Introduction to Inferential Statistics
science deals with two main concepts as far as
statistics are concerned: population and sample.
Population refers to the total number of objects,
groups, individuals or any other thing being studied
while a sample is a subset selected from the overall
population. Many studies rely on samples because they
are more manageable, less time consuming and cheaper.
Inferential statistics help researchers to make
generalizations about a population based on the sample
studied. They are used to reach conclusions that go
beyond the immediate data in question.
Inferences are prone to errors because they are made
from a relatively small subset of a population. Since
the results cannot be said to be a complete
representation of the characteristics of a population,
they are usually expressed in form of probability. For
example, they may give a probability of 93 percent.
A sample may not be representative of the target
population because of two problems:
• Sampling errors that occur by chance
• Sample bias, which stems from inadequate design
What Inferential Statistics Do
Since sample bias is a problem with the research design,
inferential statistics does not attempt to correct it.
The statistics are instead used to address sampling
errors, and they are typically used to test hypotheses.
The calculations help in determining the probability and
margin of error, which are important in accepting or
rejecting hypotheses. If the value of probability is
smaller than required, the hypothesis is rejected
because it means the sample is not truly representative
of the population. The probability or p value gives an
estimate of how often the results can be obtained by
chance if the hypothesis used is true.
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Inferential statistics analyze at least two variables,
and the types of variables determine the type of
inferential statistics applied. The type of analysis
using two variables is known as bivariate analysis while
that using more than two variables is called
The statistics help researchers determine how strong the
relationship between independent and dependent variables
is. If a hypothesis positively relates wages to age, for
example, age will be the independent variable while
wages will be the dependent variable.
Types and Examples of Variables
• Ratio/Interval, such as wage or age
• Nominal, such as gender
• Ordinal, for example class grades
Common types of tests include:
• Analysis of Variance
• Analysis of Covariance
• Cluster Analysis
• Factor Analysis
• Discriminant Function Analysis
• Multidimensional Scaling
Major inferential statistics are in a family of
statistical model called General Linear Model.
When Can Inferential Statistics be used?
• When there is a complete list of members of a
• When researchers take a random sample from the
• When the researchers can determine that the sample
size is sufficiently large using pre-established formula
While there are various types of inferential statistics,
they all determine how different variables compare to
one another. Calculations can be done either by hand or
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