30.4 The test statistic: Observations

The observed sample mean difference (observations), relative to what was expected, is found by computing the test statistic, in this case, a $t$-score. The software output (jamovi: Fig. 30.1; SPSS: Fig. 30.2) can be used, but the $t$-score can also be computed manually:

$$\begin{array}{cc}t& =\frac{\text{sample statistic}-\text{assumed population parameter, from}{H}_0}{\text{standard error for sample statistic}}\\ & =\frac{({\overline{x}}_P-{\overline{x}}_C)-({\mu }_P-{\mu }_C)}{\text{s.e.}({\overline{x}}_P-{\overline{x}}_C)}\\ & =\frac{51.594-0}{19.612}=2.631,\end{array}$$ as in the software output.