ISCAM III Glossary
Terms 
investigation 
Definition 
Inv B 
The probability of the union of
disjoint events (no shared outcomes) is the sum of the probabilities of the
individual events. 

Inv 1.2 
A statement of the parameter
values specified by the research conjecture. 

Inv 1.1 
A graphical display of
categorical data with a bar for each category. The height of the bar
indicates the frequency or the proportion of observations in that
category. Bars are typically the same width and with gaps between bars. 

Inv 5.12 
The model assuming linearity
between x and y, equal variance in responses at each x,
and normality of the responses at each x. 

Inv 1.12 
A sampling method that
consistently overrepresents or underrepresents distinct segments of the
population 

Inv 1.2 
A categorical variable with only
two possible outcomes (e.g., heads, tails) 

Inv 1.1 Expl 
A probability distribution
modeling the number of successes in a fixed number of independent trials with
a constant probability of success. 

Inv 2.9 
Selects a sample of size n from the original
sample with replacement. 

Inv 2.2 
A graphical display of the five
number summary. The box extends from the lower quartile to the upper quartile
with a vertical line at the median. Whiskers extend to min and max values or
to the most extreme nonoutlier values (using the 1.5IQR rule) 

Casecontrol study 
Inv 3.9 
Subjects are identified by response
variable and then explanatory variable is measured. 
Inv 1.2 
A variable that places
observational units into categories (e.g., small, medium, or large), rather
than measuring a numerical value. 

Inv 1.7 
The sampling distribution of a
sample proportion is approximately normal for large sample sizes with mean
equal to the population proportion/process probability and standard deviation
equal to . 

Inv 5.1 
A rightskewed probability
distribution that models the behavior of the chisquare statistic under the
null hypothesis. 

Inv 5.1 
A statistic summarizing the
discrepancies between the observed counts in a twoway table and the expected
counts under the null hypothesis. 

Inv 5.8 
The percentage of variability in
the response variable that is explained by the regression on the explanatory
variable. 

Cohort study 
Inv 3.9 
Subjects are identified by
explanatory variable and then response variable is measured. 
Inv B 
The probability of the
complement of the event equals one minus the probability of the event. 

Inv 3.1 
Calculating separate proportions
for each category of the explanatory variable 

Inv 1.5 
A set of plausible values
of the parameter based on the observed sample statistic. 

Inv 1.5 
The longrun proportion of
intervals that capture the parameter value. If the procedure is valid the
observed coverage rate under repeated random sampling will match the stated
confidence level. 

Inv 3.2 
A variable that changes
between the explanatory variable groups and potentially impacts the response
variable. 

Inv 2.5 
A group in a comparative
experimental study that receives no treatment or a placebo treatment. 

Inv 1.12 
A sample selected from a
population using the most readily available observational units or process; generally not considered representative of the population
or process. 

Inv 5.7 
A numerical measure of the
linear association between two quantitative variables. 

Inv 1.1 
The distribution of a simulated
sample of data, generated according to an assumed null model 

Inv 1.10 
The multiplier of the standard error
in a confidence interval corresponding to the nominal confidence level. 

Crossclassification study 
Inv 3.9 
Subjects are classified by
explanatory and response variables simultaneously. 
Inv 2.2 
A
function applied to data that rescales the variable, often changing the shape
and spread of the distribution. Transformations can be useful for normalizing
a distribution to allow use of normalbased methods or for linearizing
bivariate data to allow use of regression models. 

Inv 2.5, Inv 4.2, Inv 5.1 
A number related to the
number of “independent” observations in the calculation of a statistic. It is
used to index a particular member of a probability distribution family. 

Inv B 
A random variable that can take
on a finite number or a countable number of possible values. 

Inv A, Inv 1.1 
A graphical display of
quantitative data where each observational unit is represented by a dot above
the horizontal axis. 

Inv 1.5 
The correspondence between a
twosided test of significance and a confidence interval. 

Inv 1.8 
For any moundshaped, symmetric
distribution, approximately 68% of observations fall within one standard
deviation of the mean, 95% within 2 standard deviations, and 99.7% within three
standard deviations. 

Inv 5.2 
The expected number of
observations in a cell of a twoway table, assuming independence between the
row and column variables = (row total)x(column
total)/Table total 

Inv B 
In a probability distribution, a
weighted average of possible outcomes of a random variable, with weights
determined by the probability (or density) of the outcome, representing the
longrun average outcome of the random variable. 

Inv 3.3 
A study that actively imposes
the explanatory variable (or “treatments”) on the observational
(“experimental”) units. 

Inv 3.2 
The variable in a study that we
believe may be explaining the variation/behavior of the response variable.
In an experiment, this is the variable manipulated by the researchers. 

Inv 5.8 
Making predictions at
explanatory variable values far outside the range used to derive the
regression equation 

Inv 3.7 
Fixes the marginal totals in a twoway
table and uses the hypergeometric distribution to calculate the probability
of at least as many successes in group A as observed in the actual research
study. 

Inv 2.2 
The minimum, lower quartile,
median, upper quartile, and maximum 

Inv A, Inv 2.1 
A graphical display of
quantitative data that groups the values into bins and then displays bars for
each bin with height equal to the frequency or relative frequency of the
observations in that bin 

Inv 1.15, Inv 3.7 
A probability distribution that
models the probability of observing X successes being selected
randomly in a sample of n objects from a population with M
successes and NM failures. 

Inv 1.1 Prob Detour 
Random trials from a random
process where the probability of success or failure on a trial does not
depend on the outcomes of any other trials. 

Inv 5.9 
An observation whose removal
substantially changes the association between two variables. 

Inv 2.2 
The difference between the upper
quartile (75^{th} percentile) and the lower quartile (25^{th}
percentile); a measure of variability 

Inv 5.8 
The line that minimizes the sum
of the squared residuals (aka regression line) 

Inv 1.5 
The cutoff for the pvalue that
leads us to reject the null hypothesis. The probability of a type I
error. 

Inv 1.10 
The halfwith of a confidence
interval; the value that is added to and subtracted from the value of the
statistic to determine the endpoints of the confidence interval. 

Inv A, Inv 2.2 
A value such that at least 50%
of the observations in the data set are smaller than that value and at least
50% of the observations in the data set are larger than that value. 

Inv 2.2 
A boxplot that extends the
whiskers to the most extreme nonoutlying values and displays outliers
(according to 1.5IQR) separately 

Inv B, Inv 1.1 Prob Det. 
Sets of outcomes of a random
process that do not share any outcomes in common. 

Inv 1.15 
An error in the data collection
process that is not related to how the sample was selected (e.g., poor
question wording) 

Inv 1.7 
A probability model for
moundshaped symmetric, continuous distributions. Completely
characterized by the mean and standard deviation. Probabilities
correspond to areas under the curve; typically found using technology. 

Inv 1.1 
A distribution of statistics
where the statistics have been randomly generated based on an assumed chance
model 

Inv 1.2 
A statement of the parameter
values specified by the null model., typically representing "no effect"
or "no difference" 

Inv 1.1 
A chance model associated with a
null hypothesis. Usually the “by chance alone” model. 

Inv 3.3 
A study in which no variables are
manipulated by the researchers. Instead data is
recorded as it occurs naturally. 

Inv 1.2 
The people or objects about
which data are recorded. 

Inv 3.10 
The ratio of the number of
successes to the number of failures; equivalently the ratio of the
probability of success to the probability of failure. 

Inv 3.10 
The ratio of the odds of success
between two groups. 

Inv 1.8  Calculates the standardized statistic comparing the sample proportion to the hypothesized probability and uses the standard normal distribution (mean 0, std dev 1) to find the pvalue.  
Inv 1.10 
For estimating a process probability
or a population proportion:; valid when have at least 10 successes and at
least 10 failures. 

Inv 2.2 
An observation that does not
follow the general pattern of the other observations, typically an extreme
minimum or maximum value. One way to "test" for outliers is
identifying any observations that fall more than 1.5 × IQR from the
nearest quartile as outliers. 

Inv 4.9 
A confidence interval for the
mean difference in response from a paired study design. 

Inv 4.9 
A test of the mean of the
differences in response in a paired study. 

Inv 1.2 
A numerical summary describing
the larger process than generated the data or to the population from which
the sample was selected. 

Inv 3.5 
The potential effect on the
response variable of the power of suggestions (e.g., patients feeling better
because they are told they are receiving medicine to help them feel better). 

Inv 1.1 
A believable or reasonable
claim, often about a parameter value. For example, a null model that
is not rejected because the result of the study is not surprising under the
null model. 

Inv 1.11 
Adding two successes and two
failures to the sample before computing a onesample zinterval to
improve the longrun coverage rate of the procedure. 

Inv 3.8 
A ttest for comparing
two means assuming the two population standard deviations are equal and using
the pooled estimate of the standard deviation in the standard error
calculation 

Inv 1.12 
The entire collection of
observational units we are interested in. 

Inv 1.6 
The probability of rejecting the
null hypothesis at a particular alternative value of the parameter 

Inv 1.17 
The consideration of whether an
“effect” has meaning in a practical sense, given the context and the
magnitude of the effect 

Inv 2.6 
A confidence interval for
individual (future) observations (rather than the population mean) 

Inv B 
Longrun proportion of times
that an event occurs when its random process is repeated indefinitely 

Inv B 
See random process: A
sequence of outcomes generated under identical conditions, usually with
outcomes that cannot be perfectly predicted in advance. 

pvalue 
Inv 1.1 
Probability that a random
process alone would produce a statistic as (or more) extreme as the observed
statistical in the actual study 
Quantitative variable 
Inv 1.2 
A variable that takes on
numerical characteristics (where it makes sense to average the values of the outcomes) 
Inv 3.4 
Assigning experimental units to
treatments at random, each unit is equally likely to receive each of the
treatments; goal is to create treatment groups that are balanced on all
potential confounding variables. 

Inv B 
A sequence of outcomes generated
under identical conditions, usually with outcomes that cannot be perfectly
predicted in advance. 

Inv B 
A variable that assigns numbers
to outcomes from a random process. For example, X = number of heads in
5 tosses of a fair coin. 

Inv 2.5 
A study in which the
researchers decide, using random assignment, which explanatory variable group
each experiment unit will be in. 

Inv 5.8 
See
Least Squares Line. 

Inv 1.6 
The values of the statistic that
lead us to reject the null hypothesis for a particular level of significance 

Inv 3.9 
The ratio of the conditional
proportions of successes between two groups. 

Inv 5.8 
The “prediction error” between
the observed result and the predicted result 

Inv 2.2 
A numerical summary that t is not strongly affected by extreme observations (e.g.,
the median is a resistant measure of center) 

Inv 3.2 
In a study, the variable that we
think of as being explained by the explanatory variable. In an
experiment, this is the outcome variable of interest. 

Inv 1.12 
The observational units for
which we obtain measurements, a subset of the observational units in the
population. 

Inv 1.2 
The number of observational
units in the study (for which data have been recorded). Typically denoted by n. 

Inv 1.12 
An enumerated list of every
member of the population used to select the sample. 

Inv B 
The list of all possible
outcomes of a random process 

Inv 1.12 
The property that the value of a
statistic will vary from sample to sample but with a predictable pattern. 

Inv 5.6 
A graphical display of the
association between two quantitative variables. 

Inv 3.1 
A graph for displaying a
categorical response variable, with a separate bar for each category of the
explanatory variable. 

Inv 2.7 
A test of significance using the
binomial distribution to count the number of quantitative values above a
certain number (e.g., number of positive differences in paired study). 

Inv 1.12 
A sampling method that gives
every sample of size n an equal chance of being the selected sample. 

Inv B 
Artificially recreating the
outcomes of a random process, often using technology. 

Inv A, Inv B, Inv 1.7 
The square root of the variance;
a measure of spread in the outcomes of a distribution or random variable;
roughly the average deviation from the mean of the distribution. 

Inv 1.10 
An estimate of the standard
deviation of a statistic based on sample data. 

Inv 1.8 
Calculates the number of
standard deviations an observation lies from the mean of the distribution. 

Inv 1.1 
A numerical summary of a sample
of data. Common examples are the sample proportion (categorical data) or the
sample mean (quantitative data) 

Inv 1.1 
An observed result that is found
to be unlikely to happen by chance alone under the null model (small
pvalue). 

Inv 2.7 
Selects observations from
a sampling frame at fixed intervals (e.g., every kth observation) 

Inv 1.9 
A measure of the discrepancy
between the observed statistic and the parameter value(s) specified by the
null hypothesis 

Inv A 
A graph of the variable vs. the
time order of the observations 

Inv 3.1 
A test/interval comparing two
sample proportions using the normal approximation (aka two proportion ztest) 

Inv 1.4 
A significance test for which no
particular direction is specified in the alternative
hypothesis, using "not equal to" in the alternative hypothesis. 

Inv 3.1 
A summary of counts
crossreferenced by two categorical variables. Typically
the explanatory variable is used as the column variable. 

Inv 1.6 
Rejecting the null hypothesis
when it is true. 

Inv 1.6 
Failing to reject the null
hypothesis when it is false. 

Unbiased sampling method 
Inv 1.12 
A sampling method for which the
generated statistics average out to the population parameter of interest. 
Inv 1.2 
Any characteristic that varies
from observational unit to observational unit 

Inv B 
A weighted average of the
squared deviations from the outcomes of the random variable and the expected
value. 

A distribution of statistics
where the statistics have been generated according to an assumed null model. 

Inv 1.8 
Calculates the number of standard
deviations that an observation lies from the mean of the distribution. 