# Statistical Consulting

# Statistics Resource Center

Non-experimental research

Research which lacks 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 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 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 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 and is stated in that it can be rejected as an explanation for the results of the experiment.

O

Observational research

The systematic study of behavior 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 generalized 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 neutralized 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 behavior 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 behavior.

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 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.

Randomization

Introduced by R. A. Fisher in 1926 so that inferential statistics could be carried out to analyze 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 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 or 0.05.

Significance level

The probability with which the experimenter is willing to reject the null hypothesis (in favor 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 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 summaries, organize, and explain a variety of known facts, e.g. Darwin's theory of evolution. Theories are intended to logically summaries 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 (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 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.