## Statistics glossary

This section is based on the glossary in Keppel, Saufley and Tokunaga, Introduction to Design and Analysis, which is on short loan in the main library.

Click on a letter to jump to the section that you are interested in:

A B C D E F G H I J L M N O P R S T V W X Y Z

### A

- Alternative hypothesis
- The hypothesis that is accepted if the null hypothesis is rejected, usually represented by the symbol H1. Also known as the experimental or research hypothesis. The alternative hypothesis usually states that the independent variable has had an effect on the dependent variable that cannot be explained by chance alone. (N.B. You never prove that the alternative hypothesis is correct, even if the null hypothesis is rejected, there is always a chance that you have wrongly rejected it.)
- Availability sampling
- A sample based on subjects who are available and willing to participate in the study. Many experiments in psychology use undergraduates as subjects as they are cheap and easy to find.

### B

- Between subjects design
- An experimental design in which each subjects is randomly assigned to only one of the treatment conditions.

### C

- Case-study
- A research method involving the detailed study of a single individual, used mainly in clinical psychology and neuropsychology.
- Chi-squared test
- The appropriate test to investigate independent frequency counts taken from a sample.
- Classification variable
- An independent variable created by the selection of subjects on the basis of a factor such as age or gender. It is a characteristic which is observed and classified rather than imposed by the experimenter.
- Confounding variables
- One or more variables not under the control of the experimenter that vary systematically with the independent variable, decreasing the experimenter's ability to isolate cause and effect.
- Control group
- A group of subjects which does not receive the experimental treatment but in all other respects is treated in the same way as the experimental group, (so as to tease out the effects of the treatment itself). In medical studies involving the administration of drugs the control group is known as the placebo group. A neutral substance ( placebo ) is administered to this group without the subjects knowing if it is an active drug or not.
- Correlation
- A statistical relationship between two variables such that high scores on one factor tend to go with high scores on the other factor (positive correlation) or that high scores on one factor go with low scores on the other factor (negative correlation).
- Correlational design
- A type of research design in which patterns of correlations are analysed.
- Counterbalancing
- An arrangement of treatment conditions to neutralise practice effects and / or the effects of fatigue, e.g. where group A completes Task 1 followed by Task 2, and group B completes Task 2 followed by Task 1.
- Cross-sectional design
- A technique used for studying developmental factors e.g. by studying a number of groups of children of differing ages (and thus at different stages of development) at the same point in time.

### D

- Demand characteristics
- Features of the experimental situation which can affect the subjects' behaviour, in particular when the subject has expectations about what he/she is required to do, or has worked out what the experimenter "wants" to happen.
- Dependent variable
- The selected behaviour which is measured to try to gauge the effect of the independent variable in an experimental design.
- Descriptive statistics
- Data summarised in numerical form, such as mean, median, mode. This forms the first stage of data analysis. Means, standard deviations and standard errors are presented in the form of a table.
- Double-blind study
- In order to control for experimenter effects and demand characteristics, neither the subjects nor the experimenter knows which group of subjects has received which experimental treatment until after the data has been collected. This type of design is of particular use in pharmacology research when new drugs are being tested.

### E

- Empirical
- From the Greek en, (in), peira (trial), meaning derived from careful observations or experiments rather than from speculation or theory.
- Environmental variable
- An independent variable in which some aspect of the subject's physical surroundings are manipulated.
- Experiment
- A method of research which permits the inference of cause and effect. At least two groups of subjects are treated exactly alike in all ways except one, the independent variable. Differences in the behaviour of the Experimental and Control group which cannot be accounted for by experimental error are then attributed to the effect of the experimental treatment.
- Experimental design
- The plan of the experiment which specifies the treatment conditions (independent variables ), what is to be measured (dependent variables ) and methods of assigning subjects to groups.
- Experimental error
- Uncontrolled sources of variability in the results which occur randomly during the experiment. Much of this error is due to individual differences among subjects.
- Experimental hypothesis
- See Alternative hypothesis.
- Explanatory research
- Where the experimenter attempts to identify cause and effect.
- Exploratory research
- Research designed to investigate an area on which little information exists. This includes the use of pilot studies, which are trial runs of an experiment. The aim is to gain more information before doing more thorough research.
- External validity
- The degree to which results of a study with a sample of subjects can be generalised to make statements about a much larger population of subjects.

### F

- F-ratio
- A statistical index relating systematic variation in the data (caused by treatment effects plus random error) to unsystematic variability in the data (caused by random error alone). The effects of treatments plus error is the numerator and the effect of error(chance) is the denominator of the F-ratio.
- Factor
- A term which usually refers to the independent variable. If two different independent variables are used they are referred to as Factor A and Factor B. Each factor may have different levels, e.g. if Factor A is a drug treatment then doses of differing amounts are the dose levels.
- Factorial experiments
- Experimental designs in which two or more independent variables are used. This permits the analysis of interactions between variables.

### G

- Generalisation
- An inference made from a sample to a population. The researcher attempts to extend the results of his/her study to a much larger group of people.

### H

- H0
- See Null hypothesis.
- H1
- See Alternative Hypothesis.
- Hypothesis testing
- The formal process by which a decision is made concerning the rejection or acceptance of the null hypothesis.

### I

- Independent variable
- The variable manipulated by the experimenter. It is a feature of a task given to subjects, or a manipulation of the external or internal environment. Internal environment refers to attitudes, beliefs etc.
- Inferential statistics
- Procedures and measures used to make inferences about population characteristics from samples drawn from that population. The process of hypothesis testing is part of inferential statistics.
- Interval scale
- Measurements on a continuous numerical scale with equal intervals between points but where the zero point is arbitrary, as in, for example, measures of temperature in Celsius or Fahrenheit.

### J

- Jonckheere trend test
- A statistical test which investigates whether a trend exists across a number of ordered between-subjects conditions.

### L

- Linear regression line
- A "line of best fit" depicting the linear relationship between two variables. The line is characterized by two features, slope and intercept. The formula for the best-fit straight line can be used to predict one variable from another.
- Linear trend
- A linear relationship between the independent and the dependent variable, a relationship which can be represented by a straight line.
- Longitudinal study
- A form of research often used to study, e.g., developmental issues where the group of subjects is studied over an extended period of time. Measurements are taken several times at regular intervals to look at the effect of time on the dependent variable.

### M

- Matched-subjects designs
- A class of between-subjects design in which the subjects are matched on one or more relevant characteristics. This design is used to reduce between groups variability.
- Mean
- A measure of central tendency, giving an average of a set of scores (i.e. the sum of all the scores divided by the number of scores in the set).
- Median
- Measure of central tendency, giving the value of the middlemost score (above or below which half of all the scores lie). If there are an even number of scores the median is the average of the two middle scores.

### N

- Naturalistic observation
- A form of observational research in which the observer records information about naturally occurring behaviour while attempting not to intervene or affect the behaviour in any way. This research is also described as unobtrusive.
- Nominal scale
- Data is allocated into different (often named or numbered) categories. For example, the allocation of books in a library catalogue to different topics. Data on this scale cannot be meaningfully added and subtracted.
- Non-experimental research
- Research which lacks a true independent variable which is manipulated by the experimenter. Useful in situations where it is not possible or not ethical to manipulate the variable of interest.
- Non-parametric statistics
- Used when data is ordinal or nominal in scale, so that operations like addition and subtraction cannot be meaningfully applied. These tests are less sensitive than parametric tests to trends in the data (e.g. differences between conditions) but can be used with a wider range of measures.
- Normal distribution
- A theoretical data distribution which appears bell shaped, is symmetrical about the mean and has the most probable scores concentrated around the mean. Progressively less likely scores occur further away from the mean. 68.26% of the scores lie within one standard deviation either side of the mean, 95.44% of the scores lie within 2 standard deviations either side of the mean and 99.75% fall within three standard deviations.
- Null hypothesis
- This is usually a statement of "no effect", that is to say that the independent variable will not have any effect on the dependent variable and that any differences between the experimental and control groups are attributable to chance. The null hypothesis is usually represented by the symbol H0, and is stated in order that it can be rejected as an explanation for the results of the experiment.

### O

- Observational research
- The systematic study of behaviour as it occurs in the natural environment.
- Ordinal scale
- A scale of measurement where data are put in order, but where there is no fixed amount of difference between the points on the scale. For example, the rank order of premier league football teams, or World ranking of tennis players.

### P

- Paradigms
- Logical systems made up of theories and research techniques which reflect a predominant way of thinking about a particular topic.
- Parametric statistics
- Can be carried out on data which is interval or ratio scale, and thus is suitable for arithmetic operations such as addition and subtraction. This enables parameters such as mean and standard deviation to be defined.
- Participant observation
- A form of observational research in which the observer's presence is known to the subject.
- Placebo
- An inactive substance or dummy treatment administered to a control group to compare its' effects with a real substance, drug or treatment.
- Placebo effect
- A positive or therapeutic benefit resulting from the administration of a placebo to someone who believes the treatment is real.
- Population
- The total number of all possible subjects or elements which could be included in a study. If the data are valid, the results of research on a sample of subjects drawn from a much larger population can then be generalised to the population.
- Power
- The probability of correctly rejecting the null hypothesis, i.e. rejecting the null hypothesis when it is false; defined as 1 minus the probability of a type II error (See type I and type II errors).
- Practice effects
- The systematic change (increase or decrease) in the subjects' performance over a series of treatment conditions in a repeated measures (within-subjects) design. A potential source of error usually neutralised by using a counterbalancing design.
- Predictive research
- Research designed to find out if the score on a particular measure or a test result corresponds with some other behaviour of interest. e.g. do the results of an IQ test predict how well a person will perform in final exams?
- Psychology
- From the Greek, psyche (mind) logos (study), the study of the nature and functions of the mind and of human behaviour.
- Psychometric testing
- From the Greek, psyche (mind) metron (measure), testing of mental ability such as IQ, also includes the use of tests to measure interests, attitudes and personality.

### R

- Random assignment of subjects
- Procedure by which each subject has an equal probability of being assigned to each different treatment condition in an experiment.
- Randomisation
- Introduced by R. A. Fisher in 1926 so that inferential statistics could be carried out to analyse differences between groups of subjects.
- Random sample
- A group of subjects randomly chosen from a defined population.
- Random sampling
- A procedure in which each member of the population has an equal chance of being included in the sample.
- Reliability
- The consistency with which a measuring instrument (such as a psychometric test) performs its' function, gauged, for example, by comparing test scores from the same subjects at different times.

### S

- Sample
- A subgroup selected from a larger group of potential subjects (population).
- Sample size
- The number of subjects assigned to a treatment condition in an experiment or study.
- Sampling
- The process of selecting subjects for research. See random sampling, availability sampling.
- Sampling distribution
- The frequency distribution of a statistic obtained from an extremely large number of random samples drawn from a specified population.
- Significance (statistical)
- Is achieved when there is a low probability that the results of an experiment occurred by chance alone. In psychology it is conventional that results are said to be significant if the probability of their occurrence by chance is equal to or less than 5 per cent or 0.05.
- Significance level
- The probability with which the experimenter is willing to reject the null hypothesis (in favour of the alternative hypothesis) when the null hypothesis is in fact correct. Also known as the probability of a type I error.
- Standard deviation
- A measure of dispersion within a set of data, calculated from the square root of the variance, to give a value in the same range as raw scores. The standard deviation is the spread of scores around the mean of the sample.
- Standard error
- The standard deviation of the sampling distribution of the mean. A statistical estimate of the population standard deviation based on the mean and standard deviation of one sample. Calculated by dividing the standard deviation of the sample by the square root of the number of subjects in the sample.
- Subject mortality
- The loss of subjects during a research study (hopefully not due to death). Subjects may drop out of a study for a variety of reasons. It becomes a problem when subject loss is not random and occurs unequally across groups.
- Survey research
- Research using questionnaires or interviews to poll or obtain information.

### T

- t-test
- A parametric statistical test of the difference between the means of two samples.
- Task variable
- An independent variable in which some aspect of a task is manipulated by the experimenter.
- Theory
- A set of propositions which summarise, organise, and explain a variety of known facts, e.g. Darwin's theory of evolution. Theories are intended to logically summarise information and to give a framework for the generation of new tests and ideas on the topic.
- Type I error
- An error of statistical inference when the null hypothesis is rejected when it is true. This is an error of "seeing too much in the data."
- Type II error
- An error of statistical inference when the null hypothesis is retained when it is false. This is an error of "not seeing enough in the data."

### V

- Validity
- From the Latin validus (strong), the degree to which a measuring instrument measures what it is supposed to measure.
- Variability
- The degree to which differences exist among a set of scores. The standard deviation is usually used to describe the variability of scores in a sample.
- Variable
- A property that can take different values. In research designs variables are classed as independent and dependent.

### W

- Within-groups variability
- A measure of variability based on the variation of subjects treated alike in an experiment (i.e. the subjects are in the same group). The amount of within-groups variability gives a measure of experimental error.
- Within-subjects design
- An experimental design where all subjects receive all treatment conditions. Also called a repeated measures design.

### X

- X-variable
- The variable which is plotted on the X-axis of a graph (i.e. the horizontal axis). In an experiment the variable plotted on the X-axis is the independent variable.

### Y

- Y-variable
- The variable plotted on the Y-axis of a graph (vertical axis). In an experiment the Y-variable is the dependent variable.

### Z

- Z-score
- A score expressed in units of standard deviations from the mean. Also known as a standard score.