Extensions of Two-Part Tests to Compare K Independent Populations
Marwan Daoud · 2007
We consider two-part models that are mixtures of a point-mass variable with all mass at zero and a continuous random variable. The model may assume a particular distributionh(x) for the continuous part such as a log-normal or a gamma. The response variable is defined as y=(x, d), where d=1 if x > 0 and d=0 if x = 0. The probability distribution function has the following form: fx,d=p 1-d×1-p ×hx d. Lachenbruch (1976, 2001) proposed several tests to compare means of two populations for this type of data. We proposed a two-part Wald test and a two-part likelihood ratio test to compare t = (p, m) (p is the proportion of zeros and m is the mean of h(x)), hence the equality of overall means in K independent populations where h( x) is a lognormal distribution. These two test statistics have asymptotically chi-square distribution with 2(k − 1) degrees of freedom. A simulation study was conducted to compare the size and the power of the proposed tests with several other tests (ANOVA, Welch, Brown-Forsythe, and Kruskal-Wallis).