a graphical representation of categorical data. Names of each category are listed on the x axis and a bar 

is place over each category name having height equal to the frequency (or percentage) in that category.

The grouping of individuals according to some characteristic like rats in the same litter or plots of land 

at the same location. The random allocation is carried out separately within each group. 

A plot of data based on the five number summary. A line is drawn from the minimum observation to Q1; 

a box is drawn from Q1 to Q3 with a vertical line at the median and a line is drawn from Q3 to the maximum 

observation

A variable that can be classified into groups or categories such as gender, religion, zip-code, etc. Typically, words are used to describe an individual.

A study where the explanatory variable has two active treatments rather than an active 

treatment versus a control. Purpose of the study is to determine which treatment works best rather than whether 

a treatment works. Randomization together with comparison enables the researcher to control lurking variables 

and apply the laws of probability for inference.

An experimental design where all individuals participating in the experiment are 

assigned at random to the treatments.

A variable whose effect on the response variable cannot be separated from the effect of the 

explanatory variable on the response variable. (Note: Usually confounded variables are lurking variables but 

only a few lurking variables are also confounded.) 

A situation where the effect of one variable on the response variable cannot be separated from the 

effect of another variable on the response variable

An ‘inactive’ treatment where either no experimental condition or a placebo is applied to the individuals 

in order to determine whether the active treatment works. Randomizing together with a control enables the 

researcher to manage lurking variables when there is not a comparison group. Note: a control is not necessary 

for a valid experiment as long as two or more comparison treatments are used.

A sample where the researcher contacts those subjects who are readily available and does 

not use any random selection. The results are almost surely biased. 

A table or a graph that give the possible values of a variable together with the frequency of each 

value.

A one dimensional plot of a quantitative data set where each value in the data set is represented by a dot 

above its corresponding location on the x axis.

neither the subject nor the diagnostician (doctor, nurse or whomever is diagnosing the results) knows 

which treatment the subject received. Note: the researcher has to know in order to analyze the results. 

A study where a treatment is deliberately imposed on each individual in the study before responses 

are measured in order to observe responses to the treatment. A valid experiment must have 1) control or 

comparison, 2) randomization and 3) replication.

A variable that may or may not explain the outcomes (responses) of a study. It is given as a 

phrase that describes all possible treatments. Note: An observational study can have an explanatory variable, 

but a valid experiment always has an explanatory variable.

minimum, Q1, median, Q3, maximum; preferred when data are very skewed or have 

outliers.

A graphical display of a quantitative data set; data are separated into intervals of equal width and a bar

is drawn over the interval having height equal to the frequency (or percentage) of values in the interval. Values

of the variable are given on the x axis and frequencies (or percentages) are given on the y axis. (Hence, a

histogram gives a distribution.) Histograms are described by shape, center and spread.

a measure of variability recommended for skewed data or data with outliers; computed

as IQR = Q3 – Q1

A weakness in experiments where the setting of the experiment does not realistically duplicate the

conditions we really want to study.

A variable that has an important effect on the relationship among the variables in a study but is

not taken into account. (Technically, a true lurking variable “interacts” with the explanatory variable in its

effect on the response variable.)

A measure of the center of data; it’s the point such that half the numbers are smaller and the other half are

larger (the midpoint of the ordered data set).

sampling is conducted in stages; for a two-stage sample, the individuals are grouped according to some characteristic—groups are first randomly selected and then individuals are randomly selected from only those selected groups. (In a stratified sample, individuals are randomly selected from every group.) For example, states could be randomly selected; then school districts within selected states, followed by schools within selected school districts within selected states and finally students would be randomly selected from the selected schools from the selected school districts from selected states. That would be a four-stage sample.

A bell-shaped symmetric density curve used to model many data sets that have a symmetric

mound or bell shape.

A study that merely observes conditions of individuals in a population and records

information; the population is disturbed as little as possible. (Note: treatments are not imposed on units.)

An observation that falls outside the overall pattern of the data set. An observation is declared an outlier if

observation < Q1 – 1.5 IQR or if observation > Q3 + 1.5 IQR.

A graphical display of categorical data using a “pie”; each category is represented as a slice where the size of the slice is proportional to the percentage of data in that category. Not recommended by statisticians.

A location measure of the data such that has one fourth or 25% of the data is smaller than it. Found by dividing

the ordered data set in half (excluding the middle observation if n is odd) and finding the median of the lower

half of the data.

A location measure of the data that has three-fourths or 75% of the data is smaller than it. Found by dividing

the ordered data set in half (excluding the middle observation if n is odd) and finding the median of the upper

half of the data.

A table of digits consisting of digits 0 through 9 whose order cannot be determined but in

the long run, each digit occurs 10% of the time.

A method of assigning individuals in an experiment to treatment groups using some random device that eliminates bias and gives each unit the same probability of being assigned to any treatment group. Randomization “balances” the treatment groups, thus averaging out lurking and extraneous variables. Allows us

to use the laws of probability to make inferences.

The maximum observation minus the minimum observation. Given as one number in statistics (i.e. If max

= 98 and min = 12, then range = 98 – 12 = 86)

bias resulting from individuals in a sample lying or giving incorrect response because they do not have knowledge about the question or can’t recall; response bias could also result from wording of the question or from interviewers influence the responses either intentionally or unintentionally.

A variable that gives the result (may not be a number) of the outcome of a study. Describes the

measure on each individual.

A density curve where the right side of the distribution extends in a long tail; (mean >

median)

a subset of individuals in the population; the group of individuals about which we actually collect

information.

A sample of size n selected from the population in such a way that each possible sample

of size n has an equal chance of being selected.

A measure of the “average” or typical deviation of the observations about the mean;

measures variability of data about the mean.

A normal distribution with mean of zero and standard deviation of one. Probabilities are

given in Table A for values of the standard Normal variable.

Results of a study that differ too much from what we expected because of randomization

to attribute to chance.

A graphical representation of a quantitative data set. Leading values of each data point are presented as

stems and second digits are given as leaves.

A sampling scheme where the population has been divided into strata (groups) according to

some characteristic and a random sample is selected from within each stratum (group).

a density curve where the right half is a mirror image of the left half of the distribution.

(Mean = median)

A method of sample selection that consists of people choosing themselves by

responding to a general appeal.

A measure of the number of standard deviations a value or observation is from the mean, a standardized

value.