#### Abstract

Researchers often collect proportion data that cannot be interpreted as arising from a set of Bernoulli trials. Analyses based on the beta distribution may be appropriate for such data. The SAS® GLIMMIX procedure provides a tool for these analyses using a likelihood based approach within the larger context of generalized linear mixed models (GLMM). The small sample behavior of likelihood based tests to compare the means from two independently sampled beta distributions were studied via simulation when the null hypothesis of equal means holds. Two simulation scenarios were defined by equal and unequal sample sizes and equal scale parameters. A third scenario was defined by equal sample sizes and unequal scale parameters. For all three scenarios the values of the common mean μ ranged from 0 and 0.5 and values of the scale parameter ϕ ranged from 0 to 100.

#### Keywords

beta distribution, two sample problem, GLIMMIX

#### Creative Commons License

This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

#### Recommended Citation

Gbur, Edward E. and Thompson, Kevin
(2015).
"SMALL SAMPLE PROPERTIES OF THE TWO INDEPENDENT SAMPLE TEST FOR MEANS FROM BETA DISTRIBUTIONS,"
*Conference on Applied Statistics in Agriculture*.
http://newprairiepress.org/agstatconference/2015/proceedings/4

SMALL SAMPLE PROPERTIES OF THE TWO INDEPENDENT SAMPLE TEST FOR MEANS FROM BETA DISTRIBUTIONS

Researchers often collect proportion data that cannot be interpreted as arising from a set of Bernoulli trials. Analyses based on the beta distribution may be appropriate for such data. The SAS® GLIMMIX procedure provides a tool for these analyses using a likelihood based approach within the larger context of generalized linear mixed models (GLMM). The small sample behavior of likelihood based tests to compare the means from two independently sampled beta distributions were studied via simulation when the null hypothesis of equal means holds. Two simulation scenarios were defined by equal and unequal sample sizes and equal scale parameters. A third scenario was defined by equal sample sizes and unequal scale parameters. For all three scenarios the values of the common mean μ ranged from 0 and 0.5 and values of the scale parameter ϕ ranged from 0 to 100.