Obtaining t_alpha/2 for a Two-tailed Region

If you know $\alpha$ and $n$ and want the value of $t_{\alpha/2}$ for a $t$ -distribution with $n$ degrees of freedom, the appropriate formula is:

   =TINV$$(\alpha,n)$$

For example, if $\alpha=0.05$ and the sample size (degrees of freedom) is $10$ , the formula is

   =TINV$$(0.05,10)$$

When this command executes, the result is $2.23$ , which is the value of $t_{\alpha/2}$ when we have $\alpha=0.05$ and $10$ degrees of freedom.

The graph below represents this result. The shaded area goes from $-\infty$ to $-2.23$ , and from $+2.23$ to $+\infty$ , and has total area equal to $\alpha$ , or $0.05$ .

The two shaded portions each have area $0.025$ or $\alpha/2$ .

These threshold values would be used to construct a two-tailed test or confidence region.

(Note: this is the correct syntax for Excel. It is slightly different for other spreadsheets. Consult the help menu of the spreadsheet you are using to find the correct syntax for your spreadsheet program).