English for students and researchers using statistics
Statistics Vocabulary: 100 Key English Terms
Statistics has its own precise English: research articles, output from SPSS, R or Stata, textbooks and official reports all use the same terms to describe data, test hypotheses and report results. Knowing these words helps students and researchers follow lectures and papers, read their own output with confidence and write results sections that international reviewers understand. Many of the terms, such as 'significant', 'mean' and 'normal', also have everyday meanings, so learning the statistical sense is essential.
100 terms
10 topics
59 core terms
200 example sentences
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No account needed. Read the meaning, see where the term is used, then study the examples. Click any word in the lesson for help. You can also select a word and press Alt + Enter.
Descriptive Statistics
mean
noun
Meaning
The sum of all the values divided by the number of values; the usual 'average' that describes the centre of a set of numbers.
Where you use it
The most reported statistic in any results section, usually next to the standard deviation: 'M = 24.6, SD = 3.1'. You calculate, compute or report the mean; the sample mean is written x̄ (read 'x-bar') and the population mean μ ('mu').
Examples
The mean age of participants was 34.2 years (SD = 8.7).
A few very high incomes pulled the mean well above the median.
Usage note
In everyday English 'average' usually means the mean, but statisticians prefer 'mean' because the median and mode are also kinds of average. Do not confuse the noun with the verb 'mean' (to signify).
Common phrases
calculate the mean · sample mean · arithmetic mean · mean score · means and standard deviations
The middle value when the data are put in order from smallest to largest; with an even number of values, it is the mean of the two middle ones.
Where you use it
Preferred over the mean for skewed data such as income, house prices or reaction times, because extreme values hardly affect it. Reports often give the median with the interquartile range: 'median 42 (IQR 35–51)'.
Examples
Because household income is skewed, we report the median rather than the mean.
The median waiting time fell from 18 to 11 minutes after the change.
Common phrases
median income · median value · report the median · median and IQR
The value that appears most often in a data set. A distribution can have one mode, two (bimodal) or several.
Where you use it
Most useful for categorical data, where a mean is meaningless: the most common answer, brand or blood type. Also used to describe the shape of a distribution: unimodal, bimodal, multimodal.
Examples
The mode for shoe size in our sample was 42.
The histogram shows two modes, which suggests two different groups of customers.
Usage note
It has nothing to do with Turkish 'moda' (fashion). The adjective is 'modal', as in 'the modal answer' (the most frequent answer).
Common phrases
find the mode · bimodal distribution · modal category · modal value
A measure of how spread out values are around the mean; a small value means the data sit close to the mean, a large one means they are widely scattered.
Where you use it
Reported almost every time a mean is reported, often abbreviated SD (σ for a population, s for a sample). It is the square root of the variance and is expressed in the same units as the data, which makes it easier to interpret.
Examples
Scores had a mean of 72 and a standard deviation of 9.
In a normal distribution, about 95% of values lie within two standard deviations of the mean.
Usage note
Do not mix up the standard deviation (the spread of the data) with the standard error (the precision of an estimate such as the mean).
Common phrases
calculate the standard deviation · one standard deviation above the mean · sample standard deviation · large standard deviation
The average of the squared distances between each value and the mean; it measures spread, and its square root is the standard deviation.
Where you use it
Used more in theory and in methods such as ANOVA than in everyday reporting, because its units are squared. For a sample, the sum of squares is divided by n − 1 instead of n. People also say a variable 'explains' or 'accounts for' a share of the variance.
Examples
Age alone accounts for 18% of the variance in blood pressure.
Levene's test showed that the variances of the two groups were not equal.
Usage note
In everyday English 'at variance with' means 'in disagreement with'; in statistics the word is purely technical.
Common phrases
explain the variance · sample variance · equal variances · proportion of variance · analysis of variance
The difference between the largest and the smallest value in a data set; the simplest measure of spread.
Where you use it
Often given as the two end points rather than one number: 'ages ranged from 19 to 64'. Because it depends only on the two most extreme values, a single outlier can change it a lot. The verb pattern 'range from … to …' is very common in results sections.
Examples
Participants' ages ranged from 19 to 64.
The range is misleading here because of one extreme value.
Usage note
'Range' is a measure of spread; do not confuse it with 'interval', as in 'confidence interval'. Both can be translated as 'aralık' in Turkish.
Common phrases
range from … to … · wide range · narrow range · interquartile range
An observation that lies unusually far from most of the other values in a data set; it may come from an error or from a genuinely unusual case.
Where you use it
Analysts detect, check, remove or keep outliers, and should always say how they handled them. A common rule flags values more than 1.5 × IQR beyond the quartiles, which is also how box plots mark them.
Examples
One participant reported working 160 hours a week, which is clearly an outlier.
The results were similar with and without the three outliers.
The number of times a value or category occurs in a data set; a relative frequency gives the same information as a proportion or percentage.
Where you use it
Frequencies are the first thing analysts look at for categorical variables, usually in a frequency table with counts and percentages. A cumulative frequency adds up the counts up to each value. In SPSS, 'Frequencies' is the menu item that produces these tables.
Examples
The frequency table shows that 62% of respondents chose 'agree'.
Run frequencies on every variable first to catch coding errors.
Common phrases
frequency table · relative frequency · cumulative frequency · frequency distribution · run frequencies
A value below which a given percentage of the observations fall; for example, 90% of the data lie below the 90th percentile.
Where you use it
Common in growth charts, exam results, salary surveys and performance monitoring ('the 95th percentile response time'). The 25th, 50th and 75th percentiles are the quartiles, and the 50th percentile is the median. A child 'on the 80th percentile for height' is taller than about 80% of children of the same age.
Examples
Her score puts her in the 92nd percentile of all applicants.
We track the 95th percentile of page load time, not just the average.
Common phrases
the 90th percentile · percentile rank · below the 5th percentile · percentile score
Numbers, tables and charts that summarise the main features of a data set, such as its centre, spread and shape, without drawing conclusions beyond the data.
Where you use it
Usually the first table in a results section ('Table 1 shows the descriptive statistics'), with means, standard deviations, medians, ranges and frequencies. Contrasted with inferential statistics, which generalise from a sample to a population.
Examples
Descriptive statistics for all study variables are presented in Table 1.
Start with descriptive statistics so you understand the data before testing anything.
One of the three values that divide ordered data into four equal parts: the first quartile (Q1), the median (Q2) and the third quartile (Q3).
Where you use it
Used to describe skewed data and to draw box plots. 'Lower quartile' and 'upper quartile' are common alternatives for Q1 and Q3. In everyday reports, 'quartile' can also mean one of the four groups: 'students in the bottom quartile'.
Examples
The first quartile of monthly rent was 9,500 lira and the third quartile 16,000 lira.
Schools in the lowest income quartile received extra funding.
The distance between the first and third quartiles (Q3 − Q1), showing how spread out the middle 50% of the data is.
Where you use it
Abbreviated IQR and reported with the median when data are skewed: 'median 6 days (IQR 4–11)'. Note that journals often give the two quartiles in brackets rather than their difference. Unlike the range, it is not affected by extreme values.
Examples
Hospital stay had a median of 6 days and an interquartile range of 4 to 11 days.
Because of the outliers, the interquartile range is a better measure of spread here than the standard deviation.
Common phrases
median and interquartile range · calculate the interquartile range · 1.5 times the IQR · report the IQR
An average in which some values count more than others: each value is multiplied by a weight, the results are added, and the total is divided by the sum of the weights.
Where you use it
Used for grade point averages, price indices, combining results from groups of different sizes and survey weighting. 'Weighted mean' is the more technical name. In surveys, weights correct for groups that were over- or under-represented in the sample.
Examples
The final grade is a weighted average: the exam counts for 60% and the project for 40%.
Don't just average the branch means; take a weighted average by number of customers.
Common phrases
calculate a weighted average · weighted mean · survey weights · weight by population
A table that shows how the categories of two or more categorical variables combine, with the number of cases in each combination.
Where you use it
Often shortened to 'crosstab' and also called a contingency table. Used to compare groups (for example answers by gender or region) and as the basis of the chi-square test of independence. Row or column percentages make the table easier to read.
Examples
A cross-tabulation of satisfaction by region showed lower scores in the east.
Add column percentages to the cross-tabulation so we can compare the age groups.
Any characteristic that can take different values from one person, object or case to another, such as age, income, gender or test score.
Where you use it
The basic building block of any data set: in a spreadsheet, variables are usually the columns and cases the rows. You measure, code, recode, create and transform variables; types include categorical, continuous, independent and dependent.
Examples
We recoded the age variable into four groups.
Which variables did you include in the final model?
Common phrases
measure a variable · recode a variable · outcome variable · key variables · create a new variable
A variable whose values are groups or labels rather than measured quantities, such as blood type, city of residence or 'yes/no' answers.
Where you use it
Split into nominal (no natural order: colour, nationality) and ordinal (ordered: education level, 'low/medium/high'). Summarised with counts and percentages, analysed with tests such as chi-square and entered into regression as dummy variables.
Examples
Gender and region were entered as categorical variables in the model.
You can't calculate a meaningful mean for a categorical variable like eye colour.
Common phrases
nominal variable · ordinal variable · dummy-code a categorical variable · categorical data · levels of a categorical variable
A variable that can take any value within a range, including fractions, such as height, temperature, time or income.
Where you use it
Summarised with means, standard deviations or medians and analysed with t-tests, correlation and regression. Analysts are often advised not to cut continuous variables into groups, because information is lost. Contrasted with discrete variables, which take separate values such as counts.
Examples
Age was treated as a continuous variable rather than in ten-year bands.
Blood pressure is a continuous variable, so a t-test is more suitable than chi-square here.
Common phrases
continuous outcome · treat as continuous · continuous data · discrete variable
The variable that a researcher changes, controls or uses to explain changes in another variable; in an experiment it is the factor being manipulated.
Where you use it
Abbreviated IV, especially in psychology and education. In regression it is also called a predictor, explanatory variable or covariate, and on a graph it usually goes on the x-axis. Methods sections name the independent and dependent variables explicitly.
Examples
The independent variable was the type of feedback students received: written or spoken.
Plot the independent variable on the x-axis.
Usage note
'Independent' here has nothing to do with statistical independence between events; it simply names the explaining variable.
Common phrases
manipulate the independent variable · levels of the independent variable · predictor variable · explanatory variable
The outcome a study measures to see whether it changes when the independent variable changes, such as test scores, sales or recovery time.
Where you use it
Abbreviated DV. Also called the outcome, response or target variable, and plotted on the y-axis. A useful memory aid: the dependent variable 'depends on' the independent one.
Examples
The dependent variable was the number of errors made during the task.
With a binary dependent variable like 'bought or didn't buy', use logistic regression.
Common phrases
outcome variable · measure the dependent variable · binary dependent variable · effect on the dependent variable
A single unit of data, such as one person, one transaction or one measurement, usually shown as one row in a data set.
Where you use it
Software output and papers count observations ('n = 1,250 observations'). Close words are case, record and data point; for people, participant or respondent. In research design, 'observation' can also mean a data-collection method based on watching behaviour.
Examples
After cleaning, we had 3,412 valid observations.
Each observation is one customer visit, not one customer.
Common phrases
number of observations · valid observations · drop observations · independent observations
A third variable that is related to both the independent and the dependent variable and can create a false or distorted impression of the relationship between them.
Where you use it
Also called a confounder. Researchers identify, measure and adjust for confounders, either through study design (randomisation, matching) or in the analysis (adding them to a regression). Unmeasured confounding is a common limitation of observational studies.
Examples
Age is a likely confounding variable: older people both exercise less and have more health problems.
We adjusted for income, education and smoking as potential confounding variables.
Common phrases
adjust for confounding variables · potential confounder · unmeasured confounding · control for confounders
Values that should be in a data set but are not, for example because a respondent skipped a question or a measurement failed.
Where you use it
Researchers must report how much data were missing and how they handled it: listwise deletion, mean imputation or, usually better, multiple imputation. Missing data are classed as MCAR, MAR or MNAR, depending on why the values are missing.
Examples
About 8% of the income data were missing, so we used multiple imputation.
How did you deal with missing data in the follow-up survey?
Usage note
In formal statistical writing 'data' is often treated as plural ('the data were missing'), although 'the data was' is common in business English.
Common phrases
handle missing data · pattern of missing data · multiple imputation · missing at random · listwise deletion
A number between 0 and 1 that expresses how likely an event is: 0 means it cannot happen and 1 means it is certain.
Where you use it
Written P(A) and read 'the probability of A'. In speech it is often given as a percentage ('a 30% probability'). 'Chance' and 'likelihood' are less formal near-synonyms, although 'likelihood' also has a separate technical meaning in statistics.
Examples
The probability of rolling a six with a fair die is 1/6.
What's the probability that at least one of the ten machines fails this month?
Common phrases
the probability of an event · high probability · calculate the probability · probability theory · probability distribution
A variable whose value is determined by the outcome of a random process, such as the number of heads in ten coin tosses or the waiting time for a bus.
Where you use it
A core idea in probability courses, usually written with a capital letter (X), while its observed values use lower case (x). A random variable is discrete or continuous and has a probability distribution, an expected value and a variance.
Examples
Let X be a random variable representing the number of customers arriving per hour.
A discrete random variable can only take separate values such as 0, 1, 2 and so on.
Common phrases
discrete random variable · continuous random variable · let X be a random variable · independent random variables
The long-run average result of a random variable if the same process were repeated many times, found by weighting each possible value by its probability.
Where you use it
Written E(X) and read 'the expected value of X'. Used in probability exercises, insurance, games of chance and decision analysis. The expected value need not be a value that can actually occur.
Examples
The expected value of a single roll of a fair die is 3.5.
Each ticket costs 10 lira but has an expected value of only 4 lira.
Usage note
In statistics 'expected' does not mean 'most likely'; it means 'average over many repetitions'.
Common phrases
calculate the expected value · the expected value of X · positive expected value · expected value and variance
Events where knowing that one has happened does not change the probability of the other; for two such events, P(A and B) = P(A) × P(B).
Where you use it
A key assumption in probability exercises (coin tosses, dice) and in many tests that require independent observations. Do not confuse 'independent' with 'mutually exclusive': two mutually exclusive events with non-zero probabilities can never be independent.
Examples
Two tosses of a fair coin are independent events, so the chance of two heads is 0.25.
Breakdowns of machines on the same production line are probably not independent events.
The probability that an event happens given that another event has already happened, written P(A | B) and read 'the probability of A given B'.
Where you use it
Calculated as P(A and B) / P(B). Central to medical testing, risk analysis and Bayes' theorem. A classic mistake is to treat P(A | B) and P(B | A) as the same, for example confusing the chance of a positive test given disease with the chance of disease given a positive test.
Examples
What is the conditional probability that a customer buys again, given that they complained last month?
The table lets you read off conditional probabilities for each age group.
Common phrases
conditional probability of A given B · calculate a conditional probability · conditional on · given that
A rule for updating the probability of an event or hypothesis in the light of new evidence, linking P(A | B) to P(B | A): P(A | B) = P(B | A) × P(A) / P(B).
Where you use it
Classic examples involve medical tests and spam filters. It is the basis of Bayesian statistics, in which a prior belief is combined with data to give a posterior distribution. Named after the 18th-century English minister Thomas Bayes.
Examples
Bayes' theorem explains why most positive results from a screening test for a rare disease can be false positives.
Apply Bayes' theorem to update the probability once you know the test result.
Usage note
The apostrophe goes after the s ('Bayes' theorem'); 'Bayes's theorem' is also seen, but 'Baye's theorem' is wrong. 'Bayes' rhymes with 'days'.
Common phrases
apply Bayes' theorem · Bayesian statistics · prior probability · posterior probability
Describes events or categories that cannot happen or be true at the same time, such as rolling a 2 and rolling a 5 on a single throw of a die.
Where you use it
In probability, P(A or B) = P(A) + P(B) when A and B are mutually exclusive. In survey design, answer options should be mutually exclusive (no overlap) and exhaustive (covering all cases), e.g. age bands 18–24 and 25–34, not 18–25 and 25–35.
Examples
Make sure the income categories are mutually exclusive; right now someone earning exactly 20,000 fits two boxes.
Since the events are mutually exclusive, we simply add their probabilities.
The pattern showing which values a variable takes and how often each one occurs, often pictured as a histogram or a curve.
Where you use it
Statisticians constantly describe a distribution's shape (symmetric, skewed, bimodal), centre and spread. The word also names theoretical models such as the normal, binomial or t distribution. You look at, plot, describe or compare distributions.
Examples
Before choosing a test, look at the distribution of the scores.
The distribution of response times is strongly right-skewed.
Common phrases
the distribution of scores · normal distribution · skewed distribution · frequency distribution · probability distribution
A symmetric, bell-shaped distribution in which most values cluster around the mean and become rarer further away from it; its mean, median and mode are equal.
Where you use it
Also called the Gaussian distribution or the bell curve. Many tests assume that the data, or the residuals, are 'normally distributed', so analysts check normality with plots or tests such as Shapiro–Wilk. Roughly 68%, 95% and 99.7% of values fall within one, two and three standard deviations of the mean.
Examples
A Shapiro–Wilk test showed that the data did not follow a normal distribution.
Adult height roughly follows a normal distribution within each sex.
Usage note
'Normal' here is a technical name, not a judgement: a non-normal distribution is not 'abnormal' or wrong.
Common phrases
follow a normal distribution · standard normal distribution · approximately normal · bell-shaped curve · test for normality
Describes a distribution that is not symmetric and has a longer tail on one side; in a right-skewed distribution a few very large values stretch the tail to the right.
Where you use it
Data are 'positively' or 'right-skewed' when the tail goes to the right (income, waiting times) and 'negatively' or 'left-skewed' when it goes to the left (scores on an easy exam). The noun is 'skewness'. Informally, 'skewed' also means unfairly distorted: 'skewed results'.
Examples
House prices are heavily skewed, so we log-transformed them before the analysis.
The distribution of exam scores was negatively skewed because most students found the test easy.
Usage note
When data are right-skewed, the mean is usually larger than the median, a quick check you can make from a summary table.
Common phrases
right-skewed · heavily skewed · skewed distribution · positively skewed · skewed to the left
The probability distribution of the number of successes in a fixed number of independent trials, each with the same probability of success, such as heads in 20 coin tosses.
Where you use it
Defined by two parameters, n (number of trials) and p (probability of success); its mean is np. Used for yes/no outcomes such as faulty items in a batch, patients who respond to a treatment or customers who click.
Examples
If 10% of parts are faulty, the number of faulty parts in a box of 50 follows a binomial distribution.
Use the binomial distribution to find the probability of exactly 3 successes in 10 trials.
Common phrases
follow a binomial distribution · binomial probability · binomial test · number of trials
A probability distribution for the number of times an event happens in a fixed period or space when events occur independently at a constant average rate.
Where you use it
Used for counts such as calls per hour, accidents per month or typos per page. Its single parameter λ (lambda) is both the mean and the variance; when the variance is clearly larger, analysts talk about 'overdispersion'. Named after the French mathematician Siméon Denis Poisson.
Examples
The number of emergency calls per hour follows a Poisson distribution with a mean of 4.
The variance is far bigger than the mean, so a Poisson distribution doesn't fit these data well.
Usage note
The name is French and sounds roughly like 'pwah-SON'; it has nothing to do with 'poison'.
Common phrases
Poisson process · Poisson regression · follow a Poisson distribution · rate parameter lambda
The result that the distribution of sample means gets closer to a normal distribution as the sample size grows, whatever the shape of the population distribution, as long as its variance is finite.
Where you use it
Abbreviated CLT. It explains why normal-based methods such as t-tests and confidence intervals work well for means even with non-normal data, once samples are reasonably large. Textbooks often give n ≥ 30 as a rough rule, though very skewed data need more.
Examples
Thanks to the central limit theorem, the mean of 200 waiting times is approximately normal, even though the times themselves are skewed.
Can someone explain the central limit theorem without formulas?
Common phrases
by the central limit theorem · apply the central limit theorem · the CLT holds · large-sample approximation
A value showing how many standard deviations an observation lies above or below the mean, found by subtracting the mean and dividing by the standard deviation.
Where you use it
Used to compare scores from different scales, to spot unusual values (|z| > 3 is often flagged) and to look up probabilities in the standard normal table. Converting values to z-scores is called standardising, and a z-score is also known as a standard score.
Examples
A z-score of 2 means the student scored two standard deviations above the class mean.
We converted all test results to z-scores so the two exams could be compared.
Usage note
Americans say 'zee-score' and British speakers usually say 'zed-score'.
Common phrases
calculate a z-score · convert to z-scores · standard score · z-score table
The whole group of people, items or events that a study wants to draw conclusions about, for example all adults in a country or all invoices issued in one year.
Where you use it
Defined before sampling: researchers describe the 'target population' and then draw a sample from it. A value that describes the population (such as μ) is called a parameter; one calculated from a sample is a statistic.
Examples
The target population was all registered nurses working in public hospitals in Izmir.
We can't survey the entire population, so we'll take a random sample of 1,200 households.
Usage note
In statistics a population does not have to be people: all the light bulbs a factory produced or all transactions in a year can also be a population.
Common phrases
target population · population mean · study population · general population · generalise to the population
A smaller group selected from a population and actually studied, so that conclusions about the whole population can be drawn from it.
Where you use it
Used both as a noun (a sample of 400 students) and as a verb (we sampled 400 students). Methods sections describe how the sample was drawn and how representative it is; common adjectives are random, representative, small, large and biased.
Examples
The sample consisted of 412 undergraduate students from three universities.
Our sample is too small to compare regions separately.
Common phrases
draw a sample · representative sample · a sample of 500 people · the sample consisted of
The number of observations or participants included in a study, usually written as n (or N for the total).
Where you use it
Discussed at the planning stage (how many people do we need?) and in limitations sections (the small sample size limits generalisability). A power analysis is the usual way to decide the sample size before collecting data.
Examples
With two groups of 64, a total sample size of 128 gives us 80% power to detect a medium effect.
The main limitation of the study is its small sample size (n = 24).
Common phrases
determine the sample size · small sample size · increase the sample size · required sample size
A sample chosen so that every member of the population has a known, usually equal, chance of being selected, which helps avoid systematic bias.
Where you use it
The ideal behind most inferential statistics. A 'simple random sample' gives everyone exactly the same chance; in practice researchers often use stratified or cluster designs instead. Do not call a group of people who were simply easy to reach a random sample.
Examples
We drew a simple random sample of 300 patients from the hospital register.
Because this was not a random sample, the results may not apply to all teachers.
Usage note
In statistics 'random' means chosen by a chance process, not 'careless' or 'unplanned' as in casual speech.
Common phrases
simple random sample · draw a random sample · select at random · truly random sample
The natural difference between a value calculated from a sample and the true population value, which arises simply because only part of the population was studied.
Where you use it
It is random, not a mistake, and it gets smaller as the sample size increases; the standard error and margin of error quantify it. Errors from poor questions, bad sampling frames or nonresponse are called non-sampling errors and do not shrink with a bigger sample.
Examples
A two-point difference between the polls is well within sampling error.
A bigger sample reduces sampling error, but it cannot fix a badly worded question.
Common phrases
within sampling error · reduce sampling error · non-sampling error · random sampling error
A systematic error that pushes results in one direction, so that estimates are consistently too high or too low rather than just randomly off.
Where you use it
Many types have names: selection bias, response bias, nonresponse bias, recall bias. Researchers introduce, reduce, avoid or correct for bias. An estimator is 'unbiased' if it is right on average across repeated samples.
Examples
Recruiting volunteers through a fitness app introduced selection bias.
Self-reported weight tends to be biased downwards.
A sampling method in which the population is first divided into subgroups (strata), such as regions or age groups, and a random sample is then taken from each one.
Where you use it
Used when every important subgroup must be properly represented. Sampling can be proportional to each stratum's size, or small groups can be oversampled, which then requires weighting. Singular 'stratum', plural 'strata'.
Examples
We used stratified sampling by region so that all seven regions of Türkiye were represented.
Stratified sampling gave us more precise estimates than a simple random sample of the same size.
Common phrases
stratified random sampling · stratify by region · proportional stratified sampling · within each stratum
The actual list or source from which a sample is drawn, such as a student register, a customer database or a list of addresses.
Where you use it
Ideally it matches the target population exactly; in practice it rarely does, and the gap (coverage error) can cause bias. Methods sections should name the sampling frame and say how up to date it was.
Examples
Our sampling frame was the company's customer database, so people who only pay in cash were missed.
An outdated sampling frame can leave out whole groups of the population.
Common phrases
construct a sampling frame · incomplete sampling frame · coverage error · draw from the sampling frame
A sample made up of people who are easy to reach, such as students in the researcher's own class or visitors to a website, rather than people chosen at random.
Where you use it
Common in student projects and early-stage work because it is cheap and fast, but the results cannot safely be generalised to a wider population. Limitations sections usually say so openly: 'the study used a convenience sample of…'. Related non-random methods are snowball and quota sampling.
Examples
Because we used a convenience sample of university students, the findings may not apply to older adults.
A convenience sample is fine for testing the questionnaire, but not for estimating national figures.
A range of values, calculated from sample data, that is likely to contain the true population value; a 95% interval comes from a method that captures the true value in 95% of repeated samples.
Where you use it
Abbreviated CI and often reported in square brackets: 'mean difference 4.2, 95% CI [1.8, 6.6]'. Many journals now expect confidence intervals alongside or instead of p-values. A narrow interval means a precise estimate; a wide one signals uncertainty.
Examples
The 95% confidence interval for the mean saving runs from €31 to €53.
The confidence interval is wide because we only had 40 participants.
Usage note
It is a common mistake to say there is a 95% probability that the true value lies inside one particular calculated interval; the 95% describes the method, not a single interval.
Common phrases
95% confidence interval · narrow confidence interval · calculate a confidence interval · the interval includes zero
Methods that use data from a sample to draw conclusions, with a measured level of uncertainty, about a larger population.
Where you use it
Covers hypothesis tests, confidence intervals and most statistical models. Courses and textbooks are often split into a descriptive part and an inferential part. The verb is 'infer' and the noun 'inference': 'we can infer from the sample that…'.
Examples
Inferential statistics only make sense if the sample was drawn properly.
The second half of the course moves from descriptive to inferential statistics.
Common phrases
use inferential statistics · statistical inference · draw an inference · inferential test
The standard deviation of an estimate, such as a sample mean, across repeated samples; it shows how precise the estimate is likely to be.
Where you use it
Abbreviated SE (SEM for the standard error of the mean). It shrinks as the sample size grows: for a mean it equals the standard deviation divided by √n. Standard errors appear next to every coefficient in regression output and are used to build confidence intervals.
Examples
The error bars in Figure 2 show the standard error of the mean.
The coefficient is 0.8 with a standard error of 0.3.
Usage note
Always say which one your error bars show: a chart with standard errors looks much more precise than the same chart with standard deviations.
Common phrases
standard error of the mean · robust standard errors · small standard error · coefficient and standard error
To calculate an approximate value for an unknown population quantity, such as a mean, a proportion or a regression coefficient, from sample data.
Where you use it
Researchers estimate a parameter, a model or an effect; the result is 'an estimate' and the formula used is an 'estimator'. The verb ends in /eɪt/, the noun in /ət/. Common adjectives with the noun: rough, precise, unbiased, conservative.
Examples
We estimated average household spending from a sample of 800 receipts.
The model estimates that each extra year of schooling raises earnings by about 8%.
Usage note
'Estimate' (calculate from data) is not the same as 'predict' (a future or unseen value) or 'guess' (without data), although Turkish may use 'tahmin' for all three.
Common phrases
estimate a parameter · estimate the effect · rough estimate · unbiased estimate · estimated coefficient
A single number calculated from sample data as the best guess of a population value, for example a sample mean of 4.7 used to estimate the true mean.
Where you use it
Usually reported together with an interval estimate, a confidence interval, because a single number hides the uncertainty. Typical phrases: 'the point estimate was …', 'point estimate and 95% CI'.
Examples
The point estimate for the vaccination rate was 71%, with a 95% CI of 68% to 74%.
Don't report the point estimate on its own; readers need to see the uncertainty.
Common phrases
point estimate and confidence interval · interval estimate · report the point estimate · best point estimate
The amount added to and subtracted from an estimate to form a confidence interval, showing how far the sample result may differ from the true population value.
Where you use it
Common in opinion polls and survey reports: '48% support the plan, with a margin of error of ±3 percentage points'. It usually refers to a 95% confidence level and covers only sampling error, not problems such as biased questions.
Examples
With 1,000 respondents, the margin of error is about ±3 percentage points.
The difference between the two brands is within the margin of error, so we can't say which is more popular.
Usage note
When the margin applies to a percentage, write 'percentage points', not 'percent': a change from 48% to 51% is a rise of 3 percentage points.
Common phrases
within the margin of error · a margin of error of ±3 points · reduce the margin of error · large margin of error
The distribution of a statistic, such as the sample mean, that you would get if you took many samples of the same size from the same population.
Where you use it
A theoretical idea at the heart of inference: standard errors, confidence intervals and p-values are all based on it. Students often confuse it with the distribution of the data in a single sample; teachers use simulations to show the difference.
Examples
The standard error is the standard deviation of the sampling distribution of the mean.
Let's simulate 10,000 samples and plot the sampling distribution.
Common phrases
sampling distribution of the mean · approximate sampling distribution · simulate the sampling distribution · shape of the sampling distribution
A clear, testable statement about a relationship or difference that a study sets out to check with data, for example 'sleep loss slows reaction time'.
Where you use it
Researchers state, formulate, test, support or reject hypotheses. In academic writing, data 'support' a hypothesis; they rarely 'prove' it. Hypotheses are often numbered (H1, H2) in theses and articles.
Examples
Our first hypothesis was that remote workers would report higher job satisfaction.
The results support Hypothesis 2 but not Hypothesis 3.
Usage note
The plural is 'hypotheses' (/haɪˈpɑːθəsiːz/), not 'hypothesises'. The verb is 'hypothesise' (UK) or 'hypothesize' (US).
Common phrases
test a hypothesis · formulate a hypothesis · support the hypothesis · research hypothesis
The default claim in a statistical test that there is no effect, no difference or no relationship; the test checks whether the data give enough evidence against it.
Where you use it
Written H₀ and read 'H-nought' or 'H-zero'. Results are phrased as 'reject' or 'fail to reject' the null hypothesis; saying the null is 'accepted' or 'proved' is considered incorrect. Often shortened to 'the null' in speech.
Examples
The null hypothesis states that the two teaching methods produce the same mean score.
With p = .31, we fail to reject the null hypothesis.
Common phrases
test the null hypothesis · reject the null hypothesis · fail to reject the null · under the null hypothesis
The probability of getting a result at least as extreme as the one observed if the null hypothesis were true; a small value means the data would be surprising under the null.
Where you use it
Compared with the significance level, usually 0.05. In APA style it is written as an italic p with no leading zero (p = .032, p < .001). Statisticians warn that a p-value is not the probability that the null hypothesis is true and says nothing about the size of an effect.
Examples
The p-value for the interaction term is 0.004, well below our 0.05 threshold.
A large p-value does not prove that there is no effect.
Usage note
p < .05 is read 'p is less than point oh five'. 'P-hacking' means trying many analyses until a p-value falls below .05, which is seen as a serious research problem.
Common phrases
report the p-value · small p-value · exact p-value · adjusted p-value · p-value threshold
The conclusion that a result is unlikely to be due to chance alone, judged by comparing the p-value with a chosen significance level such as 0.05.
Where you use it
Mostly used in its adjective form: 'a statistically significant difference', 'not statistically significant'. Good reports pair it with an effect size, because in a very large sample even a tiny, unimportant effect can be statistically significant.
Examples
The difference in recovery time did not reach statistical significance.
Women scored statistically significantly higher than men, t(198) = 2.45, p = .015.
Usage note
'Significant' here does not mean 'important' or 'large'. Turkish 'anlamlı fark' is 'significant difference' in English; 'important difference' would mislead the reader.
Common phrases
reach statistical significance · statistically significant difference · level of statistical significance · test for statistical significance
The statement that there is a real effect, difference or relationship; it is the claim a researcher usually expects, and the data support it when they give strong evidence against the null hypothesis.
Where you use it
Written H₁ or Hₐ. It can be two-sided ('the means differ') or one-sided ('the new drug lowers blood pressure more than the old one'). The direction must be decided before looking at the data.
Examples
The alternative hypothesis is that customers in the new store layout spend more per visit.
We used a two-sided alternative hypothesis because the effect could go either way.
Common phrases
two-sided alternative hypothesis · one-sided alternative · state the alternative hypothesis · null and alternative hypotheses
The threshold, chosen before a test, below which a p-value is treated as statistically significant; it is also the accepted risk of a Type I error.
Where you use it
Written α (alpha) and most often set at 0.05, sometimes at 0.01 or 0.10. Typical phrases are 'at the 5% significance level' and 'significant at α = .05'. Lowering alpha reduces false positives but also reduces power.
Examples
All tests used a significance level of 0.05.
The effect is significant at the 5% level but not at the 1% level.
Common phrases
set the significance level · at the 5% significance level · alpha level · a significance level of 0.01
To conclude, after a test, that the data give enough evidence against the null hypothesis, usually because the p-value is below the significance level.
Where you use it
The standard way to state a test decision. Its opposite is 'fail to reject the null hypothesis' (or 'retain' it), never 'accept' or 'prove' it, because absence of evidence is not evidence of absence. Exam answers are expected to use exactly these words.
Examples
Since p = .002, we reject the null hypothesis of equal means.
At α = 0.05 we cannot reject the null hypothesis, so the data show no clear difference between the two suppliers.
Usage note
Turkish textbooks often write 'H0 kabul edilir', but in English write 'we fail to reject H₀', not 'we accept H₀'.
Common phrases
fail to reject the null hypothesis · reject H₀ at the 5% level · the decision to reject · grounds to reject
A hypothesis test that compares means: one group's mean with a fixed value, the means of two independent groups, or two measurements of the same people.
Where you use it
The three main types are the one-sample, independent-samples and paired-samples t-test. Results are reported as t(df) = value, p = …, for example 't(58) = 2.14, p = .037'. Welch's version is used when the two groups have unequal variances.
Examples
An independent-samples t-test showed that the treatment group improved more than the control group, t(58) = 2.14, p = .037.
Use a paired t-test, because the same patients were measured before and after treatment.
Common phrases
run a t-test · independent-samples t-test · paired t-test · one-sample t-test · Welch's t-test
A test used with counts in categories, most often to check whether two categorical variables are related or whether observed frequencies match the expected ones.
Where you use it
Written χ² and reported as 'χ²(2, N = 300) = 8.41, p = .015'. The two common versions are the test of independence (on a cross-tabulation) and the goodness-of-fit test. Expected counts should not be too small; otherwise Fisher's exact test is often used.
Examples
A chi-square test showed that smoking status was associated with gender, χ²(1, N = 420) = 6.12, p = .013.
Several cells have expected counts below 5, so the chi-square test may not be reliable.
Usage note
'Chi' is pronounced /kaɪ/, rhyming with 'sky', not 'chee'. The spelling 'chi-squared' is also common.
Common phrases
chi-square test of independence · chi-square goodness-of-fit test · Pearson's chi-square · chi-square statistic
Short for analysis of variance: a family of tests that compare the means of three or more groups at once by comparing variation between the groups with variation within them.
Where you use it
Said as one word, 'a-NO-va'. Types include one-way, two-way and repeated-measures ANOVA. Results are reported with an F statistic, e.g. 'F(2, 87) = 5.36, p = .006'. A significant ANOVA only says that at least one mean differs; post hoc tests show which.
Examples
A one-way ANOVA showed a significant effect of teaching method on scores, F(2, 87) = 5.36, p = .006.
Why not run three t-tests instead of an ANOVA? Because that inflates the Type I error rate.
Common phrases
one-way ANOVA · two-way ANOVA · repeated-measures ANOVA · run an ANOVA · ANOVA table
Rejecting a null hypothesis that is actually true, in other words concluding that an effect exists when it does not; a false positive.
Where you use it
Its probability is set by the significance level α, so with α = .05 you accept a 5% risk of a Type I error in each test. Running many tests without correction inflates the overall Type I error rate. Usually written with a capital T and a Roman numeral: Type I.
Examples
A Type I error here would mean approving a drug that doesn't actually work.
The Bonferroni correction keeps the overall Type I error rate at or below 5%.
Common phrases
Type I error rate · commit a Type I error · risk of a Type I error · control the Type I error rate
Failing to reject a null hypothesis that is actually false, in other words missing an effect that really exists; a false negative.
Where you use it
Its probability is written β (beta), and statistical power equals 1 − β. Small samples make Type II errors more likely, which is why a non-significant result from a small study is weak evidence that there is no effect.
Examples
With only 20 participants per group, the risk of a Type II error is high.
A screening test that misses real cases is making a Type II error.
Usage note
An easy way to remember the difference: a Type I error is a false alarm, a Type II error is a missed signal.
Common phrases
Type II error rate · commit a Type II error · probability of a Type II error · false negative
The probability that a test will detect an effect when a real effect of a given size exists; it equals one minus the probability of a Type II error.
Where you use it
Researchers usually aim for 80% or 90% power. Power increases with a larger sample, a larger effect and a less strict significance level. A power analysis, done before the study with tools such as G*Power, shows how many participants are needed.
Examples
The study had 80% statistical power to detect a 5-point difference.
Most of these early studies lacked statistical power, so their null results tell us little.
Common phrases
power analysis · adequate statistical power · underpowered study · increase power · 80% power
The number of values in a calculation that are free to vary once certain constraints are fixed; it sets the exact shape of distributions such as t, chi-square and F.
Where you use it
Abbreviated df and reported in brackets after the test statistic: t(28), χ²(3), F(2, 45). For a one-sample t-test it is n − 1. Students rarely calculate it by hand today, but they must read it from software output and report it.
Examples
With 30 participants, the one-sample t-test has 29 degrees of freedom.
Don't forget to report the degrees of freedom in brackets after t.
Common phrases
report the degrees of freedom · with 29 degrees of freedom · residual degrees of freedom · lose a degree of freedom
A hypothesis test that looks for a difference in either direction, so the rejection region is split between both ends (tails) of the distribution.
Where you use it
The default in most research, also called a two-sided test. A one-tailed (one-sided) test checks only one direction and must be justified before seeing the data; switching to a one-tailed test afterwards to get p < .05 is poor practice.
Examples
All p-values are from two-tailed tests.
We chose a two-tailed test because the new process could make delivery times either shorter or longer.
Common phrases
two-tailed p-value · one-tailed test · two-sided test · two-tailed at α = .05
A condition that must hold, at least approximately, for a statistical test or model to give valid results, such as normality, equal variances or independent observations.
Where you use it
Researchers check, test, meet or violate assumptions: 'the normality assumption was violated'. Methods sections should explain how assumptions were checked and what was done when they did not hold, for example using a nonparametric test or a transformation.
Examples
The assumption of equal variances was checked with Levene's test.
If the normality assumption is badly violated, switch to the Mann–Whitney U test.
Common phrases
check the assumptions · violate an assumption · meet the assumptions · normality assumption · assumption of independence
A test that does not assume the data follow a specific distribution such as the normal, often working with ranks instead of the raw values.
Where you use it
Used for small samples, ordinal data or clearly non-normal data. Common examples are the Mann–Whitney U test (instead of an independent t-test), the Wilcoxon signed-rank test (instead of a paired t-test) and the Kruskal–Wallis test (instead of a one-way ANOVA). Also spelled 'non-parametric'.
Examples
Since reaction times were heavily skewed, we used a nonparametric test.
The Kruskal–Wallis test is the nonparametric alternative to a one-way ANOVA.
Common phrases
nonparametric alternative · Mann–Whitney U test · rank-based test · nonparametric methods
A follow-up test run after a significant overall result, such as an ANOVA, to find out exactly which groups differ from each other.
Where you use it
Common examples are Tukey's HSD, Bonferroni and Scheffé tests, which adjust for the many comparisons being made. 'Post hoc' is Latin for 'after this'. The phrase is also used for analyses that were not planned in advance, which should be reported as exploratory.
Examples
Tukey post hoc tests showed that Group C differed from both A and B.
The ANOVA was significant, so we ran a post hoc test to locate the differences.
Common phrases
post hoc comparisons · Tukey's HSD · Bonferroni correction · run post hoc tests
A relationship between two variables in which they tend to change together, either in the same direction (positive) or in opposite directions (negative).
Where you use it
You find, observe or report a correlation 'between' two variables, and it can be strong, moderate, weak, positive or negative. It is measured with a coefficient such as Pearson's r. The sentence 'correlation does not imply causation' is repeated in every statistics course.
Examples
There was a moderate positive correlation between study time and exam scores (r = .42).
The correlation between ice cream sales and drownings is explained by hot weather, which drives both.
Common phrases
strong correlation · positive correlation · correlation between X and Y · find a correlation · correlation matrix
A family of methods for modelling how an outcome variable changes with one or more predictor variables, used both to explain relationships and to make predictions.
Where you use it
You run, fit or estimate a regression, and you 'regress' the outcome 'on' the predictors. Types include linear, multiple and logistic regression. Results are discussed through coefficients, standard errors, p-values and R-squared.
Examples
We ran a regression of monthly sales on advertising spend and price.
In the regression, income remained a significant predictor after controlling for education.
Usage note
'Regression to the mean' is a different idea: an extreme measurement tends to be followed by one closer to the average.
Common phrases
run a regression · regression model · regression analysis · regress Y on X · regression output
A number between −1 and +1 that measures the strength and direction of the linear relationship between two variables; 0 means there is no linear relationship.
Where you use it
The most common is Pearson's r; Spearman's rho (ρ) is used for ranked or non-normal data. Reported as 'r = .42, p < .001' or 'r(98) = .42'. Rough guidelines call values around .1 small, .3 medium and .5 large, but context matters.
Examples
The correlation coefficient between sleep hours and mood was r = .38.
A correlation coefficient close to zero doesn't rule out a strong curved relationship.
Common phrases
Pearson correlation coefficient · Spearman's rank correlation coefficient · calculate the correlation coefficient · a coefficient of .60
A regression method that models the outcome as a straight-line function of one or more predictors, estimating an intercept and one slope per predictor.
Where you use it
Simple linear regression has one predictor; multiple linear regression has several. It is usually estimated by ordinary least squares (OLS). Its main assumptions are linearity, independent errors, constant variance of the residuals and roughly normal residuals.
Examples
A simple linear regression was used to predict salary from years of experience.
Check the residual plots before you trust a linear regression.
Common phrases
simple linear regression · fit a linear regression · linear regression model · ordinary least squares
The share of the variation in the outcome variable that a regression model explains, ranging from 0 to 1; also called the coefficient of determination.
Where you use it
Written R² and often reported as a percentage: 'the model explains 34% of the variance'. It always rises when predictors are added, so adjusted R-squared is used to compare models with different numbers of predictors. A high R-squared does not prove that a model is correct.
Examples
The model had an R-squared of 0.34, so most of the variation in sales remains unexplained.
Adjusted R-squared went down when we added the extra variables.
Common phrases
adjusted R-squared · high R-squared · an R-squared of 0.6 · increase in R-squared
The difference between an observed value and the value a model predicts for that observation; it shows how far the model misses each data point.
Where you use it
Residuals are plotted and inspected to check regression assumptions: they should look like random noise with a constant spread. Patterns, funnels or curves in a residual plot suggest that the model is missing something. Also used as an adjective: residual variance, residual plot.
Examples
The residuals fan out as income increases, which suggests heteroscedasticity.
Plot the residuals against the fitted values before you interpret the coefficients.
Common phrases
residual plot · plot the residuals · standardised residuals · residual variance · large residual
A method of fitting a line or model by choosing the parameter values that make the sum of the squared residuals as small as possible.
Where you use it
The standard way to estimate a linear regression, usually called ordinary least squares (OLS). Economists often say 'an OLS regression' or 'we estimated the model by OLS'. Variants include weighted and generalised least squares.
Examples
The coefficients were estimated by ordinary least squares.
Least squares is very sensitive to outliers, so we also tried a robust method.
Common phrases
ordinary least squares · least squares estimate · least squares line · weighted least squares · estimate by OLS
A relationship in which a change in one variable directly produces a change in another, as opposed to the two simply moving together.
Where you use it
Most often heard in the phrase 'correlation does not imply causation'. Establishing causation normally needs a randomised experiment or careful causal-inference methods. Related words: cause, causal effect, causal relationship, causality.
Examples
This is an observational study, so we can't claim causation.
The headline confused correlation with causation.
Usage note
Watch the spelling: 'causal' (about cause) is often mistyped as 'casual' (relaxed, informal).
A regression model with two or more predictor variables, used to estimate the effect of each one while holding the others constant.
Where you use it
One of the most used methods in social, health and business research. Each coefficient is interpreted 'holding the other variables constant' or 'controlling for' them. Problems to watch for include multicollinearity and too many predictors for the sample size (overfitting).
Examples
A multiple regression with age, income and education explained 41% of the variance in life satisfaction.
In the multiple regression, the effect of advertising shrank once price was included.
Common phrases
multiple linear regression · hierarchical multiple regression · run a multiple regression · predictors in the model
A regression method for an outcome with two categories, such as yes/no or pass/fail, that models the probability of one of the outcomes from the predictors.
Where you use it
Results are usually reported as odds ratios (OR) with confidence intervals: 'OR = 1.8, 95% CI [1.2, 2.7]'. Widely used in medicine, the social sciences and credit scoring. Extensions handle outcomes with more than two categories (multinomial or ordinal logistic regression).
Examples
Logistic regression showed that smokers had higher odds of developing the condition (OR = 2.3).
We used logistic regression to predict whether a customer would cancel their subscription.
Common phrases
binary logistic regression · odds ratio · fit a logistic regression · multinomial logistic regression
A number in a regression model showing how much the outcome is expected to change when a predictor increases by one unit, with the other predictors held constant.
Where you use it
Written b or B for unstandardised and β (beta) for standardised coefficients, and reported with its standard error, confidence interval and p-value. The sign shows the direction: a negative coefficient means the outcome tends to fall as the predictor rises.
Examples
With pay measured in thousands of lira, a regression coefficient of 1.2 for experience means each extra year goes with about 1,200 lira more per month.
Standardised regression coefficients let you compare predictors measured on different scales.
Common phrases
standardised regression coefficient · estimated coefficient · the coefficient for age · negative coefficient · interpret the coefficients
A situation in regression where two or more predictors are strongly correlated with each other, which makes their separate effects hard to estimate.
Where you use it
It inflates standard errors and can make coefficients unstable or even flip their sign, while the model's overall predictions may still be fine. Usually checked with the variance inflation factor (VIF); values above about 5 or 10 are often treated as a warning sign.
Examples
Height and weight are so closely related that including both caused multicollinearity.
Check for multicollinearity before you interpret individual coefficients.
Common phrases
check for multicollinearity · variance inflation factor · severe multicollinearity · high VIF values
To remove or account for the influence of a variable in an analysis, usually by including it in a model, so that the effect of interest is not mixed up with it.
Where you use it
Extremely common in results sections: 'after controlling for age and income…', 'controlling for baseline scores…'. 'Adjust for' is a close synonym, especially in medicine. Controlling for measured variables does not remove confounders that were never measured.
Examples
After controlling for age and income, the effect of education was much smaller.
Did you control for the time of day when comparing the two machines?
Usage note
Do not confuse 'control for a variable' (an analysis step) with 'control group' (a design feature) or with everyday 'control' (manage, check).
Common phrases
control for age · after controlling for · adjust for confounders · statistically control for
How well a model or a theoretical distribution matches the observed data, measured with statistics such as R-squared, chi-square or information criteria.
Where you use it
Often hyphenated before a noun: 'goodness-of-fit test', 'goodness-of-fit statistics'. In structural equation modelling, researchers report fit indices such as CFI and RMSEA. A good fit does not by itself mean that the model is the right explanation.
Examples
A chi-square goodness-of-fit test suggested that the dice were not fair.
Compare the goodness of fit of the two models using AIC.
Common phrases
goodness-of-fit test · model fit · fit indices · assess goodness of fit · poor fit
A method of collecting information by asking a set of questions to a group of people, usually a sample, in person, by phone, on paper or online.
Where you use it
You design, conduct or carry out a survey; people take part in, complete or respond to it. 'Survey' is the whole study or method, while 'questionnaire' is the actual list of questions. It is also a verb: 'we surveyed 2,000 adults'.
Examples
The survey was conducted online between March and May 2024.
We surveyed 1,500 small business owners about their use of digital payments.
Usage note
As a noun the stress is on the first syllable (SUR-vey); as a verb it is often on the second (sur-VEY).
Common phrases
conduct a survey · online survey · survey respondents · survey data · take part in a survey
The printed or online form containing the set of questions that respondents answer in a survey.
Where you use it
You design, develop, pilot, translate or administer a questionnaire, and respondents complete it or fill it in (UK) / fill it out (US). Methods sections describe the items, the response scales and the reliability, often with Cronbach's alpha.
Examples
The questionnaire contained 24 items and took about ten minutes to complete.
We translated the questionnaire into Turkish and back into English to check accuracy.
Usage note
Watch the spelling, with a double n. The word starts like 'question': /ˌkwestʃəˈner/.
Common phrases
design a questionnaire · administer a questionnaire · self-report questionnaire · complete a questionnaire · questionnaire items
The share of people invited to take part in a survey who actually complete it, usually given as a percentage.
Where you use it
Always reported in survey research, because a low response rate raises concerns about nonresponse bias. Researchers try to increase it with reminders, short questionnaires and incentives. Online surveys often have much lower response rates than face-to-face ones.
Examples
Of the 2,000 employees invited, 640 responded, giving a response rate of 32%.
Two email reminders raised the response rate from 18% to 27%.
Common phrases
low response rate · improve the response rate · overall response rate · a response rate of 40%
A rating scale on which respondents show how much they agree or disagree with statements, typically with five or seven ordered options from 'strongly disagree' to 'strongly agree'.
Where you use it
Named after the psychologist Rensis Likert. Strictly, one question is a 'Likert item' and the summed set of items is the 'Likert scale'. There is long-running debate about whether such ordinal data can be analysed with means and t-tests.
Examples
Job satisfaction was measured on a five-point Likert scale.
Should we use a five- or a seven-point Likert scale for the customer survey?
Usage note
The name is traditionally pronounced 'LICK-ert' (/ˈlɪkərt/), although 'LIKE-ert' is also widely heard.
Common phrases
five-point Likert scale · Likert-type item · Likert scale responses · rate on a Likert scale
The group in an experiment that does not receive the treatment being tested, or receives a placebo or the usual treatment, so that it can be compared with the treatment group.
Where you use it
The comparison group in experiments and trials; its counterpart is the treatment, intervention or experimental group. Without a control group it is hard to tell whether a change comes from the treatment or from time, practice or expectations.
Examples
Students in the control group followed the standard curriculum.
Without a control group, we can't say whether the training itself improved sales.
Common phrases
treatment and control groups · assign to the control group · compared with the control group · waiting-list control group
Placing participants into the groups of an experiment by chance, for example with computer-generated random numbers, so that the groups are similar at the start.
Where you use it
Also called randomisation (UK) or randomization (US). It balances known and unknown confounders on average, which is why randomised controlled trials (RCTs) are the strongest design for showing causation. Do not confuse it with random sampling, which decides who enters the study.
Examples
Random assignment made the two groups similar in age and baseline scores.
Classes, not individual students, were the unit of random assignment.
Common phrases
random assignment to groups · randomised controlled trial · block randomisation · randomly assign participants
A small trial run of a study, carried out before the main study, to test the questionnaire, the procedures and the timing and to find problems early.
Where you use it
Researchers pilot, or pilot-test, a questionnaire with a small group similar to the target population. The results are used to reword confusing questions, check completion time and sometimes plan the sample size. Also a verb: 'we piloted the survey with 20 teachers'.
Examples
The pilot study showed that two of the questions were being misunderstood.
We ran a pilot study with 25 nurses before the main data collection.
Common phrases
conduct a pilot study · pilot-test the questionnaire · pilot phase · results of the pilot
Bias that arises when the people who do not take part in a survey differ in important ways from those who do, so the results misrepresent the population.
Where you use it
Also spelled 'non-response bias'. A worry when response rates are low, but a high response rate does not guarantee its absence. Researchers compare respondents with known population figures, follow up non-respondents or apply weights to reduce it.
Examples
Busy managers were less likely to reply, so nonresponse bias may have lowered our estimate of working hours.
To check for nonresponse bias, we compared early and late respondents.
Common phrases
risk of nonresponse bias · assess nonresponse bias · adjust for nonresponse · non-respondents
A graph that shows the relationship between two numeric variables by placing one dot for each observation according to its two values.
Where you use it
The first chart to draw before computing a correlation or fitting a regression, because it reveals curves, clusters and outliers. Also written 'scatterplot' and called a scatter graph or scatter diagram. A fitted line or trend line is often added.
Examples
The scatter plot shows a clear positive relationship between temperature and electricity use.
Add the regression line to the scatter plot so readers can see the trend.
Common phrases
draw a scatter plot · scatter plot matrix · add a trend line · points on the scatter plot
A chart of touching bars showing how many observations of a numeric variable fall into each interval, called a bin.
Where you use it
Used to check the shape of a distribution: symmetry, skewness, peaks and gaps. The chosen bin width can change the picture a lot. Unlike a bar chart, the x-axis is a numeric scale, so there are no gaps between the bars.
Examples
The histogram of delivery times has a long tail to the right.
Try a narrower bin width; this histogram hides too much detail.
Common phrases
plot a histogram · bin width · histogram of residuals · frequency histogram
A number that shows how large a difference or relationship is, independently of sample size, such as Cohen's d, a correlation coefficient or an odds ratio.
Where you use it
Journals that follow APA style expect effect sizes next to p-values, because a p-value only says whether an effect is likely to exist. Cohen's rough benchmarks for d are 0.2 (small), 0.5 (medium) and 0.8 (large). Effect sizes are also needed for power analysis and meta-analysis.
Examples
The effect size was small (d = 0.21), even though the result was statistically significant.
Please add effect sizes and confidence intervals to Table 3.
Common phrases
report the effect size · small effect size · Cohen's d · standardised effect size · effect size estimate
A chart that shows the median, the quartiles and the spread of the data as a box with lines (whiskers) extending from it, with outliers marked as separate points.
Where you use it
Also written 'boxplot' and called a box-and-whisker plot. Very useful for comparing distributions across groups side by side. In the common Tukey version, the whiskers reach the most extreme values within 1.5 × IQR of the box.
Examples
The box plot shows that salaries in the sales team are much more spread out.
Put the three box plots side by side so we can compare the regions.
A chart that compares categories using separate rectangular bars whose lengths show counts, percentages or other values.
Where you use it
Used for categorical data, with gaps between the bars. Bars can be vertical or horizontal, and grouped or stacked. A common rule for honest reporting is that the value axis should start at zero; otherwise differences look larger than they are.
Examples
The bar chart compares the share of respondents in each age group.
Use a bar chart, not a pie chart; it's easier to compare eight categories that way.
Usage note
A bar chart shows categories with gaps between the bars; a histogram shows a numeric variable with touching bars. In American English 'bar graph' is also common.
Common phrases
stacked bar chart · grouped bar chart · horizontal bar chart · error bars
A small set of numbers that describe a data set at a glance, typically the number of observations, the mean, standard deviation, median, minimum and maximum.
Where you use it
Very close in meaning to descriptive statistics, but used more for the actual numbers in a table or in software output, such as R's summary() or Stata's summarize command. Economists and data teams often say 'summary stats'.
Examples
Table 2 reports summary statistics for all variables used in the analysis.
Can you send me the summary statistics before we meet? Just n, mean and SD by group.
Common phrases
table of summary statistics · summary stats · compute summary statistics · summary statistics by group
To repeat a study, usually with new data, to see whether the original results are found again.
Where you use it
Findings 'replicate' or 'fail to replicate', and researchers replicate a study or a finding. The noun is 'replication', as in 'replication study' and the 'replication crisis' in psychology and medicine. 'Reproduce' is often used for re-running the same analysis on the same data.
Examples
The effect did not replicate in a larger sample.
We share our code and data so that others can replicate the analysis.
Common phrases
replicate a finding · fail to replicate · replication study · independent replication
To change a number to a simpler nearby value with fewer digits; for example, 3.4762 rounded to two decimal places is 3.48.
Where you use it
Common phrases: 'round to two decimal places', 'round up', 'round down', 'rounded to the nearest whole number'. Reporting guides usually ask for two decimals for most statistics and two or three for p-values. A table note such as 'percentages may not sum to 100 due to rounding' is standard.
Examples
All values are rounded to two decimal places.
Percentages may not add up to 100 because of rounding.
Usage note
English uses a decimal point (3.48) and a comma for thousands (1,250); Turkish does the opposite (3,48 and 1.250). Mixing them up is a common error in English reports written by Turkish speakers.
Common phrases
round to two decimal places · round up · round down · rounding error · rounded figures
Ten questions from this glossary. Pick the right meaning for each term and see your score.
How to learn statistics vocabulary
Read real texts from the field regularly: the methods and results sections of journal articles in your area, the help pages of your statistics software and the methodology notes published with official statistics.
Learn terms in pairs that are easy to confuse: sample and population, standard deviation and standard error, Type I and Type II error, correlation and causation.
Practise reading results aloud: 't(58) = 2.14, p = .037' is said 't with fifty-eight degrees of freedom equals two point one four, p equals point oh three seven'.
Watch everyday words with a technical meaning: in statistics 'significant' is not 'important', 'mean' is not 'meaning', 'normal' is not 'usual' and 'random' is not 'careless'.
After each analysis, write one plain English sentence that interprets the result, the way you would in the results section of a paper.
Frequently asked questions
How can I learn English vocabulary for statistics?
Read real texts from the field and notice the words around the numbers: results sections of journal articles, statistics textbooks, software output and methodology notes. Learn each term with the verbs it goes with (calculate the mean, test a hypothesis, fit a model, reject the null hypothesis) and use the new terms when you write up your own analyses, even in short notes.
What does 'significant' mean in statistics?
In statistics, 'significant' is short for 'statistically significant': the result is unlikely to be explained by chance alone at the chosen significance level, often p < .05. It does not mean that the effect is important, large or useful, which is why good reports also give an effect size and a confidence interval. When translating 'anlamlı fark', write 'significant difference', not 'meaningful difference' or 'important difference'.
How do I report statistical results in English?
Most fields follow APA style or a similar guide: give the test statistic with its degrees of freedom, the exact p-value and an effect size, for example 't(58) = 2.14, p = .037, d = 0.56'. Statistical symbols are written in italics, APA style drops the leading zero in p-values, and most numbers are rounded to two decimal places. Then add a plain sentence explaining what the result means for your research question.
What is the difference between 'statistics' and 'a statistic'?
'Statistics' as the name of the field is uncountable and takes a singular verb: 'Statistics is a required course.' Used as a plural, 'statistics' means numerical facts: 'These statistics show a rise in exports.' 'A statistic' is a single value calculated from a sample, such as a mean or a test statistic; the matching value for the whole population is called a parameter.
Should I learn the Turkish or the English statistics terms?
Both. Turkish university courses, theses and journals use well-established Turkish terms such as örneklem, anakütle (or evren), standart sapma, güven aralığı and anlamlılık düzeyi. Statistical software, international journals and most online resources are in English, and some words such as ANOVA and post hoc are used as they are. Knowing both lets you read SPSS or R output in English and still explain it clearly in a Turkish thesis or class.
