception of the amount of supervision required of the person with Alzheimer’s; the amount of physical care required; and psychological distress.

The researchers displayed their results in a correlation table.

Questions

• What is the strongest predictor of caregiver psychological distress? What is your  rationale for your answer?

Based on the correlation matrix, the strongest predictor of caregiver psychological distress is the caregiving tasks per week. That is, the amount of care giving tasks the family caregiver has to perform each week. The rationale behind this is that the correlation coefficient between the two variables is 0.70 which is the highest correlation coefficient that caregivers’ psychological distress has with any of the other variables. This indicates that caregivers with more tasks per week also have more psychological distress.

• What is your interpretation of the correlation 0.10?

A correlation of 0.10 is a weak linear correlation coefficient. This means that the two variables are not linearly related to one another. However as shown by Rummel (1976), this does not mean that they are not strongly related with respect to some other distribution. The correlation coefficient r only determines the strength of the linear relationship between two variables, but fails to give a valid interpretation on the non-linear relationship of the variables.

References

Boneau, C. Alan (1960). The effects of violations of assumptions underlying the t test. Psychological Bulletin, 57 (1): 49–64.

Jarque, Carlos M.; Bera, Anil K. (1987). “A test for normality of observations and regression residuals”. International Statistical Review, 55 (2): 163–172.

Levene, Howard (1960). Robust tests for equality of variances. Stanford University Press.

McPherson, G. (1990). Statistics in scientific investigation: its basis, application and interpretation. Springer-Verlag.

Rummel, R. (1976). Understanding Correlation. Retrieved January 29, 2011  from: http://www.mega.nu/ampp/rummel/uc.htm