On the Distribution of Type II Errors in Hypothesis Testing

Author(s)
Skip Thompson

ABSTRACT

When a statistical test of hypothesis for a population mean is performed, we are faced with the possibility of committing a Type II error by not rejecting the null hypothesis when in fact the population mean has changed. We consider this issue and quantify matters in a manner that differs a bit from what is commonly done. In particular, we define the probability distribution function for Type II errors. We then explore some interesting properties that we have not seen mentioned elsewhere for this probability distribution function. Finally, we discuss several Maple procedures that can be used to perform various calculations using the distribution.

When a statistical test of hypothesis for a population mean is performed, we are faced with the possibility of committing a Type II error by not rejecting the null hypothesis when in fact the population mean has changed. We consider this issue and quantify matters in a manner that differs a bit from what is commonly done. In particular, we define the probability distribution function for Type II errors. We then explore some interesting properties that we have not seen mentioned elsewhere for this probability distribution function. Finally, we discuss several Maple procedures that can be used to perform various calculations using the distribution.

KEYWORDS

Complementary Error Function, Hypothesis Testing, Power Curves, Power Surfaces, Type II Errors

Complementary Error Function, Hypothesis Testing, Power Curves, Power Surfaces, Type II Errors

Cite this paper

nullS. Thompson, "On the Distribution of Type II Errors in Hypothesis Testing,"*Applied Mathematics*, Vol. 2 No. 2, 2011, pp. 189-195. doi: 10.4236/am.2011.22021.

nullS. Thompson, "On the Distribution of Type II Errors in Hypothesis Testing,"

References

[1] D. C. Montgomery, “Statistical Process Control,” John Wiley & Sons, 1991.

[2] D. S. Wackerly, W. Mendenhall, and R. L. Scheaffer, “Mathematical Statistics with Applications,” Duxbury Press, 1996.

[3] S. Thompson, “Maple Worksheets for Investigating Type II Errors,” 2010. http://www.radford.edu/thompson/TypeIIErrors/index.html

[4] Maplesoft, Waterloo Maple Inc., Waterloo, 2010.

[1] D. C. Montgomery, “Statistical Process Control,” John Wiley & Sons, 1991.

[2] D. S. Wackerly, W. Mendenhall, and R. L. Scheaffer, “Mathematical Statistics with Applications,” Duxbury Press, 1996.

[3] S. Thompson, “Maple Worksheets for Investigating Type II Errors,” 2010. http://www.radford.edu/thompson/TypeIIErrors/index.html

[4] Maplesoft, Waterloo Maple Inc., Waterloo, 2010.