NCEA Level 3 Statistics key terms

The complete set of all individuals or units that a study is interested in. Researchers usually cannot measure every member, so they take a sample and use it to draw conclusions about the whole group.

A subset of units selected from a population, used to gather data. A well-chosen sample allows inferences about the population without measuring every member.

A numerical summary of a whole population, such as a population mean or proportion. Its value is usually unknown and is estimated from sample data.

A numerical summary calculated from sample data, such as a sample mean or sample proportion. It is used to estimate the corresponding unknown population parameter.

The natural variation between statistics from different random samples drawn from the same population. It explains why repeated samples give slightly different estimates and underpins margins of error.

The distribution of a statistic (such as the sample mean) over all possible random samples of a given size from a population. Its spread and shape determine how precise estimates are likely to be.

A selection method in which every unit in the population has an equal chance of being chosen and every possible sample of a given size is equally likely. It reduces selection bias.

A method that divides the population into groups (strata) sharing a characteristic, then randomly samples within each stratum. It can improve precision when strata differ markedly.

A method where the population is divided into clusters (often geographic), a random selection of clusters is chosen, and all or many units within chosen clusters are measured. It is practical but often less precise.

A list or register of the population units from which a sample is actually selected. If it omits or duplicates members, the resulting sample may not represent the intended population.

A systematic tendency for a sample statistic to differ from the true population value in a consistent direction. It is not fixed by increasing sample size and arises from poor selection, non-response, or question wording.

Errors in survey data not caused by which units are selected, including non-response, measurement error, data-entry mistakes, and poorly worded questions. These can distort results even in large samples.

The number of units included in a sample. Larger samples generally give more precise estimates and smaller margins of error, though they do not remove bias.

A measure of the uncertainty in a survey estimate, often half the width of a confidence interval. It indicates how far a sample statistic might plausibly be from the population parameter.

A range of values, calculated from sample data, likely to contain the unknown population parameter. The confidence level describes how often such intervals capture the parameter across repeated sampling.

The long-run proportion of confidence intervals that would capture the true parameter if sampling were repeated many times, commonly 90%, 95%, or 99%. It is not the probability that a particular interval contains the parameter.

The standard deviation of a statistic's sampling distribution. It measures the typical distance between a sample statistic and the population parameter, and shrinks as sample size increases.

A key result stating that the sampling distribution of the sample mean becomes approximately normal as sample size grows, regardless of the population shape. This allows normal-based inference for means.

A formal procedure that assesses evidence against a null hypothesis by comparing observed data with what would be expected if the null were true. It produces a test statistic and a p-value.

The statement of no effect, no difference, or no relationship that a hypothesis test begins by assuming. It is retained unless the data provide sufficiently strong evidence against it.

The statement that there is an effect, difference, or relationship, which the test is designed to detect. It may be one-sided or two-sided and directs how the p-value is calculated.

The probability, assuming the null hypothesis is true, of obtaining a test statistic at least as extreme as the one observed. Smaller values indicate stronger evidence against the null hypothesis.

The threshold probability, often 0.05, chosen before a test against which the p-value is compared. If the p-value is below it, the result is declared statistically significant.

Rejecting a true null hypothesis, that is, concluding an effect exists when it does not. Its probability is controlled by the significance level chosen for the test.

Failing to reject a false null hypothesis, that is, missing a real effect. Its probability decreases when the effect is larger, the sample is bigger, or a higher significance level is used.

The probability that a test correctly rejects a false null hypothesis, equal to one minus the Type II error rate. Power increases with larger samples, larger effects, and less variability.

A result is statistically significant when the p-value is below the chosen significance level, suggesting the observed effect is unlikely under the null hypothesis. It does not by itself imply practical importance.

Whether an observed effect is large enough to matter in a real context, judged from the effect size and consequences rather than from statistical significance alone. Large samples can make trivial effects statistically significant.

A standardised measure of the strength of a difference or relationship, such as the difference between means expressed in standard deviation units. It helps compare results across studies and judge practical importance.

The use of chance to assign experimental units to treatment groups or to select samples. It protects against confounding by balancing unknown variables across groups.

A variable associated with both the explanatory variable and the response that can distort or create an apparent relationship. Randomisation and control help prevent confounding in experiments; observational studies must adjust for it.

A study in which researchers observe and measure units without assigning treatments. It can reveal associations but generally cannot establish causation because of possible confounding.

A study in which researchers deliberately assign treatments to units, usually using randomisation and a control group. Well-designed experiments can provide evidence of a causal relationship.

The group of units in an experiment that receives no treatment or a standard treatment, providing a baseline for comparison. It helps isolate the effect of the treatment being studied.

A relationship in which a change in one variable directly produces a change in another. Establishing causation typically requires a well-randomised experiment or strong supporting evidence beyond simple correlation.

A measure of the strength and direction of a linear association between two numerical variables, usually summarised by the correlation coefficient r between -1 and 1. It does not imply causation.

The line of best fit through a scatter plot, used to predict a response variable from an explanatory variable. Its slope estimates the average change in the response for a one-unit increase in the explanatory variable.

The difference between an observed value and the value predicted by a model, calculated as observed minus predicted. Residual plots help check whether a regression model is appropriate.

A method for fitting a line or curve by choosing coefficients that minimise the sum of squared residuals. It gives the standard regression line used in bivariate data analysis.

A graph plotting one numerical variable against another, with each point representing one unit. It reveals the direction, strength, and form of an association and highlights outliers.