Statistics Glossary
from
Prophet

>
alternative hypothesis:

The
null hypothesis
for a statistical test is the assumption that the test uses for calculating the probability of observing a result at least as extreme as the one that occurs in the data at hand. An
alternative hypothesis
is one that specifies that the null hypothesis is not true.
For the
onesample t test
, the null hypothesis is that the
population
mean equals a specific value. For a
twosided
test, the alternative hypothesis is that the mean does not equal that value. It is also possible to have a
onesided
test with the alternative hypothesis that the mean is greater than the specified value, if it is theoretically impossible for the mean to be less than the specified value. One could alternatively perform onesided test with the alternative hypothesis that the mean is less than the specified value, if it were theoretically impossible for the mean to be greater than the specified value.
Onesided tests usually have more
power
than twosided tests, but they require more stringent assumptions. They should only be used when those assumptions (such as the mean always being at least as large as they specified value for the onesample t test) apply.

>
between effects:

In a
repeated measures
ANOVA, there will be at least one factor that is measured at each level for every subject. This is a
within
(repeated measures) factor. For example, in an experiment in which each subject performs the same task twice, trial (or trial number) is a within factor. There may also be one or more factors that are measured at only one level for each subject, such as gender. This type of factor is a between or grouping factor.

>
bias:

An estimator for a parameter is
unbiased
if its expected value is the true value of the parameter. Otherwise, the estimator is
biased
.

>
binary variable:

A binary
random variable
is a discrete random variable that has only two possible values, such as whether a subject dies (event) or lives (nonevent). Such events are often described as success vs failure.

>
boxplot:

A boxplot is a graph summarizing the
distribution
of a set of data values. The upper and lower ends of of the center box indicate the 75th and 25th percentiles of the data, the center box indicates the median, and the center
+
indicates the mean. Suspected
outliers
appear in a boxplot as individual points
o
or
x
outside the box. The
o
outlier values are known as
outside
values, and the
x
outlier values as
far outside
values.
If the difference (distance) between the 75th and 25th percentiles of the data is
H
, then the outside values are those values that are more than 1.5H but no more than 3H above the upper quartile, and those values that are more than 1.5H but no more than 3H below the lower quartile. The far outside values are values that are at least 3H above the upper quartile or 3H below the lower quartile.
Examples
of these plots illustrate various situations.
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