# Difference between revisions of "t-Distribution Table"

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

## 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. (...)

### 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
$t_{1-\alpha,\nu} = -t_{\alpha,\nu}$
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 $\alpha = 0.05$. For a two-sided test, we compute $1 - \alpha/2$, or $1 - 0.05/2 = 0.975$ when $\alpha = 0.05$. 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.