Chapter 5
Overview of
Inferential Statistics
Why do we need inferential
statistics?

Typically, we are interested in the
population, not the sample
– When we study an intervention, for
example, we want to be able to generalize
to the larger group (the population)
– But we usually can’t gather the whole
population of scores
Why do we need inferential
statistics?

Variability
– Remember that measurements in the
sciences are variable; they change from
observation to observation
– We need inferential statistics to assess
this variability and aid in our decision
making
What do we learn from
inferential statistics?
Inferential statistics provides us with
educated guesses about quantitative
characteristics of populations
(“parameters”)
 For example, is the central tendency of
one group different than the central
tendency of a second group

Varieties of Inferential
Procedures
Parameter estimation – using data
from a random sample to estimate a
parameter of the population from which
the sample is drawn
 Hypothesis testing – formulating
opposing hypotheses and determining
from samples which is most likely
correct

Hypothesis Testing
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This may seem to be overly complicated, but
It provides an elegant way of answering
research questions
For example, we may want to determine
which of these two hypotheses is correct:
– 1. The whole language teaching method
improves reading scores
– 2. The whole language teaching method does
not improve reading scores
We may be able to learn how
best to teach children to read.
Parameter Estimation vs.
Hypothesis Testing
By using inferential procedures, we
can learn from data and make
decisions about important features of
our world, like which method to use to
teach children to read
 Even though we may have little interest
in estimating the parameters of the
population

Types of Hypothesis Testing

Parametric hypothesis tests – tests
about specific population parameters,
usually mean or variance
– Since parametric tests generally require
computation of mean and variance, these
tests are only appropriate for interval or
ratio level data
Types of Hypothesis Testing

Non-Parametric hypothesis tests –
tests about the shape or location of the
population
Random Sampling
Inferential statistical procedures will
only yield accurate predictions when
they are based on Random samples
 Inferential statistics depend on
probability theory which requires
random samples

Random Sample

A Random Sample is one which has
been obtained such that
– 1. each observation has an equal chance
of being included in the sample, and
– 2. the selection of one observation does
not influence the selection of any other
observation
How to create a Random
Sample
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Place all the measurements in a population
into a hat,
Close your eyes, reach in the hat, and
Select one slip of paper
Return the slip of paper to the hat, mix and
Repeat
But this is not
very practical
Creating a Random Sample
with a random number table


Using a random number table, like Table H
in the text book, requires that you assign
every observation a number (from 1 to N)
Going down the columns of Table H, your
sample will use those observations
associated with the numbers you encounter
in the column
Creating a Random Sample
with a random number
generator

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With computers, however, Tables are no
longer needed
Many computer programs use algorithms for
generating random numbers
Excel, for example, has several functions
(e.g., RAND, RANDBETWEEN) that can
help you generate random numbers
Biased Samples

Procedures that do not produce
Random samples are those that
produce Biased samples
– Telephone polls exclude people that do
not own a telephone
– Magazine surveys exclude those that
don’t read that magazine
– Website samples don’t include people
that frequent that website
Overgeneralizing

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Inferential statistics require random samples
However, inferences require care and
should be restricted to the population
sampled
When a researcher does not adequately
restrict their conclusions to the population
sampled, but goes “too far” we term this
problem “overgeneralizing”
Or drawing an inference to a population
other than the one randomly sampled