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experiment, or the sample size for the new experiment is sufficiently large so that the normal distribution is a good approximation to the t distribution; and 3) the laboratory is confident that there is no actual difference in the means, the most optimistic case. It is not common for all three of these assumptions to hold. The formula above should be treated most often as an initial approximation. Deviations from the three assumptions will lead to a larger required sample size. In general, we recommend seeking assistance from someone familiar with the necessary methods.

这是一种改进过的ESD检验，它可以从一个正态分布的总体当中发现预先设定数量（r）的异常值。对于仅检测1个异常值的情况，极端学生化偏离检验也就是常说的Grubb's检验。不建议将Grubb's检验用于多个异常值的检验。设定r=2,而n=10。

Table 8. Common Values for a Standard Normal Distribution

Confidence Level 99% 95% 90% 80% One-sided (a) 2.326 1.645 1.282 0.842 z-Values Two-sided (a/2) 2.576 1.960 1.645 1.282

When a log transformation is required to achieve normality, the sample size formula needs to be slightly adjusted as

shown below. Instead of formulating the problem in terms of the population variance and the largest acceptable difference, δ, between the two procedures, it now is formulated in terms of the population %RSD and the largest acceptable proportional difference between the two procedures.

where

and r represents the largest acceptable proportional difference between the two procedures ((alternative-current)/current), and the population %RSDs are assumed known and equal.

APPENDIX F: EQUIVALENCE TESTING AND TOST

In classical statistical hypothesis testing, there are two hypotheses, the null and the alternative. For example, the null may be that two means are equal and the alternative that they differ. With this classical approach, one rejects the null hypothesis in favor of the alternative if the evidence is sufficient against the null. A common error is to interpret failure to reject the null as evidence that the null is true. Actually, failure to reject the null just means the evidence against the null was not sufficient. For example, the procedure used could have been too variable or the number of determinations too small.

The consequence of this understanding is that, when one seeks to demonstrate similarity, such as results from two laboratories, then one needs similarity as the alternative hypothesis. A statistical test for an alternative hypothesis of similarity is referred to as an equivalence test. It is important to understand that ―equivalence‖ does not mean ―equality.‖ Equivalence should be understood as ―sufficiently similar‖ for the purposes of the laboratory(ies). As noted earlier in this chapter, how close is close enough is something to be decided a priori.

As a specific example, suppose we are interested in comparing average results, such as when transferring a procedure from one laboratory to another. (Such an application would also likely include a comparison of precision; see Appendix D.) A priori, we determine that the means need to differ by no more than some positive value, δ, to be considered equivalent or sufficiently similar. (Appendix E provides some guidance on choosing δ.) Our hypotheses are then: 这是一种改进过的ESD检验，它可以从一个正态分布的总体当中发现预先设定数量（r）的异常值。对于仅检测1个异常值的情况，极端学生化偏离检验也就是常说的Grubb's检验。不建议将Grubb's检验用于多个异常值的检验。设定r=2,而n=10。

Alternative (H1): |μ1?μ2| <δ Null (H0): |μ1?μ2| >δ

where m1 and m2 are the two means being compared.

The two one-sided tests (TOST) approach is to convert the above equivalence hypotheses into two one-sided

hypotheses. The rationale is that one can conclude |m1? m2| δ< if one can demonstrate both

μ1?μ2 < +δ andμ1?μ2 < ?δ

As one-sided tests, they can be addressed with standard one-sided t-tests. In order for the test of the equivalence hypotheses to be of level a, both one-sided tests are conducted at level a (typically, but not necessarily, 0.05). Often, the two one-sided test is performed using a confidence interval. In this case, reject the null in favor of the equivalence hypothesis if the 100(1 ? 2a)% two-sided confidence interval is entirely contained in (?δ, +δ). This is the approach described earlier in the Accuracy section.

APPENDIX G: ADDITIONAL SOURCES OF INFORMATION

附录G：其他的信息来源

There may be a variety of statistical tests that can be used to evaluate any given set of data. This chapter presents several tests for interpreting and managing analytical data, but many other similar tests could also be employed. The chapter simply illustrates the analysis of data using statistically acceptable methods. As mentioned in the Introduction, specific tests are presented for illustrative purposes, and USP does not endorse any of these tests as the sole approach for handling analytical data.

可能有许多统计检验可以用于评估任何给定的数据组。本章展示了一些检验被用来解释和管理分析数据，但是许多其他的相似检验也可以使用。本章使用统计上可授受的方法简单阐述了数据分析。如在“介绍”所述，为了说明的目的，使用了特定的方法，同时USP并不将这些方法中的任何一种检验作为处理分析数据的唯一方法。 Additional information and alternative tests can be found in the references listed below or in many statistical textbooks. 其他的信息和替代的检验可以从下列参考文献或者许多统计教材中获得。

Control Charts:

1. Manual on Presentation of Data and Control Chart Analysis, 6 ed., American Society for Testing and Materials (ASTM), Philadelphia, 1996.

2. Grant, E.L., Leavenworth, R.S., Statistical Quality Control, 7 ed., McGraw-Hill, New York, 1996.

3. Montgomery, D.C., Introduction to Statistical Quality Control, 3 ed., John Wiley and Sons, New York, 1997.

4. Ott, E., Schilling, E., Neubauer, D., Process Quality Control: Troubleshooting and Interpretation of Data, 3 ed., McGraw-Hill, New York, 2000.

Detectable Differences and Sample Size Determination:

1. CRC Handbook of Tables for Probability and Statistics, 2 ed., Beyer W.H., ed., CRC Press, Inc., Boca Raton, FL, 1985.

2. Cohen, J., Statistical Power Analysis for the Behavioral Sciences, 2 ed., Lawrence Erlbaum Associates, Hillsdale, NJ, 1988.

3. Diletti, E., Hauschke, D., Steinijans, V.W., ―Sample size determination for bioequivalence assessment by means of confidence intervals,‖ International Journal of Clinical Pharmacology, Therapy and Toxicology, 1991; 29,1–8. 4. Fleiss, J.L., The Design and Analysis of Clinical Experiments, John Wiley and Sons, New York, 1986, pp. 369–375.

5. Juran, J.A., Godfrey, B., Juran's Quality Handbook, 5 ed., McGraw-Hill, 1999, Section 44, Basic Statistical Methods.

6. Lipsey, M.W., Design Sensitivity Statistical Power for Experimental Research, Sage Publications, Newbury Park, CA, 1990.

7. Montgomery, D.C., Design and Analysis of Experiments, John Wiley and Sons, New York, 1984.

8. Natrella, M.G., Experimental Statistics Handbook 91, National Institute of Standards and Technology, Gaithersburg, MD, 1991 (reprinting of original August 1963 text).

9. Kraemer, H.C., Thiemann, S., How Many Subjects<: Statistical Power Analysis in Research, Sage Publications, Newbury Park, CA, 1987.

10. van Belle G., Martin, D.C., ―Sample size as a function of coefficient of variation and ratio of means,‖ American Statistician 1993; 47(3):165–167.

11. Westlake, W.J., response to Kirkwood, T.B.L.: ―Bioequivalence testing—a need to rethink,‖ Biometrics 1981; 37:589–594.

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