C.1 Symbols and standard errors

• The following table lists the statistics used to estimate unknown population parameters.

• When the sampling distribution is approximately normally distributed, under appropriate statistical validity conditions, this is indicated by ✔.

• The value of the mean of the sampling distribution (the sampling mean) is:

  • unknown, for confidence intervals.
  • assumed to be the value given in the null hypothesis, for hypothesis tests.

		Sampling distribution
		Parameter, and	Normal	Standard
	Statistic	sampling mean	distn?	error	Ref.
Proportion	$\hat{p}$	$p$	✔	CI: $\displaystyle \sqrt{\frac{ \hat{p} \times (1 - \hat{p})}{n}}$	Ch. 22
			✔	HT: $\displaystyle \sqrt{\frac{ p \times (1 - p)}{n}}$	Ch. 26
Mean	$\bar{x}$	$\mu$	✔	$\displaystyle \frac{s}{\sqrt{n}}$	Chs. 23, 27
Mean difference	$\bar{d}$	$\mu_d$	✔	$\displaystyle \frac{s_d}{\sqrt{n}}$	Ch. 29
Difference between means	$\bar{x}_1 - \bar{x}_2$	$\mu_1 - \mu_2$	✔	$\displaystyle \sqrt{\text{s.e.}(\bar{x}_1)^2 + \text{s.e.}(\bar{x}_2)^2}$	Ch. 30
Difference between proportions	$\hat{p}_1 - \hat{p}_2$	$p_1 - p_2$	✔	CI: $\displaystyle \sqrt{\text{s.e.}(\hat{p}_1)^2 + \text{s.e.}(\hat{p}_2)^2}$	Ch. 31
			✔	HT: $\displaystyle \sqrt{\text{s.e.}(\hat{p}_1)^2 + \text{s.e.}(\hat{p}_2)^2}$ using common proportion $\hat{p}$	Ch. 31
Odds ratio (OR)	Sample OR	Pop. OR	✘	(Not given)	Ch. 31
Correlation	$r$	$\rho$	✘	(Not given)	Ch. 33
Regression: slope	$b_1$	$\beta_1$	✔	$\text{s.e.}(b_1)$ (value from software)	Ch. 33
Regression: intercept	$b_0$	$\beta_0$	✔	$\text{s.e.}(b_0)$ (value from software)	Ch. 33

---

Copyright © Peter K. Dunn, 2025