C.5 Other formulas

To calculate $z$ -scores (Sect. 20.4), use
$z = \frac{\text{value of variable} - \text{mean of the distribution of the variable}}{\text{standard deviation of the distribution of the variable}}.$ $t$ -scores are like $z$ -scores. When the 'variable' is a sample estimate (such as $\bar{x}$ ), the 'standard deviation of the distribution' is a standard error (such as $\text{s.e.}(\bar{x})$ ).
The unstandardising formula (Sect. 20.8) is $x = \mu + (z\times \sigma)$ .
The interquartile range (IQR) is $Q_3 - Q_1$ , where $Q_1$ and $Q_3$ are the first and third quartiles respectively (or, equivalently, the $25$ th and $75$ th percentiles).
The smallest expected value (for assessing statistical validity when forming CIs and conducting hypothesis tests with proportions or ORs) is
$\frac{(\text{Smallest row total})\times(\text{Smallest column total})}{\text{Overall total}}.$
The regression equation in the sample is $\hat{y} = b_0 + b_1 x$ , where $b_0$ is the sample intercept and $b_1$ is the sample slope.