This guide provides
a brief description of some "popular" statistical inference tests.
Bear in mind
that the purpose of statistical inference is to test
hypotheses about population parameters using sample
data.
Univariate Tests:
Univariate tests involve only one variable and can fall
into the following types:
-
t-test for hypotheses about the mean (population standard
deviation is unknown). Use this test to assess whether a given sample
supports a hypothesis that the mean value of a numerical variable in the
population is =, ¹, > or
< a particular number.
-
z-test for the proportion. Use this test to
assess whether a given sample supports a hypothesis that the population
proportion is =, ¹, > or
< a particular number.
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Bivariate Tests:
Bivariate tests involve two variables and include the
following types:
-
Correlation t-test. Use this test to assess
whether two numerical variables in the population are related (in a linear
way) to each other. Specifically, this test assesses whether the
population correlation coefficient is =, ¹,
> or < a particular number (usually zero).
The test statistic is computed from a sample containing information on
two numerical variables.
-
Separate variance t-test for the difference in two means
(population standard deviations are unknown). Use this test to assess
whether the difference between two population group means is =, ¹,
> or < a specified value. If the specified
difference is set to zero, the test can be used to assess whether one group's
mean is =, ¹, > or
< the other group's mean. The test statistic is computed from
data for a numerical variable generated by sampling two independent groups.
-
t-test for the mean difference between related (paired)
samples (population standard deviation of the difference is unknown).
Use this test to assess whether the mean difference, in the population,
between two numerical variables is =, ¹,
> or < a specified value (usually zero).
The test statistic is computed from data on two numerical variables generated
by a sample that matches (pairs) the two variables to each other (i.e.,
the two variables are not drawn from samples that are independent of each
other). Equivalent results can also be generated using the
t-test
for hypotheses about the mean (population standard deviation is unknown)
if the latter test analyzes the difference between each pair's numerical
values.
-
One-WayAnalysis of Variance (Anova). Use this
test to assess whether two or more independent population groups have means
that are = or ¹ to
each other. The test statistic is computed from data for a numerical
variable generated by sampling two or more independent groups.
-
Z test for the two population proportions. Use
this test to assess whether the difference between two population group
proportions is =, ¹, > or
< a specified value. If the specified difference is set
to zero, the test can be used to assess whether one group's proportion
is =, ¹, > or <
the other group's mean. The test statistic is computed from data
for a categorical variable generated by sampling two independent groups.
-
Chi-squared (c2)
test for differences in two or more proportions. Use this
test to assess whether the population proportions of two or more groups
are the same. The test statistic is computed from data generated
by sampling two or more independent groups organized into a contingency
table.
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Multivariate Analysis: Multiple
Regression:
When the behavior of a
particular dependent variable is influenced by more than one explanatory
factor, multiple regression is a more appropriate analysis
method than bivariate methods. Using sample
data, regression analysis estimates the degree of influence,
if any, each explanatory variable has on the
dependent variable in the general population, holding
the influence of the other explainers constant.
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