Congratulations on making it to the end of the module! We hope you found it a useful introduction to the world of statistics. If you would like to learn more, particularly about other statistical tests, you may find one or more of the following resources helpful:
The following glossary explains statistical terms used throughout this module. For more information about a term, click on the relevant link.
A C D E H I L M N O P Q R S T V
Alternative hypothesis
Also known as the research hypothesis and denoted by \(\textrm{H}_\textrm{A}\), the alternative hypothesis states the opposite of the null hypothesis. It states that there is a difference or relationship between variables in a population.
See Hypothesis testing, Null hypothesis, Variable.
Categorical data
Data that is grouped into categories, such as data for a ‘gender’ or ‘smoking status’ variable. Categorical data can be further classified as nominal or ordinal.
See Data, Nominal data, Ordinal data.
Chi-square test of independence
A non-parametric test used to determine whether there is a statistically significant association between two categorical variables. The chi-square value is represented by \(\chi^2\)
See Categorical data, Non-parametric test.
Cohen’s \(d\)
A measure of effect size which determines how many standard deviations two means are separated by. It is commonly used to evaluate practical significance for \(t\) tests.
See Effect size, \(t\) test, One-way ANOVA.
Confidence interval
A range of values that a population statistic, such as the population mean, is expected to lie between with a given level of confidence. This level is known as the confidence coefficient and is typically \(95\%\), in which case it is called a \(95\%\) confidence interval.
See Population.
Confounding variable
A variable that may have an influence on the dependent (outcome) variable.
See Variable.
Continuous data
Data that is measured on a continuous numerical scale and can take a large number of possible values, such as data for a ‘weight’ or ‘distance’ variable. Continuous data can be further classified as interval or ratio.
See Interval data, Ratio data, Variable.
Cross-tabulation (contingency table)
A table used to display information for two categorical variables. Categories of one variable are listed in the rows and categories of the other variable are listed in the columns. Each cell contains the frequency (number) of subjects that fall into that combination of categories. Percentages and totals are often also included.
See Categorical data, Dependent variable, Independent variable.
Data
Observations and measurements that have been collected in some way, often through research. Quantitative data measures quantities and is recorded as numbers, while qualitative data records qualities as categories or as thoughts, feelings and opinions.
Discrete data
Data which measures counts or numbers of events, such as data for a ‘class attendance’ variable. It can be treated as either categorical or continuous, depending on how many values are possible.
See Data.
Degrees of freedom
The number of values that are free to vary when calculating an estimate. Degrees of freedom are commonly reported as part of the results of various hypothesis tests.
See Hypothesis testing.
Dependent variable (outcome variable)
When testing for a relationship between variables, the dependent variable is the one that is potentially influenced, affected or predicted by another variable.
See Variable.
Descriptive statistics
Statistics that are used to summarise and describe a variable or variables for a sample of data.
See Data, Sample, Variable.
Effect size
Effect size measures the magnitude of a difference or relationship between variables. It provides information about whether the difference or relationship is meaningful in a practical sense (i.e. in real life) and is calculated differently for different statistical tests.
See Cohen’s \(d\), Odds ratio, Practical significance, Variable.
Hypothesis testing
Hypothesis testing is used to determine whether a difference or relationship observed in a sample is statistically significant in terms of the population from which the sample was drawn. This can be assessed by interpreting the resulting \(p\) value.
See Alternative hypothesis, Null hypothesis, \(p\) value, Population, Sample, Statistical significance.
Independent samples \(t\) test
A parametric inferential statistical test used to determine whether there is a statistically significant difference between the mean of a continuous variable for two independent (unrelated) groups.
See Continuous data, Inferential statistics, Mean, Parametric test, Statistical significance.
Independent variable (predictor or exposure variable)
When testing for a relationship between pairs of variables, the independent variable is the one that potentially influences, affects or predicts the other variable.
See Variable.
Inferential statistics
Statistics that are used to draw inferences about the wider population from which a sample of data was drawn.
See Population, Sample.
Interquartile range
The interquartile range is a measure of dispersion that is appropriate when the median is used as the measure of central tendency. It is calculated by finding the difference between the first and third quartiles.
See Measure of central tendency, Measure of dispersion, Median, Quartiles.
Interval data
Continuous data that does not have an absolute zero, and where negative numbers also have meaning, such as for a ‘temperature in degrees Celsius variable’.
See Continuous data.
Level of significance
In a hypothesis test, the level of significance (denoted by \(\alpha\)) determines how small the \(p\) value needs to be before the null hypothesis is rejected. It is typically \(5\%\) (\(.05\))
See Hypothesis testing, Null hypothesis, \(p\) value
Linear regression
A statistical technique used to examine the relationship between one or more independent variables and a continuous dependent variable.
See Continuous data, Dependent variable, Independent variable.
Logistic regression
A statistical technique used to examine the relationship between one or more independent variables and a categorical dependent variable.
See Categorical data, Dependent variable, Independent variable.
Mean
The mean is the arithmetic average of a data set, calculated by adding all the values together and dividing by the total number of values. It is the most commonly used measure of central tendency. The sample mean is denoted by \(\bar{x}\), while the population mean is denoted by \(\mu\).
See Measure of central tendency, Population, Sample.
Measure of central tendency
A descriptive statistic that summarises a variable by identifying its average, central or typical value. Examples include the mean, median and mode.
See Continuous data, Descriptive statistic, Mean, Median, Mode.
Measure of dispersion
A descriptive statistic that summarises a variable by showing how widely the data is spread. Examples include the range, interquartile range, variance and standard deviation.
See Continuous data, Descriptive statistic, Interquartile range, Range, Standard deviation, Variance.
Median
The median is a more appropriate measure of central tendency than the mean when the data is affected by outliers or is skewed. It is the middle value when the data set is sorted from smallest to largest. If there are two middle values, the median is their average.
See Mean, Measure of central tendency, Outlier, Skewness.
Mode
The mode is the most frequently occurring value (or values) in the data set; it is a less commonly used measure of central tendency.
See Measure of central tendency.
Nominal data
Categorical data where the categories do not have an order, such as for a ‘marital status’ variable. If there are only two categories, then the terms binary and/or dichotomous are often also used.
See Categorical data.
Non-parametric test
An inferential statistical test that does not require continuous data to follow a particular distribution, such as the normal distribution. Non-parametric tests can also be used with some types of data that are not continuous, such as ordinal data.
See Continuous data, Inferential statistics, Normal distribution.
Normal distribution
A distribution (spread) of data that has two key properties:
1. The mean, median and mode are all equal.
2. Fixed proportions of the data lie within certain numbers of standard deviations from the mean (\(68\%\) within one standard deviation, \(95\%\) within two standard deviations and \(99.7\%\) within three standard deviations).
See Data, Mean, Median, Mode, Standard deviation.
Null hypothesis
Denoted by \(\textrm{H}_\textrm{0}\), the null hypothesis states that there is no difference or relationship between variables in a population.
See Alternative hypothesis, Hypothesis testing, Variable.
Odds ratio
A measure that compares the odds of an outcome between groups or shows how the odds of an outcome change as an independent variable changes. An odds ratio of \(1\) indicates no difference in the odds, a value greater than \(1\) indicates higher odds, and a value less than \(1\) indicates lower odds.
See Chi-square test of independence, Logistic regression.
One sample \(t\) test
A parametric inferential statistical test used to determine whether the mean of a continuous variable in a population is significantly different from a test value (some hypothesised value).
See Continuous data, Inferential statistics, Mean, Parametric test, Statistical significance.
One-way ANOVA (analysis of variance)
A parametric inferential statistical test used to determine whether there are any statistically significant differences between the means of a continuous variable for three or more independent (unrelated) groups.
See Continuous data, Inferential statistics, Mean, Parametric test, Statistical significance.
Ordinal data
Categorical data where the categories do have an order, such as for a ‘satisfaction level’ variable.
See Categorical data.
Outlier
An outlier is a data point that lies well above or below the other data. One way to identify possible outliers is to look for values more than \(1.5\) interquartile ranges below the first quartile or above the third quartile.
See Interquartile range, Quartiles.
\(p\) value
The \(p\) value for a hypothesis test is the probability of obtaining the observed test statistic, or one more extreme, if the null hypothesis is true. A small \(p\) value means that a result this extreme would be unlikely if the null hypothesis were true. If the \(p\) value is less than or equal to the level of significance, we reject the null hypothesis.
See Hypothesis test, Level of significance, Null hypothesis, Statistical significance, Test statistic.
Paired samples \(t\) test
A parametric inferential statistical test used to determine whether there is a statistically significant difference between the means of a continuous variable measured for two related groups or under two related conditions.
See Continuous data, Inferential statistics, Mean, Parametric test, Statistical significance.
Parametric test
An inferential statistical test that requires at least one continuous variable, and which requires continuous variables to be normally distributed (or the sample size to be large enough that the sampling distribution of the mean approximates a normal distribution).
See Continuous data, Inferential statistics, Normal distribution.
Pearson’s correlation coefficient
Pearson’s correlation coefficient, denoted by \(r\), measures the strength and direction of the linear relationship between two continuous variables. It can range from \(-1\) to \(1\). Values close to \(-1\) indicate a strong negative linear correlation, values close to \(1\) indicate a strong positive linear correlation, and values close to \(0\) indicate little or no linear correlation.
See Continuous data.
Percentiles
Values that show the position of a data point within an ordered data set. They can be used to show the relative standing of a particular value.
See Measure of dispersion.
Population
A population is every member of a group of interest. Normally it is not possible or feasible to collect data from the entire population, so a random sample is used instead to draw inferences about the population.
See Data, Inferential statistics, Sample.
Power
The power of a hypothesis test is the probability that the test will find an effect if one actually exists. In other words, it is the probability of correctly rejecting an incorrect null hypothesis.
See Hypothesis test, Null hypothesis.
Practical significance
Practical significance refers to whether a difference or relationship between variables is meaningful in a practical sense (i.e. in real life). It can be evaluated by calculating an effect size.
See Effect size, Variable.
Quartiles
Specific percentiles that divide an ordered data set into four parts. The\(25\)th percentile is known as the first or lower quartile, the \(50\)th percentile is known as the median, and the \(75\)th percentile is known as the third or upper quartile.
See Median, Percentiles
Range
The simplest measure of dispersion, the range is the difference between the smallest and largest value in a data set.
See Measure of dispersion.
Ratio data
Continuous data that does have an absolute zero, and where negative numbers do not have meaning, such as for a ‘height’ variable.
See Continuous data.
Sample
A sample is a subset of a population. It can be analysed using descriptive statistics, or used to draw inferences about the wider population using inferential statistics.
See Descriptive statistics, Inferential statistics, Population.
Standard deviation
Standard deviation is a commonly used measure of dispersion and is appropriate when the mean is used as the measure of central tendency. It is the square root of the variance and measures how much the values typically vary around the mean. The sample standard deviation is denoted by \(s\), while the population standard deviation is denoted by \(\sigma\).
See Mean, Measure of central tendency, Measure of dispersion, Population, Sample, Variance.
Statistical significance
Statistical significance refers to whether there is enough evidence from a sample to conclude that a difference or relationship exists in the population. It is determined by conducting a hypothesis test.
See Hypothesis test, Sample, Variable.
Test statistic
A value calculated as the result of a hypothesis test, the test statistic compares the value of the sample statistic (for example, the sample mean) with the value specified by the null hypothesis for the population statistic.
See Hypothesis testing, Mean, Null hypothesis, Population, Sample.
Variable
A characteristic or attribute for which you observe, measure or record data, such as height, weight, eye colour or dog breed.
See Data.
Variance
A measure of dispersion that shows how much the data varies around the mean. The square root of the variance is the standard deviation.
See Mean, Measure of dispersion, Standard deviation.