Statistics

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bar graph

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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.

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bias

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A condition that occurs when the design of a study systematically favors certain outcomes.

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blocking

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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.

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boxplot

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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.

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categorical variable

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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.

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comparative study

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A study where the explanatory variable has two active treatments rather than an active
treatment versus a control. Purpose of 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.

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completely randomized design

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An experimental design where all individuals participating in the experiment are
assigned at random to the treatments

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confounded variable

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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

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confounding

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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.

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control

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An ‘inactive’ treatment where no experimental condition 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.

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convenience sample

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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.

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distribution

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A list or a graph that shows the possible values of a variable together with the frequency of each
value.

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dotplot

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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

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double blind

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neither the subject nor the doctor, nurse or whomever is diagnosing the results knows which
treatment the subject received.

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experiment

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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

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explanatory variable

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

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factor

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Another term for explanatory variable.

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first rule of data analysis

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plot the data

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five number summary

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

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histogram

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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.

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individual

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the basic unit (or subject) of the experiment upon which a treatment is applied

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interquartile range (IQR)

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a measure of variability recommended for skewed data or data with outliers; computed
as IQR = Q3 – Q1

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lack of realism

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A weakness in experiments where the setting of the experiment does not realistically duplicate the
conditions we really want to study.

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left skewed

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A density curve where the left side of the distribution extends in a long tail. (Mean < median.)

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lurking variable

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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.)

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mean

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A measure for the center of the data.; it’s the point that “balances” the data.

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median

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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)

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multi-stage sample

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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 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.

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non-response bias

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bias resulting when individuals selected to be in a survey either cannot be contacted or refuse
to answer survey questions.

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Normal distribution

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: A bell-shaped symmetric density curve used to model many data sets that have a symmetric
mound or bell shape.

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observational study

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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.)

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outlier

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An observation that falls outside the overall pattern of the data set. Can be detected by checking:
observation < Q1 – 1.5 IQR or observation > Q3 + 1.5 IQR.

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pie chart

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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.

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placebo effect

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The response of patients to any treatment even though it has no physical effect

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population

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The entire group of individuals about whom we desire to collect information.

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probability sample

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a sample selected using a random device where each individual in the population has a chance
(doesn’t have to be equal) of being selected. Probability samples are necessary for making inferences. Examples
include: SRS, stratified and multistage

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quantitative variable:

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A variable with numerical values such as height or weight. This type of data is required for
both variables in regression analysis.

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randomization

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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.

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range

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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)

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replication

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Having more than one individual in each treatment group. Replication is necessary for measuring
variability. Also, the greater the replication, the more precise the results.

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response bias

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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.

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response variable

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

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right skewed distribution

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

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sample

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

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simple random sample

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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.

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standard deviation

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A measure of the “average” or typical deviation of the observations about the mean;
measures variability of data about the mean.

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standard Normal curve

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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.

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statistically significant

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Results of a study that differ too much from what we expected because of randomization
to attribute to chance.

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stemplot

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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.

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stratified sampling

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A sampling scheme where the population has been divided into strata according to some
characteristic and a simple random sample is selected from within each stratum.

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symmetric distribution

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a density curve where the right half is a mirror image of the left half of the distribution. (Mean = median)

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undercoverage bias

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Bias that occurs because the list of the population from which the sample is drawn is
incomplete—meaning that some people in the population are not listed for selection.

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voluntary response sample

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A method of sample selection that consists of people choosing themselves by
responding to a general appeal.

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z-score

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

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An experimental design where all experimental units are assigned at random to treatments.

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completely randomized

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Type of sampling required for inference

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probability sample

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A condition that occurs when the design of a study systematically favors certain outcomes

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nias

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symbol for the response variable

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y

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symbol for the explanatory variable

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x

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symbol for correlation coefficient

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r

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normal distribution that has a mean of zero and a standard deviation of one

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standard normal distribution

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A measure of the number of standard deviations of a value or observation from the mean.

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z score

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A list of the possible values of a variable together with the frequencies of each variable.

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distribution

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The shape of a distribution where the mean exceeds the median

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right skewed

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The shape of a histogram where the median exceeds the mean

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left skewed

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The recommended plot for displaying small quantitative data sets

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stemplot