EXAMPLE 7.17

Degrees of freedom for directed reading assessment. For the DRP study of Example 7.11, the following table summarizes the data:

For greatest accuracy, we will use critical points from the t distribution with degrees of freedom given by the preceding equation:

$$\begin{array}{lll}{\displaystyle \text{df}}\hfill & {\displaystyle =}\hfill & {\displaystyle \frac{(\frac{11.{01}^2}{21}+\frac{17.{15}^2}{23}{)}^2}{\frac{1}{20}(\frac{11.{01}^2}{21}{)}^2+\frac{1}{22}(\frac{17.{15}^2}{23}{)}^2}}\hfill \\ \hfill & {\displaystyle =}\hfill & {\displaystyle \frac{344.486}{9.099}=37.86}\hfill \end{array}$$

This is the value that we reported in Example 7.14 (pages 441–442), where we gave the results produced by software.