# Finding critical value $t^*$ given significance level $\alpha$, using the table with critical $t$ values

Assuming a table with a row per degrees of freedom and a column per upper tail probability
 Two sided Reject the null hypothesis if the observed $t$ falls in one of the two most extreme $\alpha$ / 2 areas of the $t$ distribution. In order to find the critical values $t^*$ and $-t^*$ that correspond to these tail areas: Find the row with the appropriate degrees of freedom (df) Find the column for the upper tail probability equal to $\alpha / 2$ At the intersection point of this row and column, you find the positive critical value $t^*$. Observed $t$ values that are at least as extreme as $t^*$ (positive or negative), are significant. In other words, observed $t$ values that are equal to or larger than $t^*$, and observed $t$ values that are equal to or smaller than $-t^*$, lead to rejection of the null hypothesis Right sided Reject the null hypothesis if the observed $t$ falls in the highest $\alpha$ area of the $t$ distribution. In order to find the critical value $t^*$ that corresponds to this upper tail area: Find the row with the appropriate degrees of freedom (df) Find the column for the upper tail probability equal to $\alpha$ At the intersection point of this row and column, you find the critical value $t^*$. Observed $t$ values that are equal to or larger than $t^*$, lead to rejection of the null hypothesis Left sided Reject the null hypothesis if the observed $t$ falls in the lowest $\alpha$ area of the $t$ distribution. In order to find the critical value $t^*$ that corresponds to this lower tail area: Find the row with the appropriate degrees of freedom (df) Find the column for the upper tail probability equal to $\alpha$ Multiply the value at the intersection point of this row and column, by -1. The resulting value is the critical value $t^*$. Observed $t$ values that are equal to or smaller than $t^*$, lead to rejection of the null hypothesis