A Note on Confidence Interval for the Power of the One Sample 𝑡 Test
In introductory statistics texts, the power of the test of a one-sample mean when the variance is known is widely discussed. However, when the variance is unknown, the power of the Student's 𝑡-test is seldom mentioned. In this note, a general methodology for obtaining inference concerning a sca...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2010-01-01
|
| Series: | Journal of Probability and Statistics |
| Online Access: | http://dx.doi.org/10.1155/2010/139856 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832567152910008320 |
|---|---|
| author | A. Wong |
| author_facet | A. Wong |
| author_sort | A. Wong |
| collection | DOAJ |
| description | In introductory statistics texts, the power of the test of a one-sample mean when the variance is known is widely discussed. However, when the variance is unknown, the power of the Student's 𝑡-test is seldom mentioned. In this note, a general methodology for obtaining inference concerning a scalar parameter of interest of any exponential family model is proposed. The method is then applied to the one-sample mean problem with unknown variance to obtain a (1−𝛾)100% confidence interval for the power of the Student's 𝑡-test that detects the difference (𝜇−𝜇0). The calculations require only the density and the cumulative distribution functions of the standard normal distribution.
In addition, the methodology presented can also be applied to determine the required sample size when the effect size and the power of a size 𝛼 test of mean are given. |
| format | Article |
| id | doaj-art-1e85c0b322e04767b467a4db671b4e8f |
| institution | Kabale University |
| issn | 1687-952X 1687-9538 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Probability and Statistics |
| spelling | doaj-art-1e85c0b322e04767b467a4db671b4e8f2025-02-03T01:02:10ZengWileyJournal of Probability and Statistics1687-952X1687-95382010-01-01201010.1155/2010/139856139856A Note on Confidence Interval for the Power of the One Sample 𝑡 TestA. Wong0Department of Mathematics and Statistics, York University, Toronto, Ontario, M3J 1P3, CanadaIn introductory statistics texts, the power of the test of a one-sample mean when the variance is known is widely discussed. However, when the variance is unknown, the power of the Student's 𝑡-test is seldom mentioned. In this note, a general methodology for obtaining inference concerning a scalar parameter of interest of any exponential family model is proposed. The method is then applied to the one-sample mean problem with unknown variance to obtain a (1−𝛾)100% confidence interval for the power of the Student's 𝑡-test that detects the difference (𝜇−𝜇0). The calculations require only the density and the cumulative distribution functions of the standard normal distribution. In addition, the methodology presented can also be applied to determine the required sample size when the effect size and the power of a size 𝛼 test of mean are given.http://dx.doi.org/10.1155/2010/139856 |
| spellingShingle | A. Wong A Note on Confidence Interval for the Power of the One Sample 𝑡 Test Journal of Probability and Statistics |
| title | A Note on Confidence Interval for the Power of the One Sample 𝑡 Test |
| title_full | A Note on Confidence Interval for the Power of the One Sample 𝑡 Test |
| title_fullStr | A Note on Confidence Interval for the Power of the One Sample 𝑡 Test |
| title_full_unstemmed | A Note on Confidence Interval for the Power of the One Sample 𝑡 Test |
| title_short | A Note on Confidence Interval for the Power of the One Sample 𝑡 Test |
| title_sort | note on confidence interval for the power of the one sample 𝑡 test |
| url | http://dx.doi.org/10.1155/2010/139856 |
| work_keys_str_mv | AT awong anoteonconfidenceintervalforthepoweroftheonesamplettest AT awong noteonconfidenceintervalforthepoweroftheonesamplettest |