Statistical Methods and Demographic Calculations

Vocabulary flashcards covering core formulas and concepts in sampling theory, error calculation, and demographic analysis.

Absolute Error Formula ($\Delta$)

The magnitude of the difference between an observed or estimated value and the baseline or true value, expressed as $\Delta = |x - x_0|$.

Relative Error Formula ($\delta$)

The ratio of the absolute error to the baseline or true value, expressed as a percentage: $\delta = \frac{\Delta}{x} \times 100\%$.

Standard Error of the Mean ($\mu$)

The standard deviation of the sample mean distribution, calculated from population standard deviation $\sigma$ and sample size $n$ as $\mu = \frac{\sigma}{\sqrt{n}}$.

Margin of Sampling Error ($\Delta$)

The maximum expected difference between the sample estimate and the true population parameter, given by $\Delta = t \cdot \mu$, where $t$ is the confidence coefficient.

Confidence Interval for the Mean

The interval estimate within which the true population mean is expected to fall, constructed as $[\bar{x} - \Delta;\; \bar{x} + \Delta]$.

Standard Error of a Proportion ($\mu_w$)

The sampling error for an attribute proportion $w$ in a sample of size $n$, calculated as $\mu_w = \sqrt{\frac{w \cdot (1 - w)}{n}}$.

Required Sample Size Formula ($n$)

The formula used to determine the necessary sample size for estimating a mean: $n = \frac{t^2 \cdot \sigma^2}{\Delta^2}$.

Sampling Fraction ($f$)

The ratio of the sample size $n$ to the total population size $N$, calculated as $f = \frac{n}{N}$.

Finite Population Correction Factor

The correction multiplier applied to sampling error when sampling without replacement from a finite population, given as $\left(1 - \frac{n}{N}\right)$.

Critical Value for $0.954$ Probability

The confidence coefficient $t = 2$, which corresponds to a normal distribution probability of approximately $0.954$ ($95.4\%$).

Confidence Probability for Critical Value $t = 3$

The probability coverage of $0.997$ ($99.7\%$) associated with a critical value multiplier of $t = 3$ in a normal distribution.

Response Rate

The proportion of targeted sample units that successfully provide data in a survey (e.g., $680$ respondents out of an $800$-unit sample yields an $85\%$ response rate).

Non-response Rate

The proportion of targeted sample units that fail or refuse to provide data (e.g., $120$ non-respondents out of an $800$-unit sample yields a $15\%$ non-response rate).

Demographic Balance Equation

The formula determining population size at the end of a period: $S_{\text{end}} = S_{\text{start}} + \text{Births} - \text{Deaths} + \text{Immigration} - \text{Emigration}$.