THE USE OF RANGE IN PLACE OF STANDARD DEVIATION IN THE TERT-TEST
成果类型：
Article
署名作者：
LORD, E
刊物名称：
BIOMETRIKA
ISSN/ISSBN：
0006-3444
DOI：
10.2307/2332512
发表日期：
1947
页码：
4167
关键词：
摘要：
The t-test compares the deviation of a sample mean from the assumed population value with a root-mean-square estimate of the standard error of that difference in samples from a normal population. For routine testing of exptl. data of various types, particularly data for control of quality of manufactured products, it is desirable to have a test of this nature which requires less computation. The ratio of the observed range to the known mean range in samples from a normal population with unit standard deviation provides an easily computed estimate of the population standard deviation. While use of the range in thjs modified form of the t-test necessarily entails some loss in precision, the loss is small or samples not much larger than ten items. For larger samples, it is suggested that they be broken into random sub-samples of equal smaller size and the mean range for the several sub-samples be used to estimate the standard deviation. A modified statistic is defined, using the mean range in m samples of size n to estimate the standard deviation, and tables are given of the 10%, 5%, 2%, 1%, 0.2% and 0.1% levels for n from 2 to 20 and m from 1 to 60. An appendix to the article demonstrates the independence of the mean and certain linear estimates (including the range estimate) of the standard deviation in random samples from a normal distribution. This independence had been assumed in obtaining the distribution of the modified t-statistic.