An analysis of the type I error in the one sample Student t-test
作者:
Richard H. Browne,
D. B. Owen,
Faming Ju,
期刊:
Communications in Statistics - Simulation and Computation
(Taylor Available online 1978)
卷期:
Volume 7,
issue 6
页码: 593-603
ISSN:0361-0918
年代: 1978
DOI:10.1080/03610917808812098
出版商: Marcel Dekker, Inc.
关键词: bivariate noncentral t-distribution;α-error partitioning;normal distribution
数据来源: Taylor
摘要:
In the one-sample Student t-test, the occurrence of a type-I error is dependent on the estimates of the mean and standard deviation for a fixed sample size, n. The statistic can achieve significance either by the sample mean being too different from the hypothesized mean or by the sample standard deviation being too small. The critical region is partitioned to determine the characteristics of samples in the critical region, assuming the null hypothesis is true. As might be conjectured from the use of the t-statistic, mis-estimation of the mean is shown to be the predominant characteristic of samples in the critical region for sample sizes larger than 20 and significance level greater than 0.01. Underestimation of the variance, unless accompanied by a misestimation of the mean, is a far less frequent characteristic of critical region samples.
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