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N318b Winter 2002
Nursing Statistics
Lecture 7
Specific statistical tests
Chi-square (2)
Today’s Class
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5 basic statistical tests covered in course
Parametric and non-parametric tests
Degrees of freedom
<< 10 min break >>
Example of chi-square test
Applying knowledge to assigned readings
Turk et al. (1995)
Followed by small groups 12-2 PM
Focus on interpreting chi-square results
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 6: page 2
“In Group” Session
Missing
Table 1
Focuses on an assigned reading.
Q1 example of the chi square test
Q2 example of the chi square test
Q3 criteria for non-parametric test
Key points from the Turk et al paper will
be covered in the 2nd part of the lecture
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 6: page 3
New Lecture Material
Specific statistical tests:
Parametric and nonparametric tests
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 6: page 4
Specific Statistical Tests
Course will cover five major “tests”:
1. Chi-square (2)
2. T-tests
3. Analysis of variance (ANOVA)
4. Correlation
5. Regression
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 6: page 5
Statistical Tests – cont’d
All these tests do basically the same 3 things:
1. Compare 2 or more study groups to each
other (or one group to a reference group)
2. Generate a “test statistic” whose value
increases as difference between groups
increases (i.e. larger values more significant)
3. “test statistic” follows known distributions
such that the probability of its value occurring
can be determined (i.e. its “p-value”)
Example: Z-scores
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 6: page 6
Statistical Tests – cont’d
How do you known when to use which test?
Helps to ask some basic questions:
1. What kind of data are used?
- ratio/interval or categorical (ordinal/nominal)
- dependent (e.g. follow-up) or independent
2. What kind of relationship is of interest?
- prediction, association or difference?
3. How many groups (samples) involved?
- one, two, or more than two
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 6: page 7
Non-Parametric Tests
Key point is determining type of data
For categorical (i.e. either nominal or
ordinal data) the normal distribution is
generally not applicable and population
descriptors (parameters) cannot be
estimated so non-parametric tests used
Main non-parametric test is the chi-square
test that compares expected (E) numbers
with actual or observed (O) numbers
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 6: page 8
Parametric Tests
For continuous (i.e. either interval or
ratio data) the normal distribution applies
and population descriptors (parameters,
like means) can be estimated thus
parametric tests are used instead
Main tests for this course include the t-test,
paired t-test and analysis of variance
(ANOVA), all of which test means
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 6: page 9
Parametric vs. nonparametric tests
Data used
Nonparametric
(numbers,
%’s)
Parametric
(means,
variances)
Examples
Nominal,
Chiordinal
square
(categorical)
Comments
Easy to use
but limited to
simple
situations
Interval,
T-tests,
More flexible
ratio
ANOVA,
and powerful
(continuous) regression (also more
convincing)
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 6: page 10
Degrees of Freedom
Recall the formula for SD was “adjusted”
for imprecision of small samples
SD =
(x)2
n -1
The (n-1) term is referred to as “degrees of
freedom” since it indicates how many ways
that the data can vary in a sample
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 6: page 11
Degrees of Freedom – cont’d
Value of “test statistic” derived from
many statistical tests is dependent on
this idea of “degrees of freedom” thus
some sense of what it means is useful
(e.g. see textbook page 84-85)
df = number of ways that data
can vary (or be categorized)
Example – for chi square test:
df = (number of categories –1)
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 6: page 12
Degrees of Freedom – cont’d
Example – for chi square test:
df = (number of categories –1)
Why?
If total number of subjects is known, and
they are categorized into 4 groups, then if
three tallies are known the fourth is “fixed” –
i.e. it can be derived so it is not “free” to vary
df = (4 –1) = 3
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 6: page 13
Chi square (2) test
How do you known when to use 2 test?
Referring back to the 3 “basic questions”:
1. What kind of data are used?
- categorical ( typically nominal)
- frequencies (i.e. counts or percentages)
- data can be put in a “contingency table”
2. What kind of relationship is of interest?
- association or difference
3. How many groups (samples) involved?
- usually two or more (“smallish” number)
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 6: page 14
Chi square test - example
One of the most common statistical tests !
Example: We suspect that students at UWO
love statistics a lot so we ask 100 nursing
students if they really like Nur 318b?
63 say YES, 37 say NO
Is this more than we might have expected –
i.e. are UWO nurses crazy about statistics?
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 6: page 15
Chi square test - example
If we did not think students would be more
or less likely to enjoy the course, we would
EXPECT 50 to say no and 50 to say YES
Study hypotheses
H0: no difference in OBS versus EXP counts
Ha: OBS count is NOT equal to EXP
2 compares observed vs expected numbers
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 6: page 16
Chi square test - example
YES NO
at UWO
(observed)
67
In general
(expected)
50
=
33
2
50
(67-50)2 + (33-50)2
50
= (O-E)2
E
= 11.56
50
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 6: page 17
Chi square test - example
As with Z-scores, we now look this number
(11.56) up in a table of critical values, in this
case for the chi square distribution
(table value is the probability that observed
and expected numbers are the same)
2 (1 df) = 11.56, p < 0.001
Thus we can conclude that UWO
nursing students must love stats !!!
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 6: page 18
10 minute break !
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 6: page 19
Chi square test - assumptions
1. Data are counts, frequencies, percentages
2. Smallest table cell counts ideally >5
3. Data in rows and columns are independent
(i.e. subjects can be in one table cell only)
4. Categories or levels set BEFORE testing
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 6: page 20
Chi square test - assumptions
Why is the chi square a nonparametric
statistical test?
1) it does not assume data are normally
distributed (in fact NO assumptions are
needed about underlying distribution)
2) categorical/nominal data are used
3) not estimating a population characteristic
(i.e. a parameter, like the mean)
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 6: page 21
Part 2:
Application to the
Assigned Readings
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 6: page 22
Turk et al. (1995)
Quick summary of the paper:
– a cross-sectional study examining the
cognitive-behavioral mediation model of
depression in chronic pain patients
– 100 chronic pain subjects divided into
two groups: 73 randomly chosen younger
(<70); and 27 older (70 yrs) patients
– found a strong link between pain and
depression for older subjects but not for
younger ones (i.e. an age effect)
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 6: page 23
Some design issues?
Do you have any concerns with design of the
study – e.g. using a cross-sectional design to
examine chronic pain and depression?
Which came first (“chicken-and-egg”)?
Can pain be more of “social” problem
with older people thus “confounding”
assessment of depression?
Was assessment of depression “blinded”?
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 6: page 24
Chi square test – example 2:
the contingency table
Observed counts from Table 1
Gender
young
old
Total
Male
45.21
(33)
37.04
(10)
43
54.79
(40)
100%
(73)
62.96
(17)
100%
(27)
Female
Total
57
100
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 6: page 25
Chi square test – example 2:
the contingency table
How did we get counts from %’s?
Just multiply % by total number in group
e.g. 45.21% male in younger group is
equal to 0.4521 x 73 = 33 males
How do we get expected counts?
Expected counts assume no association
between groups thus they are calculated
according to size of cells in groups
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 6: page 26
2 Contingency Table
Expected counts
Eij =
Ri x Cj
N
For cell 1,1:
E11 =
R1 x C1
100
For cell 1,2 = 11.6
43 x 73
=
= 31.4
100
For cell 2,2 = 15.4
For cell 2,1 = 41.6
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 6: page 27
2 Contingency Table
Expected counts
C1
R1
R2
C2
Gender
young
old
Total
Male
33
(31.4)
10
(11.6)
43
40
(41.6)
73
17
(15.4)
27
57
100
Female
Total
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 6: page 28
2 Contingency Table
Test statistic
2 = (O-E)2
E
2 + (10-11.6)2 + (40-41.6)2 + (17-15.4)2
(33-31.4)
=
31.4
11.6
41.6
15.4
2 (1 df) = 0.54, p > 0.20
Can’t reject null hypothesis, thus no association !
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 6: page 29
Next Week - Lecture 8:
T-test
For next week’s class please review:
1. Page 16 in syllabus
2. Textbook Chapter 4, pages 97-107
3. Syllabus paper:
Turk et al. (1995)
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 6: page 30