# Difference between revisions of "t-Distribution Table"

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** QUOTE: This table contains critical values of the Student's t distribution computed using the cumulative distribution function. The t distribution is symmetric so that | ** QUOTE: This table contains critical values of the Student's t distribution computed using the cumulative distribution function. The t distribution is symmetric so that | ||

::: <math>t_{1-\alpha,\nu} = -t_{\alpha,\nu}</math> | ::: <math>t_{1-\alpha,\nu} = -t_{\alpha,\nu}</math> | ||

− | :: The [[t-table]] can be used for both one-sided (lower and upper) and two-sided tests using the appropriate value of α. | + | :: The [[t-Distribution Table|t-table]] can be used for both one-sided (lower and upper) and two-sided tests using the appropriate value of α. |

:: The [[significance level]], α, is demonstrated in the graph below, which displays a [[t distribution]] with 10 degrees of freedom. The most commonly used significance level is <math>\alpha = 0.05</math>. For a two-sided test, we compute <math>1 - \alpha/2</math>, or <math>1 - 0.05/2 = 0.975</math> when <math>\alpha = 0.05</math>. If the absolute value of the test statistic is greater than the critical value (0.975), then we reject the null hypothesis. Due to the symmetry of the t distribution, we only tabulate the positive critical values in the table below. | :: The [[significance level]], α, is demonstrated in the graph below, which displays a [[t distribution]] with 10 degrees of freedom. The most commonly used significance level is <math>\alpha = 0.05</math>. For a two-sided test, we compute <math>1 - \alpha/2</math>, or <math>1 - 0.05/2 = 0.975</math> when <math>\alpha = 0.05</math>. If the absolute value of the test statistic is greater than the critical value (0.975), then we reject the null hypothesis. Due to the symmetry of the t distribution, we only tabulate the positive critical values in the table below. | ||

## Latest revision as of 20:45, 23 December 2019

A t-Distribution Table is a probability distribution table that includes critical values of the t-distribution calculated using a cumulative distribution function.

**Context:**- It can be used for one-tailed and two-tailed tests by using the appropriate value of significance level or upper and lower limits of the region of acceptance.
- It can be referenced by a t-Distribution Calculating System.

**Example(s):**- Table A.2 in http://home.ubalt.edu/ntsbarsh/Business-stat/StatistialTables.pdf
- Table 2 and 3 in http://www.stat.ufl.edu/~athienit/Tables/tables

**Counter-Example(s):****See:**Student's t-Distribution, Statistical Distribution Table.

## References

### 2017

- (Wikipedia, 2016) ⇒ http://en.wikipedia.org/wiki/Student's_t-distribution#Table_of_selected_values
- Most statistical textbooks list
*t*-distribution tables. Nowadays, the better way to a fully precise critical*t*value or a cumulative probability is the statistical function implemented in spreadsheets, or an interactive calculating web page. The relevant spreadsheet functions are`TDIST`

and`TINV`

, while online calculating pages save troubles like positions of parameters or names of functions.The following table lists a few selected values for

*t*-distributions with ν degrees of freedom for a range of*one-sided*or*two-sided*critical regions. For an example of how to read this table, take the fourth row, which begins with 4; that means ν, the number of degrees of freedom, is 4 (and if we are dealing, as above, with*n*values with a fixed sum,*n*= 5). Take the fifth entry, in the column headed 95% for*one-sided*(90% for*two-sided*). The value of that entry is 2.132. Then the probability that*T*is less than 2.132 is 95% or Pr(−∞ <*T*< 2.132) = 0.95; this also means that Pr(−2.132 <*T*< 2.132) = 0.9. (...)

- Most statistical textbooks list

### 2013

- (NIST/SEMATECH, 2013) ⇒ Retrieved on 2017-03-12 from NIST/SEMATECH e-Handbook of Statistical Methods "1.3.6.7.2.-Critical Values of the Student's t Distribution" http://www.itl.nist.gov/div898/handbook/eda/section3/eda3672.htm
- QUOTE: This table contains critical values of the Student's t distribution computed using the cumulative distribution function. The t distribution is symmetric so that

- [math]t_{1-\alpha,\nu} = -t_{\alpha,\nu}[/math]

- The t-table can be used for both one-sided (lower and upper) and two-sided tests using the appropriate value of α.
- The significance level, α, is demonstrated in the graph below, which displays a t distribution with 10 degrees of freedom. The most commonly used significance level is [math]\alpha = 0.05[/math]. For a two-sided test, we compute [math]1 - \alpha/2[/math], or [math]1 - 0.05/2 = 0.975[/math] when [math]\alpha = 0.05[/math]. If the absolute value of the test statistic is greater than the critical value (0.975), then we reject the null hypothesis. Due to the symmetry of the t distribution, we only tabulate the positive critical values in the table below.

### 2002a

- (Dougherty, 2002) ⇒ Statistical Tables in Dougherty (2002) "Introduction to Econometrics" (second edition 2002, Oxford University Press, Oxford) http://home.ubalt.edu/ntsbarsh/Business-stat/StatistialTables.pdf

### 2002b

- (Hildebrand,2002) ⇒ http://www.stat.ufl.edu/~athienit/Tables/tables