A simulation study of several tests of the equality of binomial probabilities against ordered alternatives

Abstract

Four test statistics, namely isotonic test based on arcsin transformation, isotonic test, likelihood ratio test and contrast test, which test the equality of binomial probabilities against ordered alternatives were compared with respect to size and power by extensive simulation. We found that the estimated sizes of the isotonic test based on arcsin transformation and the contrast test overstate the nominal test levels. However, the estimated sizes of the isotonic test and the likelihood ratio test are in close agreement with their corresponding nominal levels. Particularly, when sample sizes are as small as ten, the isotonic test is far better than the likelihood ratio test. For large sample sizes, the former holds little advantage over the latter.

Keywords:

• Binomial probabilities
• ordered alternatives
• isotonic regression
• isotonic test based on arcsin transformation
• isotonic test
• likelihood ratio test
• contrast test
• Monte Carlo simulation
• power comparison

^*Present address: Izumi High School, Izumi, Kagoshima, Japan.

^*Present address: Izumi High School, Izumi, Kagoshima, Japan.

Notes

^*Present address: Izumi High School, Izumi, Kagoshima, Japan.