Glossary

A family of distributions, dependent on degrees of freedom, similar to the normal distribution but with more variability built in

A working hypothesis that is contradictory to the null hypothesis

Evidence that is based on personal testimony and collected informally

A relationship between variables

An experiment with the following characteristics:

- There are only two possible outcomes (called “success” and “failure”) for each trial.
- The probability (p) of a success is the same for any trial (so the probability q = 1 − p of a failure is the same for any trial).

A distribution that has two modes

A random variable that counts the number of successes in a fixed number (n) of independent Bernoulli trials each with probability of a success (p)

Data consisting of two variables, often in search of an association

Not telling participants which treatment they are receiving

Grouping individuals based on a variable into "blocks" and then randomizing cases within each block to the treatment groups

A study that compares a group that has a certain characteristic to a group that does not, often a retrospective study for rare conditions

The central tendency or most typical value of a dataset

If there is a population with mean μ and standard deviation σ, and you take sufficiently large random samples from the population, then the distribution of the sample means will be approximately normally distributed.

Found by adding the lower limit and upper limit, then dividing by two

The difference in consecutive lower class limits

A method of sampling where the population has already sorted itself into groups (clusters), and researchers randomly select a cluster and use every individual in the chosen cluster as the sample

A numerical measure of the percentage or proportion of variation in the dependent variable (y) that can be explained by the independent variable (x)

Longitudinal study where a group of people (typically sharing a common factor) are studied and data is collected for a purpose

The complement of an event consists of all outcomes in a sample space that are NOT in the event.

Dividing participants into treatment groups randomly

The likelihood that an event will occur given knowledge of another event

An interval built around a point estimate for an unknown population parameter

A variable that has an effect on a study even though it is neither an explanatory variable nor a response variable

A table in a matrix format that displays the frequency distribution of different variables

When statisticians add or subtract .5 to values to improve approximation

A random variable (RV) whose outcomes are measured as an uncountable, infinite number of values

A group in a randomized experiment that receives no (or inactive) treatment but is otherwise managed exactly as the other groups

Type of experiment where variables are manipulated and data is collected in a controlled setting

Selecting individuals that are easily accessible and may result in biased data

A numerical measure that provides a measure of strength and direction of the linear association between the independent variable x and the dependent variable y

Point on a distribution that acts as a cut-off value for accepting or rejecting the null hypothesis

Data collection on a population at one point in time (often prospective)

A function that gives the probability that a random variable takes a value less than or equal to x

The sum of the relative frequencies for all values that are less than or equal to the given value

Actual values (numbers or words) that are collected from the variables of interest

Process of collecting, organizing, and analyzing data

The number of objects in a sample that are free to vary

Methods of organizing, summarizing, and presenting data

Data collection where variables are manipulated in a controlled setting

The difference in the means of two independent populations

A random variable that takes on a countable amount of values

The possible values a variable can take on and how often it does so

The act of blinding both the subjects of an experiment and the researchers who work with the subjects

Roughly 68% of values are within one standard deviation of the mean, roughly 95% of values are within two standard deviations of the mean, and 99.7% of values are within three standard deviations of the mean

An outcome or subset of outcomes of an experiment in which you are interested

Mean of a random variable

Any individual or object to be measured

The independent variable in an experiment; the value controlled by researchers

The process of predicting outside of the observed x values

Variables in an experiment

The number of times a value occurs in the data

Organizing, summarizing, or presenting data visually in graphs, figures, or charts

A decision-making procedure for determining whether sample evidence supports a hypothesis

The occurrence of one event has no effect on the probability of the occurrence of another event.

The person, animal, item, place, etc. about which we collect information

The facet of statistics dealing with using a sample to generalize (or infer) about the population

Observed data points that do not follow the trend of the rest of the data and have a large influence on the calculation of the regression line

The shared or common outcomes of two events (i.e., elements are in both A and B)

Quantitative data where the difference or gap between values is meaningful

As the number of trials in a probability experiment increases, the relative frequency of an event approaches the theoretical probability

Certain values of variables in an experiment

A mathematical model of a linear association

Collecting data multiple times on the same individuals over a period of time, usually in fixed increments

The lower end of a bin or class in a frequency table or histogram

How much a point estimate can be expected to differ from the true population value; made up of the standard error multiplied by the critical value

Very similar individuals (or even the same individual) receive two different treatments (or treatment vs. control), then the results are compared

A number that measures the central tendency of the data

A measure of an observation's standing relative to the rest of the dataset

The middle number in a sorted list

How many peaks or clusters there appear to be in a quantitative distribution

The most frequently occurring value

Two events that cannot happen at the same time; sharing no common outcomes

Categorical data where the the categories have no natural, intuitive, or obvious order

A commonly used symmetric, unimodal, bell-shaped, and continuous probability distribution

The claim that is assumed to be true and is tested in a hypothesis test

Numbers that summarize some aspect of a dataset, often calculated

Data collection where no variables are manipulated

Categorical data where the the categories have a natural or intuitive order

A particular result of an experiment

An observation that stands out from the rest of the data significantly

The probability that an event will occur, assuming the null hypothesis is true

A number that is used to represent a population characteristic and can only be calculated as the result of a census

An inactive treatment that has no real effect on the explanatory variable

The value that is calculated from a sample used to estimate an unknown population parameter

Using sample data to calculate a single statistic as an estimate of an unknown population parameter

Estimate of the common value of p1 and p2

The whole group of individuals who can be studied to answer a research question

The arithmetic mean, or average, of a population

The mean of the differences in a matched pairs design

The number of individuals that have a characteristic of interest divided by the total number in the population

The probability of failing to reject a true hypothesis

The study of randomness; a number between zero and one, inclusive, that gives the likelihood that a specific event will occur

A function that defines a continuous random variable and the likelihood of an outcome

A random experiment where the result is not predetermined

A function that gives the probability that a discrete random variable is exactly equal to some value (x)

A mathematical representation of a random process that lists all possible outcomes and assigns probabilities to each

Collecting information as events unfold

Data that describes qualities or puts individuals into categories; also known as categorical data

Points in a distribution that relate to the rank order of values in that distribution

Data produced by a variable that takes on an uncountable, infinite number of values

Numerical data with a mathematical context

Data produced by a variable that takes on a countable number of values

A representation of a probability model

Quantitative data where the difference or gap between values is meaningful AND has a true 0 value

The percentage, proportion, or ratio of the frequency of a value of the data to the total number of outcomes

When an individual goes through a single treatment more than once

A residual measures the vertical distance between an observation and the predicted point on a regression line

The dependent variable in an experiment; the value that is measured for change at the end of an experiment

Collecting or using data after events have taken place

Not affected by violations of assumptions such as outliers

A subset of the population studied

The arithmetic mean, or average, of a dataset

The number of individuals that have a characteristic of interest divided by the total number in the sample, often found from categorical data

The set of all possible outcomes of an experiment

Bias resulting from all members of the population not being equally likely to be selected

The probability distribution of a statistic at a given sample size

The idea that samples from the same population can yield different results

The visual appearance of a dataset

Probability that a true null hypothesis will be rejected, also known as type I error and denoted by α

Each member of the population is equally likely to be chosen for a sample of a given sample size and each sample is equally likely to be chosen

Tells us how the dependent variable (y) changes for every one unit increase in the independent (x) variable, on average

The level of variability or dispersion of a dataset; also commonly known as variation/variability

The average distance (deviation) of each observation from the mean

The standard deviation of a sampling distribution

A normal random variable with a mean of 0 and standard deviation of 1 which z-scores follow; denoted N(0, 1)

A number calculated from a sample

Using information from a sample to answer a question, or generalize, about a population

Finding sufficient evidence that the observed effect is not just due to variability, often from rejecting the null hypothesis

Dividing a population into groups (strata) and then using simple random sampling to identify a proportionate number of individuals from each

Using some sort of pattern or probability-based method for choosing your sample

A measure of the difference between observations and the hypothesized (or claimed) value

Combinations of levels of variables in an experiment

Different values or components of the explanatory variable applied in an experiment

Diagram that helps calculate and organize the number of possible outcomes of an event or problem

The decision is to reject the null hypothesis when, in fact, the null hypothesis is true

Erroneously rejecting a true null hypothesis or erroneously failing to reject a false null hypothesis

A probability distribution in which all outcomes are equally likely

The set of all outcomes in two (or more) events (i.e., elements are in A or B)

The upper end of a bin or class in a frequency table or histogram

Possible observations of the variable

A characteristic of interest for each person or object in a population

The square of the standard deviation; a computational step along the way to calculating the standard deviation

The level of variability or dispersion of a dataset; also commonly known as spread or variability

A diagram that shows all possible relations between a collection of different sets

The value of y when x is 0 in a regression equation

A measure of location that tells us how many standard deviations a value is above or below the mean