Transcript Main presentation title goes here.

Comparing Proportions &
Analysing Categorical Data
Scott Harris
October 2009
Learning outcomes
By the end of this session you should be able to choose between,
perform (using SPSS and CIA) and interpret the results from the
following methods of analysing categorical data:
– A test for association or independence (Chi-square or
Fisher’s exact test).
– A test for assessing if a sample proportion differs from a
specified proportion (Chi-square).
– A test for a change in categorical response (McNemar’s test).
– A test of agreement of categories between 2 raters (Kappa
test).
You should also be aware of the concept of odds, odds ratios
and how to calculate them from a 2x2 table.
2
Contents
• Introduction
– Refresher - types of data.
– Data requirements.
– The example dataset: CISR data.
• Association between 2 variables
– Test information.
– ‘How to’ in SPSS and CIA.
• One sample versus a specified proportion
– Test information.
– ‘How to’ in SPSS and CIA.
3
Contents
• Change in response
– Test information.
– ‘How to’ in SPSS and CIA.
• Quick crosstabs
– Summary Data tables in SPSS: ‘How to’
• Agreement between 2 raters
– Test information.
– ‘How to’ in SPSS and CIA.
4
Refresher: Types of data
• Quantitative – a measured quantity.
– Continuous – Measurements from a continuous scale:
Height, weight, age.
– Discrete – Count data: Children in a family, number of days
in hospital.
• Qualitative – Assessing a quality.
– Ordinal – An order to the data: Likert scale (much worse,
worse, the same, better, much better), age group (18-25, 2630…).
– Categorical / Nominal – Simple categories: Blood group (O,
A, B, AB). A special case is binary data (two levels): Status
(Alive, dead), Infection (yes, no).
5
Data requirements
• The Statistical tests that will be covered in this talk compare a
sample with a categorical outcome against either:
– a published or hypothesised proportion,
– another group / another category or multiple categories,
– a repeated categorical outcome from the same individual,
– another measurement of the same outcome from another
source or
– a gold standard ‘true’ outcome.
• A different type of test / method is used in each of the situations
above.
6
Example dataset: Information
CISR (Clinical Interview Schedule: Revised) data:
– Measure of depression – the higher the score the worse the
depression.
– A CISR value of 12 or greater is used to indicate a clinical
case of depression.
– 3 groups of patients (each receiving a different form of
treatment: GP, CMHN and CMHN problem solving).
– Data collected at two time points (baseline and then a followup visit 6 months later).
– An additional reading at 6 months was taken by another
researcher.
7
Example CISR dataset: Raw data
8
Example CISR dataset: Labelled data
9
Association / Independence
(Difference in proportions)
Chi-square test or
Fisher’s exact test
Chi-square statistic
• The most common statistic used when dealing with categorical
data. Alongside the t test this is the most often seen statistical
technique.
2
χ
• The Chi-square ( ) or Pearson Chi-squared statistic compares
the observed proportion of a categorical response with an
expected value.
• The null hypothesis (as always) is that there is no difference or
no association between the variables (depending on the context).
• As the difference between these observed and expected values
increases then the evidence supporting a difference or an
association builds up.
11
Theory: Chi-square statistic
The following equation is used to calculate the chi-square statistic:
χ 
2
O bse rve d Expe cte d
2
Expe cte d
Observed =
The actual count in each cell.
Expected =
The number expected to be in each cell of the
table if the test proportion was true or the rows and
columns were unrelated / independent (i.e. assuming
no difference in response).
This is distributed with (n1-1) x (n2-1) degrees of freedom.
Number of levels for column variable
Number of levels for row variable
12
Chi-square statistic: Example
We want to see if Gender is associated with Clinical status at 6 months
Table of Observed values for Clinical status at 6
months, split by Gender
Clinical case
Non case
Total
Male
15
22
37
Female
24
48
72
Total
39
70
109
13
Theory: Chi-square statistic
Table of Observed values (Expected values)
Clinical case
Non case
Total
Male
15 (13.24)
22 (23.76)
37
Female
24 (25.76)
48 (46.24)
72
39
70
109
Total
The expected values are produced by multiplying together the 2 marginal
totals and then dividing by the grand total.
For Male clinical cases: 37 x 39 = 1443
,
1443 / 109 = 13.24 (2dp)
14
Theory: Chi-square statistic
χ2  
Observed Expected2
Expected
For Male clinical cases:
(15 - 13.24)2 / 13.24 = 3.0976 / 13.24 = 0.23 (2dp)
For Male non cases:
(22 – 23.76)2 / 23.76 = 3.0976 / 23.76 = 0.13 (2dp)
For Female clinical cases:
(24 – 25.76)2 / 25.76 = 3.0976 / 25.76 = 0.12 (2dp)
For Female non cases:
(48 – 46.24)2 / 46.24 = 3.0976 / 46.24 = 0.07 (2dp)
Chi-square statistic = 0.23 + 0.13 + 0.12 + 0.07 = 0.552 (3dp)
15
Chi-square alternative: Fisher’s exact test
• The chi-square test is only appropriate when the sample size is
large enough that there are no ‘rare’ combinations of categories
in the cross-tabulation.
• The definition of ‘rare’ is that the expected counts for all of the
cells in the table need to be at least 5.
• If at least one of the cells in the table has an expected count <5
then the Pearson Chi-square statistic should not be reported and
an alternative test called Fisher’s exact test should be used
instead.
• Fisher’s exact test is an exact permutation test for categorical
variables. It is convention to only use Fisher’s exact test when
Pearson’s Chi-square is not appropriate.
16
Chi-square statistic: SPSS
* Chi-square test for Sex and M6Cat .
CROSSTABS
/TABLES=SEX BY M6Cat
/FORMAT= AVALUE TABLES
/STATISTIC=CHISQ
/CELLS= COUNT ROW
/COUNT ROUND CELL .
Analyze  Descriptive statistics  Crosstabs…
17
Chi-square statistic: Output
2x2 cross tabulation with
suitable percentages (as
we are comparing the two
genders here we use row
percentages).
SEX * M6Cat Crosstabulation
SEX
Male
Female
Total
Count
% within SEX
Count
% within SEX
Count
% within SEX
M6Cat
Non case
Clinical case
22
15
59.5%
40.5%
48
24
66.7%
33.3%
70
39
64.2%
35.8%
Total
37
100.0%
72
100.0%
109
100.0%
Pearson Chi-square p value = 0.457
Chi-Square Tests
Pearson Chi-Square
Continuity Correction a
Likelihood Ratio
Fisher's Exact Test
Linear-by-Linear
Association
N of Valid Cases
Value
.552b
.283
.548
df
1
1
1
Asymp. Sig.
(2-sided)
.457
.595
.459
Exact Sig.
(2-sided)
Exact Sig.
(1-sided)
.529
.547
1
.459
.296
Fisher’s exact test p value
= 0.529
(Notice how only the
2-sided tests are
considered.)
109
a. Computed only for a 2x2 table
b. 0 cells (.0%) have expected count less than 5. The minimum expected count is 13.
24.
18
Fisher’s exact test: Table > 2 x 2
Everything should be set up as before, with the following
additional option:
19
Chi-square statistic: 3 x 2 Output (Exact)
TMTGR * B0Cat Crosstabulation
TMTGR
GP
CMHN
CMHN PS
Total
Count
% within TMTGR
Count
% within TMTGR
Count
% within TMTGR
Count
% within TMTGR
B0Cat
Non case
Clinical case
3
25
10.7%
89.3%
1
39
2.5%
97.5%
3
38
7.3%
92.7%
7
102
6.4%
93.6%
Total
28
100.0%
40
100.0%
41
100.0%
109
100.0%
Pearson Chi-square p value = 0.380
Fisher’s exact test p value
= 0.379
Chi-Square Tests
Pearson Chi-Square
Likelihood Ratio
Fisher's Exact Test
Linear-by-Linear
Association
N of Valid Cases
Value
1.937a
2.091
2.025
b
.170
Exact Sig.
(2-sided)
.426
.426
.379
Exact Sig.
(1-sided)
2
2
Asymp. Sig.
(2-sided)
.380
.351
1
.680
.808
.430
df
3x2 cross tabulation with
suitable percentages (as
we are comparing the
treatment groups here we
use row percentages).
Point
Probability
.176
(Again notice how only
the 2-sided tests are
considered.)
109
a. 3 cells (50.0%) have expected count less than 5. The minimum expected count is 1.80.
b. The standardized statistic is .413.
20
Info: Chi-square in SPSS
1) From the menus select ‘Analyze’  ‘Descriptive Statistics’ 
‘Crosstabs…’.
2) Put one of your categorical variables into the ‘Row(s):’ box and
the other into the ‘Column(s):’ box.
3) Click the ‘Cells…’ button and then select the box for any
percentages that you require. Then click the ‘Continue’ button.
4) Click the ‘Statistics…’ button and tick the option for ‘Chisquare’. Then click the ‘Continue’ button.
5) If your table will be bigger than a 2x2 then click the ‘Exact…’
button and tick the option for ‘Exact’. Then click the ‘Continue’
button.
6) Finally click ‘OK’ to produce the cross tabulation with the Chisquare statistic or ‘Paste’ to add the syntax for this into your
syntax file.
21
Theory: Options for a 2 x 2 table
Female
Male
Non
case
Clinical
case
Total
48
24
72
(a)
(b)
(a+b)
22
15
37
(c)
(d)
(c+d)
1.
Difference in proportions
(absolute difference):
d/c  d  ba  b
2.
Both the Chi-square test and Fisher’s
exact tests are tests for association
3.
between the two independent variables.
They do not quantify the effect size. For a
2 x 2 table there are a number of options
that you can use to quantify effects, each
of which has pros and cons.
Relative risk (multiplicative
difference):
d/c  d
b/(a  b)
Another common alternative is
the Odds ratio:
d/c a  d

b/a b  c
22
Theory: Odds and odds ratios
Female
Male
Non
case
Clinical
case
Total
48
24
72
(a)
(b)
(a+b)
22
15
37
(c)
(d)
(c+d)
Outcome of interest:
Clinical case
Odds for Females = b/a
Odds for Males = d/c
Odds ratio :
d/c a  d

b/a b  c
Odds are a tricky topic for some to
understand, but easy for others.
They are most commonly
encountered in gambling situations.The odds for females being a clinical
case are 24 to 48 or 1 to 2. For females, you would expect 1 clinical case for
every 2 non cases. Odds ratios are simply the ratio of the 2 odds (1 divided
by the other).
23
Theory: Odds and odds ratios
Outcome of interest:
Clinical case
Odds for Females = b/a = 24/48 = 0.5
This is often reported
as 2 to 1 against in
gambling situations.
Odds for Males = d/c = 15/22 = 0.68 (2dp)
d/c a  d
Odds ratio :

= 0.68 / 0.5 = 1.36 (2dp)
b/a b  c
The odds of being a clinical case are 1.36 times larger for Males than
Females. Here we have taken females as the reference category (we have
divided by the female result) thereby getting the relative ‘increase’ in odds
for being male.
Odds ratios are produced in logistic regression
24
Reminder: 95% confidence intervals in CIA
Always check that you are producing 95% CI’s:
 Options menu in CIA
25
Difference in proportions: CIA Example
Methods  Proportions and their differences
 Unpaired samples
26
Difference in proportions: CIA Example
It is Easiest to have the group with the largest
‘feature’ proportion as Sample 1. This will produce
a positive difference.
27
Difference in proportions: CIA Example
Observed proportions
and difference in
proportions
95% confidence interval. (This
CI includes 0, therefore
agreeing with the earlier p
value from SPSS)
28
Chi-square statistic: Presentation
Table 1: Frequency table of clinical status by gender.
Figures are number (percentage).
Gender
Clinical case
Non case
Male
15 (40.5%)
22 (59.5%)
Female
24 (33.3%)
48 (66.7%)
There was found to be no significant difference (Pearson Chi
square: p = 0.457) in the proportions of clinical cases, in male
and female patients (Difference 7.2%, 95% CI: -11.1% to
25.9%).
29
One sample vs. a
specific proportion
Chi-square test or
Exact test
Chi-square statistic for one variable
• In the same way that the chi-square test can be used
when you have larger than a 2 x 2 table, it can also be
used when you have a n x 1 table.
• In this situation you are testing whether the
proportion of some event (or events) that you have
seen are different to a value that you specify.
• In this case the expected values are calculated from
the specified proportion(s) but in all other regards the
test is computed in the same way.
31
One variable Chi-square: Example
* Chi-square test for B0cat vs. 0.1 / 0.9 .
NPAR TEST
/CHISQUARE=B0Cat
/EXPECTED=0.1 0.9
/MISSING ANALYSIS
/METHOD=EXACT TIMER(5).
The specified proportions are entered
here, the ordering is important and is
dependent on how the variable was
set up.
Analyze  Nonparametric tests  Chi-square…
32
Info: One variable Chi-square in SPSS
1) From the menus select ‘Analyze’  ‘Nonparametric tests’ 
‘Chi-square…’.
2) Put your categorical variable into the ‘Test variable list:’ box.
3) Either specify expected proportions one at a time in the
‘Values’ box (in the order of the levels in the categorical
variable), each time clicking the ‘Add’ button or leave the test
to compare against equal proportions.
4) Click the ‘Exact…’ button and tick the option for ‘Exact’. Then
click the ‘Continue’ button.
5) Finally click ‘OK’ to produce the one variable Chi-square
statistic or ‘Paste’ to add the syntax for this into your syntax
file.
33
One variable Chi-square: Output
B0Cat
Non case
Clinical case
Total
Observed N
7
102
109
Expected N
10.9
98.1
Residual
-3.9
3.9
The number of observed
frequencies in each category as
well as the expected number if
the specified proportions of 0.1
and 0.9 were true.
Pearson Chi-square p value = 0.213
Test Statistics
Chi-Squarea
df
Asymp. Sig.
Exact Sig.
Point Probability
B0Cat
1.550
1
.213
.263
.064
Exact test p value = 0.263
a. 0 cells (.0%) have expected frequencies less than
5. The minimum expected cell frequency is 10.9.
34
Single sample Chi-square: CIA Example
Methods  Proportions and their differences
 Single sample
35
Single sample Chi-square: CIA Example
Decide on which proportion you would like to
produce the confidence interval for by setting
that as the ‘feature’.
36
Single sample Chi-square: CIA Example
Observed proportion
95% confidence interval (This CI
includes 0.9, therefore agreeing with
the earlier p value from SPSS)
37
Test for change in
paired proportions
McNemar test
The McNemar test
• When you have paired or repetitious binary categories then the
Chi-square test is no longer appropriate and you should make
use of an alternative test known as the McNemar test.
• An example of this type of data are the binary clinical case
variables in the example dataset. Here we have the same
information on an individual at both baseline and 6 months.
These readings are paired categorical results.
• The McNemar test looks at whether there has been a significant
shift in state in the two paired results.
• The focus of this test is whether there is a large shift in one
direction rather than the other, as well as how much change
there has actually been in the paired results.
39
Theory: McNemar test
Looking at the example cross tabulation on
the right then:
– The empty cells of the table indicate
where there is no change / difference in
outcomes 1 and 2.
– The solid red cell indicates those who
didn’t have the outcome at time 1, but
did have it at time 2.
– Vice versa the red striped cell indicates
those who had the outcome at time 1,
but not at time 2.
If both of the coloured cells are sufficiently
small in proportion then there has been little
change in response. Likewise if the
proportion in each of the shaded cells is
similar, then overall there has been little
change in response direction.
Outcome
at time 2
No
outcome
at time 2
Outcome
at time 1
No
outcome at
time 1
McNemar’s test takes both of these into account
40
McNemar test: Example
Analyze  Descriptive statistics
 Crosstabs…
* McNemar test for B0Cat and M6Cat .
CROSSTABS
/TABLES=B0Cat BY M6Cat
/FORMAT= AVALUE TABLES
/STATISTIC=MCNEMAR
/CELLS= COUNT TOTAL
/COUNT ROUND CELL .
41
Info: McNemar in SPSS
1) From the menus select ‘Analyze’  ‘Descriptive Statistics’ 
‘Crosstabs…’.
2) Put one of your paired categorical variables into the ‘Row(s):’
box and the other into the ‘Column(s):’ box.
3) Click the ‘Cells…’ button and then select the box for ‘Total’
percentages. Then click the ‘Continue’ button.
4) Click the ‘Statistics…’ button and tick the option for
‘McNemar’. Then click the ‘Continue’ button.
5) Finally click ‘OK’ to produce the cross tabulation with the
McNemar statistic or ‘Paste’ to add the syntax for this into your
syntax file.
42
McNemar statistic: Example
B0Cat * M6Cat Crosstabulation
B0Cat
Non case
Clinical case
Total
Count
% of Total
Count
% of Total
Count
% of Total
M6Cat
Non case
Clinical case
6
1
5.5%
.9%
64
38
58.7%
34.9%
70
39
64.2%
35.8%
Total
7
6.4%
102
93.6%
109
100.0%
2x2 cross tabulation with
overall percentages.
From the above table we can see that 58.7% of the total sample
were clinical cases at baseline and became non cases by 6 months,
whereas only 0.9% initially were non cases and became cases.
Chi-Square Tests
Exact Sig.
(2-sided)
.000a
Value
McNemar Test
N of Valid Cases
109
a. Binomial distribution used.
McNemar test p value: p <0.001
43
McNemar test: CIA Example
Methods  Proportions and their differences
 Paired samples
44
McNemar test: CIA Example
There is an alternative Table view that may be
easier for entering data:
45
McNemar test: CIA Example
It is easiest to put the largest change proportion
into the bottom left corner of this table. In this
way you will get positive differences:
46
McNemar test: CIA Example
Observed difference
in proportions
95% confidence interval (This CI
excludes 0, therefore agreeing with the
earlier p value from SPSS)
47
McNemar test: Presentation
Table 2: Frequency table of change in clinical status.
Figures are number (total percentage).
6 month status
Baseline status
Clinical case
Non case
Clinical case
Non case
38 (34.9%)
64 (58.7%)
1 (0.9%)
6 (5.5%)
There was found to be a highly significant change in clinical status of
depression (McNemar: p < 0.001), from baseline to 6 months (Difference
57.8%, 95% CI: 47.0% to 66.5%) in favour of a lessoning of symptoms
(reduction of clinical cases).
48
Quick Crosstabs
Dealing with summary data in SPSS
Summary Data: SPSS
If you only have access to the cross-tabulated data (or
you only have to do one quick analysis) then rather
than having to enter one row of data for each
individual in the dataset you can enter it as a
summary data table.
A summary data table will only contain one row for
each cross combination in the table (one row per
table cell). The number of observations in that table
will not affect the amount of data entry.
Summary data tables can be used for any, all
categorical technique.
50
Summary Data: SPSS
• One variable in SPSS should contain the category of
the row from the table.
• Another variable should contain the category of the
column from the table.
• A third variable (Count) should contain the number of
observations in that combination of categories.
• Once the data are entered you will need to let SPSS
know that the data have been entered to represent
more than 1 observation per row. To do this you will
need to make use of the ‘Weight cases’ option.
• You can now analyse the data in the normal way.
51
Summary Data: Example
One of the crosstabs from earlier:
Table of Observed values for Clinical status at 6
months, split by Gender
Clinical case
Non case
Total
Male
15
22
37
Female
24
48
72
Total
39
70
109
52
Summary Data: SPSS
Warning displayed in bottom left
corner of data editor, when weight
cases is on.
* Weighting the summary data .
WEIGHT
BY Count .
Data  Weight cases…
53
Chi-square statistic: Summary Data
* Chi-square test for Sex and M6Cat .
CROSSTABS
/TABLES=Gender BY Clin_status
/FORMAT= AVALUE TABLES
/STATISTIC=CHISQ
/CELLS= COUNT ROW
/COUNT ROUND CELL .
Analyze  Descriptive statistics  Crosstabs…
54
Info: Summary data in SPSS
1) One variable in SPSS should contain the category of the row from the
table.
2) Another variable should contain the category of the column from the
table.
3) A third variable should contain the number of observations in that
combination of categories
4) From the menus select ‘Data’  ‘Weight cases…’.
5) Select ‘Weight cases by’.
6) Put the third variable that contains the number of observations for each
row into the ‘Frequency Variable:’ box.
7) Finally click ‘OK’ to weight the dataset or ‘Paste’ to add the syntax for
this into your syntax file.
8) You can now conduct your analysis in the usual way.
55
Summary Data: Example 2
The following table is a classification by two radiologists
of 85 xeromammograms (Boyd et al., 1982):
Radiologist B
Radiologist A
Normal Benign
Suspected
Cancer Total
cancer
Normal
21
12
0
0
33
Benign
4
17
1
0
22
Suspected cancer
3
9
15
2
29
Cancer
0
0
0
1
1
Total
28
38
16
3
85
56
Summary Data: SPSS
57
Summary Data: SPSS
Data  Weight cases…
* Weighting the summary data .
WEIGHT
BY Count .
Warning displayed in bottom left corner
of data editor, when weight cases is on.
58
Agreement between
two raters or devices
Kappa statistic
Kappa Statistic
• It is possible to assess the level of agreement between 2 raters or 2
methods (when the responses are categorical) by making use of the
Kappa statistic.
• The Kappa statistic looks at the observed proportion of agreeing
responses between the 2 raters and compares this to what may have
been expected just by chance alone.
• It is considered a better statistic than just looking simply at the percent
agreement as it takes into account agreement occurring simply by
chance.
• Kappa can be used for any size of data table and for either nominal or
ordinal categorical data. For ordinal data there is an alternative known
as Weighted Kappa but this cannot be computed easily in SPSS.
• The diagonal of the cross tabulation that indicates agreement between
the raters is known as the ‘diagonal’ and the other cells that indicate
disagreement are know as the ‘off diagonals’.
60
Kappa Statistic: Interpretation
In a similar approach as to that
used for correlation the
emphasis for a Kappa statistic is
not placed on the significance of
the p value but the actual value
of the Kappa statistic.
The table to the right is the
most common way of assessing
the strength of the agreement.
It simply involves looking up the
Kappa statistic in the table and
reporting the appropriate level
of agreement.
Kappa (2dp)
Strength of
agreement
≤ 0.20
Poor
0.21 to 0.40
Fair
0.41 to 0.60
Moderate
0.61 to 0.80
Good
0.81 to 1.00
Very good
(D G Altman, Practical Statistics for Medical
Research, 1999)
61
Kappa statistic: SPSS
* Kappa for M6Cat and M6Cat2 .
CROSSTABS
/TABLES=M6Cat BY M6Cat2
/FORMAT= AVALUE TABLES
/STATISTIC=KAPPA
/CELLS= COUNT TOTAL
/COUNT ROUND CELL .
Analyze  Descriptive statistics  Crosstabs…
62
Info: Kappa in SPSS
1) From the menus select ‘Analyze’  ‘Descriptive
Statistics’  ‘Crosstabs…’.
2) Put one of your paired categorical variables into the
‘Row(s):’ box and the other into the ‘Column(s):’
box.
3) Click the ‘Cells…’ button and then select the box for
‘Total’ percentages. Then click the ‘Continue’
button.
4) Click the ‘Statistics…’ button and tick the option for
‘Kappa’. Then click the ‘Continue’ button.
5) Finally click ‘OK’ to produce the cross tabulation with
the Kappa statistic or ‘Paste’ to add the syntax for
this into your syntax file.
63
Kappa statistic: Example
M6Cat * M6Cat2 Crosstabulation
M6Cat
Non case
Clinical case
Total
Count
% of Total
Count
% of Total
Count
% of Total
M6Cat2
Non case
Clinical case
63
7
57.8%
6.4%
2
37
1.8%
33.9%
65
44
59.6%
40.4%
Total
2x2 cross tabulation with
overall percentages.
70
64.2%
39
35.8%
109
100.0%
From the above table we can see that there is 91.7% actual
agreement between the 2 measures (57.8% + 33.9%).
Symmetric Measures
Measure of Agreement
N of Valid Cases
Kappa
Value
.825
109
Asymp.
a
Std. Error
.055
b
Approx. T
8.657
Approx. Sig.
.000
a. Not assuming the null hypothesis.
b. Using the asymptotic standard error assuming the null hypothesis.
Kappa test p value: p <0.001
Kappa statistic, indicating very good agreement.
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Kappa statistic: CIA Example
Methods  Diagnostic studies
 Kappa
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Kappa statistic: CIA Example
It doesn’t matter which way around you enter the rows
and columns of this table, as long as the diagonal (1,1
and 2,2 in this case) indicate agreement:
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Kappa statistic: CIA Example
Observed Kappa value
95% confidence interval (This CI
excludes 0, therefore agreeing with the
earlier p value from SPSS)
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Summary
You should now be able to choose between, perform (using SPSS
and CIA) and interpret the results from the following methods of
analysing categorical data:
– A test for association or independence (Chi-square or
Fisher’s exact test).
– A test for assessing if a sample proportion differs from a
specified proportion (Chi-square).
– A test for a change in categorical response (McNemar’s test).
– A test of agreement of categories between 2 raters (Kappa
test).
–
You should also be aware of the concept of odds, odds
ratios and how to calculate them from a 2x2 table.
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References
•
Practical statistics for medical research, D Altman: Chapters 10 & 14.
•
Medical statistics, B Kirkwood, J Stern: Chapters 16 & 17.
•
An introduction to medical statistics, M Bland: Chapter 13.
•
Statistics for the Terrified: Analysing 2x2 classification tables.
•
http://statpages.org/ctab2x2.html
•
Swets JA, Pickett RM. Evaluation of diagnostic systems. New York: Academic
Press,1982.
•
Langlotz CP. Fundamental measures of diagnostic examination performance:
usefulness for clinical decision making and research. Radiology 2003; 228:3-9.
•
Hanley JA, McNeil BJ. The meaning and use of the area under a receiver operating
characteristic (ROC) curve. Radiology 1982; 143:29-36.
•
Hanley JA, McNeil BJ. A Method of Comparing the Areas under Receiver Operating
Characteristic Curves Derived from the Same Cases. Radiology 1983; 148:839843.
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