Prove the null hypothesis, based on the below data, which states that men infected with the AIDS virus may suffer a loss of mental function long before they experience other symptoms of the disease. The alternate hypothesis would be that men infected with the AIDS virus do not suffer a loss of mental function long before they experience other symptoms of the disease.
We have good narrative, but are lacking a solid statistical analysis. We are unsure of how to conduct an ANOVA analysis, and I don't think we have enough data to do a successful multiple regression calculation. I believe there are multiple tests we might run in MegaStat to prove our hypothesis, if we were savvy with the program, but we simply are not. We have been able to run some descriptive statistics including a dot plot and box plot, but need help bearing out our hypothesis using some type of statistical analysis as none of us are statisticians by trade. Can someone help point us in the right direction by running a calculation that proves or disproves our null hypothesis using the data below?
In a study published in the Annals of Internal Medicine, Dr. Igor Grant and colleagues from the University of California at San Diego recruited a sample of 55 patients and controls from a group of homosexual men in San Diego. They broke the sample into four groups: 15 with AIDS, 13 who had a less severe form of the disease, AIDS-related complex (ARC); 16 who tested positive for the AIDS virus but who showed no other symptoms, and 11 healthy men who were not infected.
The researchers gave each subject a battery of nine separate neurological and psychological examinations designed to assess their mental capabilities. They then rated each man's performance as definitely impaired, probably impaired, or unimpaired by standardized criteria. The rate of impairment was 9% in the healthy control subjects but 87% in the patients with AIDS. The ARC group had 54% impaired. Most surprising to scientists, the rate for the group that tested positive but showed no other symptoms was 44%.
This response provides guidelines on conducting an ANOVA analysis and on proving a null hypothesis.