Conditional Frequentist Test on Normal Mean Parameter and its application in entomological data

Abstract

In the traditional tests the value of type I error (α) is fixed, on the other hand, in the conditional frequentist test we propose a partition of the region of rejection and acceptance so that the probability of error presented is dependent on the distance of observed data in relation to the border of the critical region. This error probability is the Conditional Error Probability (CEP), which may be of type I or II. The objective of this study was to evaluate the behavior of the conditional frequentist test under the Normal Mean parameter and apply it to entomological data. The test was evaluated via simulation, from developed routine in R software. In each simulated case obtained the likelihood ratio, the critical value and the PEC’s for the Normal distribution. It was concluded that the highest values of PEC were obtained with the more the sample mean value approaching the critical point of the test. This occurs regardless of the decision of the test to accept or reject the null hypothesis. The increase of the sample size causes the reduction of the conditional probability of error. In the application to real data from the average lifetime of bees exposed to different temperatures, it was found that the average lifetime of bees maintained at a temperature of 20°C was found to be similar at a temperature of 15°C with conditional error very small (CEP II equal to 0.54%). For temperatures of 30°C and 35°C the hypothesis was rejected with PEC I equal to 28.35% and 47.53%, respectively. Thus the conditional errors in decision making were very high.

Keywords

• Likelihood Ratio
• Partitioning Function
• Conditional Error Probability