GB/T 4086.3-2025Data analysis and decision - Tables for statistical distributions - Part 3: t-distribution (English PDF)

Foreword

This document complies with the provisions of GB/T 1.1-2020 "Standardization Work Guidelines Part

1.Structure and Drafting Rules of Standardization Documents". Drafting. This document is Part 3 of GB/T 4086 "Statistical Distribution Numerical Tables for Data Analysis and Decision Making". GB/T 4086 has been published. The following section.

1.Normal Distribution;

---Part 2.chi^2 distribution;

---Part 3.t-distribution;

---Part 4: F-distribution;

5.Binomial Distribution;

6.Poisson Distribution;

7.Non-central t-distribution. This document replaces GB/T 4086.3-1983 "Statistical Distributions - Numerical Tables - t-Distribution". Compared with GB/T 4086.3-1983, except for the structure... Aside from adjustments and editorial changes, the main technical changes are as follows:

a) Added table footnotes for table spacing and precision (see Chapter 1);

b) In the t-distribution quantile table, "tp(nu).integral" (1 t2/nu)-(nu 1)/2 nuB(1/2,nu/2) dt=p" changed to "tp(nu) satisfies. integral" tp(nu) (1 x 2/nu) - (nu 1)/2 nuB(1/2,nu/2) dx=p (see Chapter 6, Chapter 2 of the 1983 edition). Please note that some content in this document may involve patents. The issuing organization of this document assumes no responsibility for identifying patents. This document was proposed and is under the jurisdiction of the National Technical Committee on Standardization of Statistical Methods Application (SAC/TC21). This document was drafted by the China National Institute of Standardization, the Institute of Mathematics and Systems Science of the Chinese Academy of Sciences, and Beijing University of Technology. The main drafters of this document are. Zhang Xuan, Zhao Jing, Ding Wenxing, Zhang Fan, Wu Gang, Xie Tianfa, Wang Haitao, Cao Xinyu, Yang Ziqiang, and Wei Gongyi. This document was first published in 1983, and this is its first revision.

Currently, with the widespread use of computers, using computer programs to obtain the required statistical distribution values is a good method. However, if a computer is not readily available, or if it is desirable to obtain the required statistical distribution values easily, then statistical distribution tables are still necessary. However, it is an indispensable tool. In practice, basic statistical distributions, such as the normal distribution, chi^2 distribution, t distribution, F distribution, binomial distribution, and Poisson's distribution, are essential. Loose distribution and non-central t-distribution are the distributions that people are most interested in. GB/T 4086 "Statistical Distribution Numerical Tables for Data Analysis and Decision Making" is proposed to consist of 7 parts.

1.Normal Distribution. The aim is to provide the probability density function, distribution function, and quantiles of the standard normal distribution. Numerical value.

2.Chi-square distribution. The purpose is to provide the distribution function of the chi-square distribution and the numerical values of its quantiles.

1 Scope

GB/T 4086.3-2025 is the Chinese national standard covering the Student t tables - the quantiles by degrees of freedom, one and two sided, for the confidence intervals and the comparisons of means that a laboratory does daily. Part 3 of the series. It replaces GB/T 4086.3-1983 and is already in force. Issued on 5 October 2025, it has been in force since 5 October 2025, replacing GB/T 4086.3-1983.

This document provides two numerical tables for the t-distribution, and their names, table intervals, and precision are shown in Table 1. Table

1.Names, table spacing, and precision of two numerical tables for the t-distribution. Name, Distance a, Precision b Table of distribution functions of t-distribution nu=1(1)20(2)30(5)50,60 t=0(0.1)4(0.2)5(0.5)7

6 decimal places

quantile table of t-distribution p=0.5(0.05)0.95,0.975,0.98,0.99,0.995,0.9975,0.998,0.999, 0.9995, 0.9998, 0.9999

5 decimal places

The table distance nu = 1(1)20(2)30(5)50,60 indicates that the value range of nu is 1~60, where the value interval in the range of 1~20 is 1, and the interval in the range of >20~30 is 1. The value interval within the range is 2, the value interval within the range of >30~50 is 5, and the value within the range of >50~60 is 60. b. Precision refers to the number of decimal places retained in a numerical value. This document applies to situations involving the use of t-distribution distribution function values and quantile values in data analysis and decision-making.

2 Normative references

The contents of the following documents, through normative references within the text, constitute essential provisions of this document. Dated citations are not included. For references to documents, only the version corresponding to that date applies to this document; for undated references, the latest version (including all amendments) applies. This document.

GB/T 3358.1 Statistical vocabulary and symbols Part

3 Terms and Definitions

The terms and definitions defined in GB/T 3358.1 apply to this document.

4 Overview

The quantiles given in this document correspond to the lower-side probabilities. Although the table provides 5 to 6 decimal places, the number of decimal places required in actual use depends on the specific problem. If the numerical tables listed in this document do not meet the application requirements, refer to Appendix A and Appendix B for calculations, or use interpolation methods. Rough calculation.