Alternative hypothesis-the theory that the
researcher hopes to confirm by rejecting the null
hypothesis
Association-when some of the variability in one
variable can be accounted for by the other
Bar graph-graph in which the frequencies of citegories are displayed with bars; analogous to a histogram for numerical data
Bimodal-<listribution with two (or more) most
common values; see mode
Binomial distribution-probability distribution for a
random variable X in a binomial setting;
where n is the number of independent trials, p is
the probability of success on each trial, and xis the
count of successes out of the n trials
Binomial setting (experiment}--when each of a
fixed number, n, of observations either succeeds or
fails, .independendy, with probability p
Bivariate data--having to do with two variables
Block-a grouping of experimental units thought to
be related to the response to the treatment
Block design-procedure by which experimental units
are put into homogeneous groups in an attempt to
control for the effects of the group on the response
Blocking-see block design
Boxplot (box and whisker plot}--graphical representation of the five-number summary of a dataset.
Each value in the five-number summary is located
over its corresponding value on a number line. A
box is drawn that ranges from Q 1 to Q3 and
"whiskers" extend to the maximum and minimum
values from QI and Q3.
Categorical data--see qualitative data
Census-attempt to contact every member of a
population
Center-the "middle" of a distribution; either the
mean or the median
Central limit theorem-theorem that states that the
sampling distribution of a sample mean becomes
approximately normal when the sample size is large
Chi-square (x2} goodness-of-fit test-compares a set
of observed categorical values to a set of expected
values under a set of hypothesized proportions for
the categories;
X2 =
L
(O ~E)
2
Cluster sample-The population is first divided into
sections or "clusters." Then we randomly select an
entire duster, or clusters, and include all of the
members of the duster(s) in the sample.
Coefficient of determination (12}--measures the
proportion of variation in the response variable
explained by regression on the explanatory variable
(;omplement of an event-set of all outcomes in the
sample space that are not in the event
c0 plpletely randomized design-when all subjects
(?I experimental units) are randomly assigned to
tr(atments in an experiment
ConJ,tional probability-the probability of one
eve.it succeeding given that some other event has
alrea~Y occurred·
Confidei'Ce interval-an interval that, with a given
level of confidence, is likely to contain a population va).le; (estimate) ±(margin of error)
Confidenc~ level-the probability that the procedure useJ to construct an interval will generate
an interv~ that does contain the population value
Confounding variable-has an effect on the outcomes of the study but whose effects cannot be
separated froin those of the treatment variable
Contingency table-see two-way table
Continuous data-data that can be measured, or
take on values in an interval; the set of possible
values cannot be counted
Continuous random variable-a random variable
whose values are continuous data; takes all values
in an interval
Control-see statistical control
Convenience sample-sample chosen without any
random mechanism; chooses individuals based on
ease of selection
Correlation coefficient (,,__:measures the strength of the
linear relationship between two quantitative variables;
Glossary {
i(x; -x)(Y; -Y)
r =_I
n-1.t•1
sx
sJ
Correlation is not causation-just because two variables correlate strongly does not mean that one
caused the other
Critical valu~values in a distribution that identify
certain specified areas of the distribution
Degrees of freedom-number of independent datapoints in a distribution
Density function-a function that is everywhere
non-negative and has a total area equal to 1 underneath it and above the horizontal axis
Descriptive statistiG--process of examining data
analytically and graphically
Dimension-size of a tWo-way table; r x c ·
Discrete data-data that can be counted (possibly
infinite) or placed in order
Discrete random variabl~random variable whose
values are discrete data
Dotplot-graph in which data values are identified as
dots placed above their corresponding values on a
number line
Double blind"---<:xperimental design in which neither
the subjects nor the study administrators know
what treatment a subject has received
Empirical Rule (68-95-99.7 Rule}-states that, in a
normal distribution, about 68% of the terms are
within one standard deviation of the mean,
about 95% are within two standard deviations,
and about 99. 7% are within three standard
deviations
Estimat~sample value used to approximate a value
of a parameter
Event-in probability, a subset of a sample space;
a set of one or more simple outcomes
Expected valu~mean value of a discrete random
variable
Experiment-study in which a researcher measures
the responses to a treatment variable, or variables,
imposed and controlled by the researcher
Experimental units-individuals on which experiments are conducted
Explanatory variable"---explains changes in response
variable; treatment variable; independent variable
Extrapolation-predictions about the value of a variable based on the value of another variable outside
the range of measured values
First quartil~25th percentile
365
Five-number summary-for a dataset, [minimum
value, QI, median, Q3, maximum value]
Geometric setting-independent observations, each
of which succeeds or fails with the same probability p; number of trials needed until first success is
variable of interest
Histogram-graph in which the frequencies of
numerical data are displayed with bars; analogous
to a bar graph for categorical data
Homogeneity of proportions-chi-square hypothesis in which proportions of a categorical variable
are tested for homogeneity across two or more
populations
Independent events-knowing one event occurs
does not change the probability that the other
occurs; P(A) = P(A IB)
Independent variabl~see explanatory variable
Inferential statistics-use of sample data to make
inferences about populations
Influential observation--observation, usually in the
x direction, whose removal would have a marked
impact on the slope of the regression line
Interpolation-predictions about the value of a variable based on the value of another variable within
the range of measured values
Interquartile range-value of the third quartile
minus the value of the first quartile; contains
middle 50% of the data
Least-squares regression lin~f all possible lines,
the line that minimizes the sum of squared errors
(residuals) from the line
Line of best fit·· · see least-squares regression line
Lurking variabl~ne that has an effect on the outcomes of the study but whose influence was not
part of the investigation
Margin of error-measure of uncertaihty in the estimate of a parameter; (critical value) · (standard error)
Marginal totals-row and column totals in a twoway table
Matched pairS"---experimental units paired by a
researcher based on some common characteristic
or characteristic
Matched pairs design"---<:Xperimental design that utilizes each pair as a block; one unit receives one treatment, and the other unit receives the other treatment
Mean-sum of all the values in a dataset divided by
the number of values
Median-halfway through an ordered dataset, below
and above which lies an equal number of data
values; 50th percentile
366
>
Glossary
Mode-most common value in a distribution
Mound-shaped (bell-shaped)-distribution in which
data values tend to duster about the center of
the distribution; characteristic of a normal
distribution
Mutually exclusive events-events that cannot
occur simultaneously; if one occurs, the other
doesn't
Negatively associated-larger values of one variable
are associated with smaller values of the other; see
associated
Nonresponse bias--occurs when subjects selected
for a sample do not respond
Normal curve-familiar bell-shaped density curve;
symmetric about its mean; defined in terms of its
mean and standard deviation;
_I(
/( x ) -
1
r:-e
x-µ)
2
2\a
av2n
Normal distribution-distribution of a random variable X so that P(a < X < b) is the area under the
normal curve between a and b
Null hypothesis-hypothesis being tested-usually a
statement that there is no effect or difference
between treatments; what a researcher wants to
disprove to support his/her alternative
Numerical data-see quantitative data
Observational study-when variables of interest are
observed and measured but no treatment is
imposed in an attempt to influence the response
Observed values-counts of outcomes in an experiment or study; compared with expected values in a
chi-square analysis
One-sided alternative-alternative hypothesis that
varies from the null in only one direction
One-sided test-used when an alternative hypothesis states that the true value is less than or greater
than the hypothesized value
Outcome-simple events in a probability experiment
Outlier-a data value that is far removed from the
general pattern of the data
P(A and 8)-probability that both A and B occur;
P(A and B) = P(A) · P(A jB)
P(A or 8)-probabilicy that either A or B occurs;
P(A or B) = P(A) + P(B) -P(A and B)
Pvalue-probability of getting a sample value at least
as extreme as that obtained by chance alone assuming the null hypothesis is true
Parameter-measure that describes a population
Percentile rank-proportion of terms in the distributions less than the value being considered
Placebo-an inactive procedure or treatment
Placebo effect-effect, often positive, attributable to
the patient's expectation that the treatment will
have an effect
Point estimate-value based on sample data that represents a likely value for a population parameter
Positively associated-larger values of one variable
are associated with larger values of the other; see
associated
Power of the test-probability of rejecting a null
hypothesis against a specific alternative
Probability · distribution-identification of the outcomes of a random variable together with the
probabilities associated with those outcomes
Probability histogra~histogram for a probability distribution; horizontal axis shows the outcomes, vertical axis shows the probabilities of those outcomes
Probability of an event-relative frequency of the
number of ways an event can succeed to the total
number of ways it can succeed or fail
Probability sample-sampling technique that uses a
random mechanism to select the members of the
sample
Proportion-ratio of the count of a particular outcome to the total number of outcomes
Qualitative data--data whose values range over categories rather than values
Quantitative data--data whose values are numerical
Quartiles-25th, SOth, and 75th percentiles of a
dataset
Random phenomenon-unclear how any one trial
will turn out, but there is a regular distribution of
outcomes in a large number of trials
Random sample-sample in which each member of the
sample is chosen by chance and each member of the
population has an equal chance to be in the sample
Random variable-numerical outcome of a random
phenomenon (random experiment)
Randomization-random assignment of experimental units to treatments
Range--difference between the maximum and minimum values of a dataset
Replication-repetition of each treatment enough
times to help control for chance variation
Representative sample---sample that possesses the
essential characteristics of the population from
which it was taken
Glossary
Residual-in a regression, .the actual value minus the
predicted value
Resistant statistic--one whose numerical value is
not influenced by extreme values in the dataset
Response bias-bias that stems from respondents'
inaccurate or untruthful response
Response variable-measures the outcome of a study
Robust--when a procedure may still be useful even if
the conditions needed to justify it are not completely satisfied
Robust procedure-procedure that · still works reasonably well even if the assumptions needed for it
are violated; the t-procedures are robust against the
assumption of normality as long as there are no
outliers or severe skewness.
Sample space-set of all possible mutually exclusive
outcomes of a probability experiment
Sample survey-using a sample from a population
to obtain responses to questions from individuals
Sampling distribution of a statistic-distribution of
all possible values of a statistic for samples of a
given size
Sampling frame--list of experimental units from
which the sample is selected
Scatterplot-graphical representation of a set of
ordered pairs; horizontal axis is first element in the
pair, vertical axis is the second
Shape--geometric description of a dataset: moundshaped; symmetric, uniform; skewed; etc.
Significance level (a)-probability value that, when
compared to the P-value, determines whether a
finding is statistically significant
Simple random sample (SRS}-sample in which all
possible samples of the same.size are equally likely
to be the sample chosen
Simulation-random imitation of a probabilistic
situation
Skewed-distribution that is asymmetrical
Skewed left (right}-asymmetrical with more of a
tail on the left (right) than on the right (left)
Spread-variability of a distribution
Standard deviation-square root of the variance;
'~~~(x-X)'
n-1
Standard error--estimate of population standard
deviation based on sample data
Standard normal distribution-normal distribution
with a mean of 0 and a standard deviation of 1
<
367
Standard normal probability-normal probability
calculated from the standard normal distribution
Statistic-measure that describes a sample (e.g.,
sample mean)
Statistical control-holding constant variables in an
experiment that might affect the response but are
not one of the treatment variables
Statistically significant-a finding that is unlikely to
have occurred by chance
Statistics-science of data
Stemplot (stem-and-leaf plot~graph in which
ordinal data are broken into "stems" and "leaves";
visually similar to a histogram except that all the
data are retained
Stratified random sample-groups of interest
(strata) chosen in such a way that they appear in
approximately the same proportions in the sample
as in the population
Subjects-human experimental units
Survey-obtaining responses to questions from
individuals
Symmetric-data values distributed equally above
and below the center of the distribution
Systematic bias-the mean of the sampling distribution of a statistic does not equal the rnean of the
population; see unbiased estimate
Systernati~ sample-probability sample in which
one of the first n subjects is chosen at random for
the sample and then each nth person after that is
chosen for the sample
t-distribution-the distribution with n - 1 degrees of
freedom for the t statistic
t statistic-
x-µ
s!Fn
t---
Test statisticestimator - hypothesized value
standard error
Third quartile-75th percentile
Treatment variable--see explanatory variable
Tree diagram-graphical technique for showing all
possible outcomes in a probability experiment
Two-sided alternative--alternative hypothesis that
can vary from the null in either direction; values
much greater than or much less than the null provide evidence against the null
368
>
Glossary
Two-sided test-a hypothesis test with a two-sided
alternative
Two-way table-table that lists the outcomes of two
categorical variables; the values of one category are
given as the row variable, and the values of the
other category are given as the column variable;
also called a contingency table
Type-I error-the error made when a true hypothesis
is rejected
Type-II error-the error made when a false hypothesis is not rejected
Unbiased estimate-mean of the sampling distribution of the estimate equals the parameter being
estimated
Undercoverage-some groups in a population are
not included in a sample from that population
Uniform-distribution in which all data values have
the same frequency of occurrence
Univariate data-having to do with a single variable
Variance--average of the squared deviations from
their mean of a set of observations;
s
2
=
,L (x -xl
n-1
Voluntary response bias-bias inherent when people
choose to respond to a survey or poll; bias is typically
toward opinions of those who feel most strongly
Voluntary response sample-sample in which participants are free to respond or not to a survey or a poll
Wording bias--creation of response bias attributable
to the phrasing of a question
z-score-nurnber of standard deviations a term IS
above or below the mean;
x-x
z=-s