Glossary — Statistics

Addition rule — the rule for finding the probability that at least one of two events happens. For mutually exclusive events, the probabilities are added.

Alternative hypothesis — the claim that a hypothesis test suspects instead of the null hypothesis, written $H_1$.

Binomial distribution — the distribution of the number of successes in $n$ independent trials, each with the same probability $p$ of success.

Bivariate data — data with two values recorded for each item.

Conditional probability — the probability of one event when you know that another event has happened.

Continuity correction — the adjustment made when a whole-number binomial variable is approximated by a continuous Normal variable.

Correlation — a measure of how two variables move together.

Correlation coefficient — a number between $-1$ and $1$ that measures the strength and direction of a linear relationship, written $r$.

Critical region — the set of test statistic values that lead to rejecting the null hypothesis.

Critical value — the value that separates the critical region from the acceptance region.

Data cleaning — the process of finding and dealing with values that are wrong or missing.

Discrete random variable — a variable whose value depends on the outcome of an experiment and takes only separate, listed values.

Explanatory variable — the variable you choose or control in bivariate data; it goes on the horizontal axis.

Frequency density — the frequency of a class divided by the class width; it gives the height of a histogram bar.

Hypothesis test — a procedure that uses sample evidence to decide between two claims about a population.

Independent events — two events where the chance of one does not change when you know the other has happened.

Interquartile range — the difference between the upper and lower quartiles; it measures the spread of the middle half of the data.

Mutually exclusive — two events that cannot both happen at the same time.

Normal distribution — a continuous model with a symmetric, bell-shaped curve, fixed by its mean and its standard deviation.

Null hypothesis — the claim assumed at the start of a hypothesis test, written $H_0$.

Outlier — a value that is unusually far from the rest of the data.

p-value — the probability of a result at least as extreme as the one observed, assuming the null hypothesis is true.

Population — the whole group you want to know about.

Probability distribution — a list of the possible values of a discrete random variable and their probabilities.

Random variable — a number whose value depends on the outcome of an experiment.

Regression line — a straight line drawn through the middle of the points on a scatter diagram, used to summarise the trend.

Response variable — the variable you measure in bivariate data.

Sample — a part of the population that you measure.

Sample space — the set of all possible outcomes of an experiment.

Sampling frame — the list of the population that you choose a sample from.

Sampling variability — the natural variation between the results of different samples from the same population.

Significance level — the small probability, written $\alpha$, that a test is allowed to reject a true null hypothesis by mistake.

Standard deviation — a measure of spread found from the root mean square deviation from the mean.

Standard error — the standard deviation of a sample mean, equal to $\dfrac{\sigma}{\sqrt{n}}$ for a sample of size $n$.

Standardising — the change of variable $z = \dfrac{x - \mu}{\sigma}$ that turns a Normal variable into the standard Normal variable.

Stratified sampling — a method that splits the population into groups and takes a random sample from each group.

Systematic sample — a sample taken by choosing a random start and then every $k$th member of an ordered list.

Test statistic — the value calculated from the sample and compared with the hypothesis.