Paper Type

Master's Thesis


College of Arts and Sciences

Degree Name

Master of Science in Mathematical Sciences (MS)


Mathematics & Statistics

First Advisor

Dr. Ping Sa

Second Advisor

Dr. James U. Gleaton

Third Advisor

Dr. Pali Sen


Many samples in the real world are very small in size and often do not follow a normal distribution. Existing tests for correlation have restrictions on the distribution of data and sample sizes, therefore the current tests cannot be used in some real world situations.

In this thesis, two tests are considered to test hypotheses about the population correlation coefficient. The tests are based on statistics transformed by a saddlepoint approximation and by Fisher's Z-transformation. The tests are conducted on small samples of bivariate nonnormal data and found to perfom well.

Simulations were run in order to compare the type I error rates and power of the new test with other commonly used tests. The new tests controlled type I error rates well, and have reasonable power performance.