Expected Counts and Chi-Squares
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Expected counts are predictors as to what
should happen.
If the observed counts (real data) is far from
the expected counts, there is evidence
against Ho.
Remember, with Ho, there is no association
between the treatment and the success of the
treatment.
In order to see of it is “too far”, you will need
to calculate the “chi-square statistic”…
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You will use this value and table 10.1 to
determine if there is evidence against the null
hypothesis.
◦ 1.Determine the degrees of freedom (see next
slide).
◦ 2.Look at table 10.1 for the row showing that
degree of freedom and look for a value nearest
your chi-square value. Your value must be larger
than the table value.
◦ 3.When you find the correct value, your answer will
be “P < _____” (the significance value for where
your value was located).
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All density curves are right skewed (most data
is on the left, tail on the right).
All data must be positive.
The distribution of the data is specified by
the degrees of freedom, which is calculated
by multiplying (rows – 1) x (columns – 1).
Degrees of freedom describe the number of
free choices left after a sample statistic is
calculated. (Lot of categories = lot of choices
= higher degree of freedom (df)).
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The higher the
number, the more
spread out the
density curve is.
The curve becomes
less skewed and
larger values
become more
probable.
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Df = 3, chi-square statistic = 13.
Your p-value will be less than 0.01.
Df = 5, chi-square statistic = 13.
Your p-value will be less than 0.05
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You may have no more than 20% of the
expected counts with values less than 5.
All individual counts must be of the value 1
or more.
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1. Write the null and alternative hypotheses
for the question of interest.
2. Who is the population?
3. Find the expected count for each cell.
4. Calculate the Chi-Square Statistic and
determine the degrees of freedom and PValue.
5. Write your conclusion from this study in
plain language.
See
the worksheet
being handed out
to you.