Transcript Chi-Square Test of Independence in SPSS (4)

Chi-square Test of Independence
Steps in Testing Chi-square Test of
Independence Hypotheses
Chi-square Test of Independence
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The chi-square test of independence is a statistical
test to determine whether there is a statistically
significant association between variables (mostly
categorical).
This test is probably the most frequently used
hypothesis test in the customer research and
marketing.
Independence Defined
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Two variables are independent if, for all cases, the
classification of a case into a particular category of
one variable has no effect on the probability that the
case will fall into any particular category of the
second variable (the test variable).
When two variables are independent, there is no
relationship between them. We would expect that
the frequency breakdowns of the test variable to be
similar for all groups.
Independence Demonstrated
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Suppose we are interested in the relationship
between dropouts and loan type.
If there is no relationship between dropouts and loan
type and 30% of our total sample has Individual Loans
(and 70% Group Loans), we would expect 30% of the
dropouts in our sample has Individual Loans and 30%
of the active clients has Individual Loans.
If there is a relationship between dropouts and loan
size, we would expect a higher proportion of
dropouts has Individual Loans, for example 80% IL .
Expected Frequencies versus Observed
Frequencies, Null Hypothesis
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The chi-square test of independence plugs the
observed frequencies and expected frequencies into a
formula which computes how the pattern of observed
frequencies differs from the pattern of expected
frequencies.
The null hypothesis is that the variables are
independent. This will be true if the observed counts
in the sample are similar to the expected counts. The
alpha level of significance is either 0.05 or 0.01.
Decision and Interpretation
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If the probability of the test statistic is less than or
equal to the probability of the alpha error rate, we
reject the null hypothesis. We conclude that there is
a relationship between the variables.
If the probability of the test statistic is greater than
the probability of the alpha error rate, we fail to
reject the null hypothesis. We conclude that there is
no relationship between the variables, i.e. they are
independent.
Which Cell or Cells Caused the Difference
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We are only concerned with this procedure if the
result of the chi-square test are statistically
significant.
One of the problems in interpreting chi-square tests
is the determination of which cell or cells produced
the statistically significant difference.
How we determine?
Standardized Residuals
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SPSS prints out the standardized residual (converted
to a z-score) computed for each cell.
Compare the size of the standardized residuals to
the critical values that correspond to an alpha of
0.05 (+/-1.96) or an alpha of 0.01 (+/-2.58).
Interpreting Standardized Residuals
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Standardized residuals that have a positive value
mean that the cell was over-represented in the
actual sample, compared to the expected frequency,
i.e. there were more subjects in this category than
we expected.
Standardized residuals that have a negative value
mean that the cell was under-represented in the
actual sample, compared to the expected frequency,
i.e. there were fewer subjects in this category than
we expected.