Understanding and Interpreting
the Chi-square Statistic (x2)
Rose Ann DiMaria, PhD, RN
WVU-School of Nursing
Charleston Division
Inferential statistics
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Make judgments about accuracy of
given sample in reflecting
characteristics of population from
which it was drawn
Used in testing hypothesis
Hypothesis testing
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Ability of statistics to help us make
decisions about which study outcomes
reflect fluke differences between groups
and which ones reflect true differences
Types of Statistical Tests
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Parametric: based on distributions and
assumptions
Non-parametric: distribution free and
less assumptions
Hypothesis
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Research Hypothesis: prediction of the
relationship between variables
Statistical Hypothesis:
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Every statistical test has a null and an alternate
hypothesis
Null hypothesis: No difference in the groups under
study (Null= no=Nada).
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Stats used to reject the null, showing a difference exists
Most often researchers want to reject the null hypothesis
when conducting a study, to show a difference
However, researchers can design a study to accept the
null hypothesis
Accepting or Rejecting the Null
„
Alpha level or significance level
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Always determined a priori
Usually set at the 0.05 level
IF p< 0.05 then reject the null
hypothesis, and accept the alternate
(There is a difference)
IF p > 0.05 then accept the null
hypothesis (There is no difference)
Chi-square Statistic
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Tests the Hypothesis of Independence
Non-parametric test-used when data
analyzed are not assumed to reflect a normal
distribution and when they are measured at
either the nominal or ordinal level.
Used when researchers are interested in the
number of participants or events that fall
within specified categories
x2
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Chi-square statistic does not give any
information about the strength of the
relationship
Only conveys the existence or
nonexistence of the relationships
between the variables investigated.
Assumptions of Chi-square
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Use of frequency data
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Categories are mutually exclusive
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Represents the actual number of subjects or
elements in each category
Only be in one cell and can’t overlap
Theoretical basis for categorization of
variables
Use nominal (categorical) data
Expected counts must be > 5 and none less
than 1
What does the chi-square test
do?
„
Compares counts, not means
Types of chi-square tests
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One sample
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Interested in the number of counts,
responses, objects or subjects that fall into
two or more categories
Independent Sample
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Used to determine if two categorical
variables are independent of each other
Contingency Table 2 x 2 Blood glucose
level by intervention group
Average blood
Average blood
glucose less than glucose greater
120 mg/dl
than or equal to
120 mg/dl
Experimental
25
group (6 sessions
with RD for meal)
10
Control group
Customary pt ed
25
10
An example
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RQ: Do men eat alone more frequently than
women?
RH: At the .05 sig level, men will respond yes
more frequently than women to the question
“Do you eat alone most of the time?”
For this RH and RQ we want to reject the
null, with a p< 0.05, and hope that the
percentage of men eating alone is greater
than the percentage of women eating alone.
Poll Questions
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Variables: Gender (male, female)
Eat alone: (Yes or No)
Type of Contingency table: 2 x 2
(gender by eating alone)
Null hypothesis: Eating alone is
independent of sex
Alternate hypothesis: Eating alone is
not independent of sex.
Can we run a x2
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Are the variables at the appropriate
level?
Do the subjects fit into only one cell?
Are the levels of each category mutually
exclusive?
Are expected counts of each cell > 5
and none less than 1?
Eat
alone
No
Yes
Total
Sex
Males
57 (93.4%)
Females
15 (50%)
72
4 (6.6%)
61
15 (15%)
30
19
91
Pearson chi-square =22.974 (1) , p=.0005
Total
Poll
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Accept or reject the null?
Does this support the research
question?
Turn to the Heye article
„
Which table do you think chi-square
statistics could be used and why?
Treatment control
age
21-40
14 (20%)
17 (24%)
41-60
19 (27%)
17 (24%)
61-70
2 (3%)
1(1%)
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Many times chi-square test performed
on the demographic characteristics of
the sample.
Do you think you would want
significance? Why or why not?
In results section find two places
that discuss the chi-square
Ready to go
home not
today
Ready to go
home today
Control
Intervention
12
25
Control
Use of breathing
movements not
every time
Intervention
97.1%
Use of breathing 2.9%
movements every
time
100%
Questions?