Junior Statistician Qualification Examination key terms

A measure of how far observations typically spread from the mean, computed as the square root of the average squared deviation. It is expressed in the same units as the original data.

The average of the squared deviations of observations from their mean. It quantifies dispersion in squared units and equals the square of the standard deviation.

The ratio of the standard deviation to the mean, often expressed as a percentage. It compares relative variability across groups or variables measured in different units or with very different means.

Quartiles divide ordered data into four equal parts; the interquartile range is the difference between the third and first quartiles. It describes the spread of the middle half of the data and resists distortion by outliers.

The middle value of an ordered data set, or the average of the two middle values when the count is even. It is a robust measure of central tendency that is little affected by extreme observations.

A measure of the asymmetry of a distribution. Positive skew means a long right tail with the mean pulled above the median; negative skew means a long left tail.

A graph showing the median, quartiles, and potential outliers of a distribution, usually drawn as a box with whiskers. It supports quick comparison of location and spread across groups.

A bar chart of grouped quantitative data in which bar areas represent frequencies or relative frequencies. Its shape reveals modality, skewness, gaps, and possible outliers.

A guideline for choosing the number of classes in a histogram, approximately 1 + 3.322 times the base-2 logarithm of the sample size. It gives a starting point that may be adjusted for readability.

A numerical function defined on the sample space of an experiment, assigning a real number to each outcome. It allows probabilities to be attached to numerical events.

A function giving the probability that a discrete random variable equals each of its possible values. The values are non-negative and sum to one over all possible outcomes.

A function giving the probability that a random variable is less than or equal to a given value. It is non-decreasing, right-continuous, and ranges from zero to one.

The distribution of the number of successes in a fixed number of independent trials, each with the same success probability. Its mean is n times p and its variance is n times p times one minus p.

A distribution for counts of rare events occurring independently in a fixed interval of time or space, with mean and variance both equal to the rate parameter. It often models arrivals, defects, or accidents.

A continuous, symmetric, bell-shaped distribution defined by its mean and variance. Many sampling distributions are approximately normal, which underlies much of standard inference.

The value obtained by subtracting the mean from an observation and dividing by the standard deviation. It states how many standard deviations an observation lies from the mean and permits comparison across normal distributions.

A result stating that the sampling distribution of a sum or mean of many independent, identically distributed variables approaches normality as sample size grows, regardless of the population shape, provided the variance is finite.

A value below which a specified proportion of a distribution or sample falls. Common examples are percentiles, quartiles, and the critical values used in confidence intervals and tests.

A statistic computed from sample data to approximate an unknown population parameter. Its quality is judged by properties such as unbiasedness, efficiency, and consistency.

The property that an estimator's expected value equals the true parameter over repeated sampling. An unbiased estimator may still vary widely from sample to sample.

The expected squared difference between an estimator and the true parameter. It decomposes into the estimator's variance plus the square of its bias, trading off the two sources of error.

The standard deviation of a sampling distribution of a statistic, such as a sample mean. It measures how much an estimate would vary across repeated samples and shrinks as sample size grows.

An interval computed from sample data that, under repeated sampling, covers the true parameter in a stated long-run proportion of cases. The confidence level describes the procedure, not any single interval.

The half-width of a confidence interval, typically a critical value multiplied by the standard error. It shrinks with larger samples and grows with higher confidence levels.

Complementary statements about a population parameter used in a test. The null usually asserts no effect or no difference, while the alternative states the effect the researcher suspects.

The probability, assuming the null hypothesis is true, of obtaining a test statistic at least as extreme as the one observed. It is not the probability that the null hypothesis is true.

The threshold probability chosen before testing, below which the null hypothesis is rejected. It equals the tolerated rate of Type I errors and is conventionally set at 0.05.

Rejecting a true null hypothesis, also called a false positive. Its probability is controlled by the significance level chosen for the test.

Failing to reject a false null hypothesis, also called a false negative. Its probability is denoted beta, and one minus beta gives the power of the test.

The probability of correctly rejecting a false null hypothesis. Power increases with larger effect size, larger sample size, smaller variability, and less stringent significance levels.

A standardized measure between minus one and one describing the strength and direction of linear association between two variables. It is symmetric and unaffected by linear rescaling of either variable.

A fitting principle that chooses parameter values minimizing the sum of squared residuals. In simple linear regression it yields the line with the smallest total squared vertical distances from the data points.

The proportion of total variation in the response variable explained by a regression model, ranging from zero to one. In simple linear regression it equals the square of the correlation coefficient.

The difference between an observed value and the value predicted by a fitted model. Residual plots are used to check linearity, constant variance, independence, and the presence of outliers.

The assumption that the variability of the response or of the errors is constant across levels of the predictors. Violations call for transformations, robust standard errors, or weighted methods.

The assignment of experimental units to treatments by chance. It makes treatment groups comparable in expectation and supports valid inference by removing systematic allocation bias.

Grouping experimental units that are similar before randomly assigning treatments within each group. It reduces variability from nuisance factors and increases precision.

A sampling design in which every subset of a given size has an equal chance of selection, so each unit has the same inclusion probability. It is the reference design for many sampling methods.

A design in which the population is divided into homogeneous subgroups and independent samples are drawn from each. It can reduce variance and guarantees representation of every stratum.

The list or mechanism from which a sample is actually drawn. Coverage error arises when the frame omits parts of the target population or includes ineligible units.

Distortion that occurs when sampled units who do not respond differ systematically from those who do on the measured variables. It is a concern in surveys and can be mitigated by weighting or follow-up.

A cross-tabulation of counts for two or more categorical variables. It displays joint frequencies and is the basis for tests of independence and measures of association.

A test comparing observed cell counts in a contingency table with counts expected under independence. It relies on large expected counts and uses degrees of freedom based on table dimensions.

A small adjustment subtracting 0.5 from the absolute difference between observed and expected counts in a two-by-two chi-square test. It makes the test more conservative and is debated for larger samples.

The ratio of the odds of an event in one group to the odds in another group. It is common in two-by-two tables and case-control studies and approximates the relative risk for rare outcomes.

A nonparametric test comparing the locations of two independent groups by ranking pooled observations. It does not assume normality but requires otherwise similar distribution shapes for a pure location comparison.

A simple nonparametric procedure that compares paired observations by counting how often one member exceeds the other. It uses the binomial distribution and requires only that pairs be independent.

A smoothed series formed by averaging consecutive observations over a fixed window that slides forward. It reduces short-term noise and helps reveal trend and seasonal patterns.

The correlation between a time series and lagged copies of itself. It measures persistence and is used to diagnose dependence and identify models such as autoregressive or moving-average processes.

A property of a time series whose mean, variance, and autocovariance structure do not change over time. Many forecasting models assume it, often after differencing the data.

A numerical factor expressing how far a season's typical value deviates from the overall average, often as a percentage. It is used to remove seasonal effects or to adjust forecasts.

A price index that values a fixed basket of quantities at current prices relative to base-period prices. It holds quantities fixed at base levels and therefore tends to overstate cost-of-living change.

A price index that uses current-period quantities as weights, comparing current costs with base-period prices applied to those same quantities. It tends to understate cost-of-living change relative to Laspeyres.

A computer encoding of real numbers as a sign, mantissa, and exponent, giving a wide range at limited precision. It explains rounding artifacts such as sums that are not exactly one.

The process by which values become unobserved, classified as missing completely at random, at random given observed data, or not at random. The classification determines whether deletion or imputation yields valid results.