A clinical trial is run to compare the effect of four weight loss programs. What statistical test would be most appropriate to use when comparing the weight loss effect between the four programs?
I think it can be analyzed by univariate ANOVA. Let the body weight be Xij (i=1,...,nj; j=1,...,8), the weight of the ith subject in the jth group. Use the following model to fit your data:
Xij= a+ bi +eij,
where a - overall mean,
bi- the ith group effect, i=1,2,3,4
eij- random error.
You can estimate the parameters by the least squares method and perform hypothesis testing for H0: b1=b2=...b4=0. The F-test can be useful. However, you need to be careful about the assumptions: all groups are independent, normally distributed, and have equal variances. Independence and equal variance may not be easy to validate.
For ANOVA it is extremely helpful to read Fisher's original work.
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