This project evaluates the effectiveness of different treatment types for anorexia using statistical methods, including T-tests, permutation tests, and QQ-plots. The goal is to assess whether these treatments lead to significant weight gain in patients diagnosed with anorexia.
Anorexia is primarily diagnosed when a patient's weight is less than 85% of what is considered normal for their height and age. In this study, a patient is classified as anorexic if their weight is below 90 lbs. The dataset includes three treatment types: control treatment, family treatment, and cognitive/behavioral treatment. The columns "Before" and "After" represent the weights of patients before and after treatment, respectively, while the last column (Y) indicates the weight difference (After - Before).
The dataset used in this evaluation is stored in a text file.
To determine if there is evidence of anorexia after treatment (α=0.05):
- The null hypothesis is rejected at the 95% confidence level, indicating that anorexia is present after treatment.
To assess whether the average weight gain in the cognitive/behavioral group is significant (α=0.05):
- Sufficient evidence is found to reject the null hypothesis at the 95% confidence level, confirming that weight gain from cognitive/behavioral therapy significantly differs from zero.
To determine if cognitive/behavioral treatment leads to greater weight gain than control treatment:
- The null hypothesis is not rejected, indicating insufficient evidence that the mean weight gain in the cognitive/behavioral group is significantly greater than in the control group.
Performing a permutation test (α=0.01) to compare cognitive/behavioral treatment with control:
- The null hypothesis is not rejected at the 99% confidence level, indicating insufficient evidence that the true mean weight gain is greater in cognitive/behavioral than in control.
To check the assumption of equal variances:
- The null hypothesis is not rejected, indicating insufficient evidence to claim different variances between family and control groups.
To assess normality in the family treatment and control groups, QQ-plots are generated:
- Both groups appear approximately normal, with no significant deviations from the linear pattern in the QQ-plots.
The evaluation suggests that while cognitive/behavioral treatment leads to significant weight gain, it may require multiple rounds of therapy for patients to exceed clinical diagnostic criteria for anorexia. The findings challenge common assumptions about the relationship between treatment type and weight gain in anorexic patients.