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Biostatistics: Qualitative Data - Tests 2 - Ecology of the Southwest | BIO 250, Exams of Biology

Fort Lewis College (FLC)Biology
Prof. Julie E. Korb

Material Type: Exam; Professor: Korb; Class: Ecology of the Southwest; Subject: Biology; University: Fort Lewis College; Term: Winter 2003;

Typology: Exams

Pre 2010

Uploaded on 08/05/2009

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Singapore Med J 2003 Vol 44(10) : 498-503
Basic Statistics For Doctors
Biostatistics 103:
Qualitative Data –
Tests of Independence
Y H Chan
Clinical Trials and
Epidemiology
Research Unit
226 Outram Road
Blk A #02-02
Singapore 169039
Y H Chan, PhD
Head of Biostatistics
Correspondence to:
Y H Chan
Tel: (65) 6317 2121
Fax: (65) 6317 2122
Email: chanyh@
cteru.com.sg
Parametric & non-parametric tests(1) are used when
the outcome response is quantitative and our interest
is to determine whether there are any statistical
differences between/amongst groups (which are
categorical).
In this article, we are going to discuss how to
analyse relationships between categorical variables.
Table I shows the first five cases of 200 subjects
with their gender and intensity of snoring (No, At
Times, Frequent and Always) and snoring status
(Yes or No) recorded.
Table I. Data structure in SPSS.
Subject Gender Snoring Intensity Snoring Status
1Male No No
2Male Always Yes
3 Female Frequent Yes
4 Male At times Yes
5 Female No No
Here, we have two interests. One is to
determine whether there’s an association between
gender and snoring intensity and the other is the
association between gender and snoring status.
The interpretation of the re sults for both analyses
is not similar.
Let’s discuss the 1st interest. The null hypothesis
is: There is No Association between gender and
snoring intensity. To test this hypothesis of no
association (or independence), the Chi-Square test
is performed. With the given data structure in Table I,
to perform the Chi-Square test in SPSS, use Analyse,
Descriptive Statistics, Crosstabs and the following
template is obtained:
Template I. Crosstabs.
It does not matter whether we put Snoring intensity
or Gender into the Row(s) or Columns but for “easier
interpretation” of the results (later) it is recommended
to put the “the categorical variable of outcome interest”
(in this case, the Snoring intensity) in the Columns
option. Click on the Cells button and tick the Row
Percentages (the Observed Counts is ticked by default),
then Continue.
Template II. Crosstabs: Cell Display.
The crosstabulation table is shown in Table II.
This table is a 2 X 4 (read as 2 by 4); 2 levels for Gender
and 4 levels for Snoring intensity.
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Download Biostatistics: Qualitative Data - Tests 2 - Ecology of the Southwest | BIO 250 and more Exams Biology in PDF only on Docsity!

Singapore Med J 2003 Vol 44(10) : 498-503 B a s i c S t a t i s t i c s F o r D o c t o r s

Biostatistics 103:

Qualitative Data –

Tests of Independence

Y H Chan

Clinical Trials and Epidemiology Research Unit 226 Outram Road Blk A #02- Singapore 169039 Y H Chan, PhD Head of Biostatistics Correspondence to: Y H Chan Tel: (65) 6317 2121 Fax: (65) 6317 2122 Email: chanyh@ cteru.com.sg

Parametric & non-parametric tests (1)^ are used when

the outcome response is quantitative and our interest

is to determine whether there are any statistical

differences between/amongst groups (which are

categorical).

In this article, we are going to discuss how to

analyse relationships between categorical variables.

Table I shows the first five cases of 200 subjects

with their gender and intensity of snoring (No, At

Times, Frequent and Always) and snoring status

(Yes or No) recorded.

Table I. Data structure in SPSS. Subject Gender Snoring Intensity Snoring Status

1 Male No No

2 Male Always Yes

3 Female Frequent Yes

4 Male At times Yes

5 Female No No

Here, we have two interests. One is to

determine whether there’s an association between

gender and snoring intensity and the other is the

association between gender and snoring status.

The interpretation of the results for both analyses

is not similar.

Let’s discuss the 1 st^ interest. The null hypothesis

is: There is No Association between gender and

snoring intensity. To test this hypothesis of no

association (or independence ), the Chi-Square test

is performed. With the given data structure in Table I,

to perform the Chi-Square test in SPSS, use Analyse,

Descriptive Statistics , Crosstabs and the following

template is obtained:

Template I. Crosstabs.

It does not matter whether we put Snoring intensity

or Gender into the Row(s) or Columns but for “easier

interpretation” of the results (later) it is recommended

to put the “the categorical variable of outcome interest”

(in this case, the Snoring intensity) in the Columns

option. Click on the Cells button and tick the Row

Percentages (the Observed Counts is ticked by default),

then Continue.

Template II. Crosstabs: Cell Display.

The crosstabulation table is shown in Table II.

This table is a 2 X 4 (read as 2 by 4); 2 levels for Gender

and 4 levels for Snoring intensity.

499 : 2003 Vol 44(10) Singapore Med J

To ask for the Chi-Square test , click on the

Statistics button at the bottom of Template I and

the Crosstabs:Statistics template is shown – tick the

Chi-square box.

Template III. Crosstabs: Statistics.

Table III gives the result for the Chi-Square test.

Table III. Chi-Square test result for the (2 X 4) Gender and Snoring intensity. Chi-Square Tests Value df Asymp. Sig. (2-sided) Pearson Chi-Square 9.177 a^3. Continuity Correction Likelihood Ratio 9.390 3. Linear-by-Linear Association 5.915 1. N of Valid Cases 200 a (^) 0 cells (.0%) have expected count less than 5. The minimum expected count is 5.76.

Here the Pearson Chi-Square value is 9.17 with

df (degree of freedom) = 3 and the p-value is 0.

(<0.05) – the rest of the statistics in the table is of

no interest to us! Hence we reject the null hypothesis

of no association.

The Chi-Square test only tells us whether there

is any association between two categorical variables

but does not indicate what the association is. From

Table II, by inspection, it is obvious that the difference

Table II. Crosstabulation table of Gender and Snoring intensity. Snoring intensity ALWAYS AT TIMES FREQUENT NO Total Gender Female Count 9 31 6 58 104 % within Gender 8.7% 29.8% 5.8% 55.8% 100.0% Male Count 23 26 6 41 96 % within Gender 24.0% 27.1% 6.3% 42.7% 100.0% Total Count 32 57 12 99 200 % within Gender 16.0% 28.5% 6.0% 49.5% 100.0%

lies in the males being more likely to have ‘Always’

snoring intensity compared to the females (24% vs

8.7%). Sometimes it’s not so straightforward to

interpret an association!

For the 2 nd^ interest, the null hypothesis is: There

is No Association between gender and snoring status.

The (2 x 2) crosstabulation table and the Chi-Square

test results are shown in tables IV and V respectively.

Table IV. (2 x 2) crosstabulation table of Gender and Snoring status. Gender* Snoring status Crosstabulation Snoring status NO YES Total Gender Female Count 58 46 104 % within Gender 55.8% 44.2% 100.0% Male Count 41 55 96 % within Gender 42.7% 57.3% 100.0% Total Count 99 101 200 % within Gender 49.5% 50.5% 100.0% Table V. Result for Chi-Square test for the (2 X 2) Gender and Snoring status. Chi-Square Tests Value df Asymp. Exact Exact Sig. Sig. Sig. (2-sided) (2-sided) (1-sided) Pearson Chi-Square 3.407 b^1. Continuity Correctiona^ 2.904 1. Likelihood Ratio 3.417 1. Fisher’s Exact Test .068. Linear-by-Linear Association 3.390 1. N of Valid Cases 200 a (^) Computed only for a 2x2 table. b (^) 0 cells (.0%) have expected count less than five. The minimum expected count is 47.52. This has be 0 for Pearson’s Chi-Square to be valid

501 : 2003 Vol 44(10) Singapore Med J

Before we carry out the sequence of steps as

discussed above for performing the Chi-square

test, we have to “inform” SPSS that this time each

row is not a subject but the total number of cases

are being weighted by the Count variable. In

SPSS, go to Data, Weight Cases and the following

template appears:

Template V. Weight Cases.

Click on the Weight cases by and bring the

Count variable into the Frequency Variable box ; then

perform the sequence of steps for a Chi-Square test

as described above.

Measuring the Strength of an Association (only for

2 x 2 tables).

The magnitude of the p-value does not indicate

the strength of association between two categorical

variables as we know that this value is dependent on

the sample size. To express the strength of a significant

association (only for 2 x 2 tables), the odds ratio or the

relative risk between the outcomes of the two groups

are presented. Table IX shows the crosstabulation for

Exposure and Disease.

Table IX. 2 x 2 crosstabulation for Exposure and Disease. Disease YES No Exposed Yes a b No c d

By definition, the Odds Ratio is given by OR =

(ad)/(bc): the ratio of the odds having disease

given exposed and of having disease given not

exposed and the Relative Risk (RR) = a(c+d)/

c(a+b): the ratio of the probabilities of having

disease given exposed and having disease given

not exposed.

How to obtain the odds ratio and relative

risk from SPSS? From template III, besides ticking

on the Chi-square option, tick the Risk option too.

Tables X – XI show the 2 x 2 crosstabulation and

the Risk estimates for a exposure/disease example:

Table X. Crosstabulation table for Exposure and Disease example. Exposure* Disease Crosstabulation Disease Yes=1 No=2 Total Exposure yes=1 Count 30 70 100 % within Gender 30.0% 70.0% 100.0% no=2 Count 10 90 100 % within Gender 10.0% 90.0% 100.0% Total Count 40 160 200 % within Exposure 20.0% 80.0% 100.0% p<0.001 (Pearson Chi-Square) Table XI. Risk estimates for Exposure and Disease example. Risk Estimate 95% Confidence Interval Value Lower Upper Odds Ratio for Exposure 3.857 1.767 8. (yes/no) For cohort Disease = yes 3.000 0.551 5. For cohort Disease = no .778 .673. N of Valid Cases 200

There’s a significant association between

Exposure and Disease (p<0.001). Looking at

Table XI, the Odds Ratio for an Yes/No Exposure

of having Disease (the 1 st^ column of Table X) is

3.857 (95% CI 1.767 to 8.422) which is also the OR

for the No/Yes Exposure for having No Disease.

The Relative Risk is obtained from the cohort

Disease = yes or no. For cohort Disease = yes, the

Relative Risk between Exposure and non-exposure

is 3.0 and is 0.778 for the cohort Disease = no. This

interpretation of the results is rather “straightforward”

because of the way we set up the crosstabulation

table. Observe that the codings for “yes = 1” and

“no = 2”, and SPSS will display the “yes” first and

then the “no”. What if we have coded “yes = 1” and

“no = 0” for Disease?

Table XII Exposure* Disease Crosstabulation Disease No=0 Yes=1 Total Exposure yes=1 Count 70 30 100 % within Gender 70.0% 30.0% 100.0% no=2 Count 90 10 100 % within Gender 90.0% 10.0% 100.0% Total Count 160 40 200 % within Exposure 80.0% 20.0% 100.0%

Singapore Med J 2003 Vol 44(10) : 502

Table XIII Risk Estimate 95% Confidence Interval Value Lower Upper Odds Ratio for Exposure .259 .119. (yes/no) For cohort Disease = no = 0 .778 .673. For cohort Disease = yes = 1 3.000 1.551 5. N of Valid Cases 200

There will be no change in the p-value of the

association but from Table XIII, the OR presented

now is for Yes/No Exposure of having No Disease

(the 1 st^ column of Table XII) is 0.259 (which is just

the reciprocal of 3.857!).

For a non 2 x 2 table, if a significant association

exists, we may want to find out where the differences

are. Let’s consider the example of Snoring status

and Race.

Table XIV. Crosstabulation of Race and Snoring status. RACE* Snoring status Crosstabulation Snoring status Yes No Total Race Chinese Count 47 64 111 % within RACE 42.3% 57.7% 100.0% Indian Count 9 3 12 % within RACE 75.0% 25.0% 100.0% Malay Count 43 27 70 % within RACE 61.4% 38.6% 100.0% Others Count 2 5 7 % within RACE 28.6% 71.4% 100.0% Total Count 101 99 200

% within RACE 50.5% 49.5% 100.0% p = 0.013 (Fisher’s Exact test).

There’s an association between Race and Snoring

status (p=0.013) and from Table XIV, it’s not obvious

where this association is. Since Race is a nominal

categorical variable, we can create four dummy

variables: Chinese vs non-Chinese, Malay vs non-

Malays, etc. That is the new variable Chinese has

only two levels: Chinese or non-Chinese and then we

perform the Chi-Square test using these four dummy

variables with Snoring status.

Table XV shows the crosstabulation for the

Chinese and Snoring Status and the p-value for this

association is 0.010 which is statistically significant

even after we adjusted for the type 1 error for

multiple comparison (1)^ (p<0.05/4 = 0.125). The

risk estimate table XVI shows that the Chinese

compared to the non-Chinese were less likely to

snore (OR = 0.476).

Table XV. Crosstabulation of Chinese vs Non-Chinese with Snoring status. Crosstab Snoring Status Yes No Total Chinese Chinese Count 47 64 111 % within Chinese 42.3% 57.7% 100.0% Other Count 54 35 89 % within Chinese 60.7% 39.3% 100.0% Total Count 101 99 200 % within Chinese 50.5% 49.5% 100.0% p = 0.010 (Chi-Square test) Table XVI. Risk estimate for Chinese vs non-Chinese and Snoring status. Risk Estimate 95% Confidence Interval Value Lower Upper Odds Ratio for Exposure .476 .270. (Chinese/Other) For cohort Snoring status = yes .698 .531. For cohort Snoring status = no 1.466 1.083 1. N of Valid Cases 200

Tables XVII and XVIII indicate that the Malays

compared to the non-Malays had a higher likelihood

to snore but we have to be cautious about this

conclusion after we have taken into consideration

the adjustment of the type 1-error for multiple

comparison!

Table XVII. Crosstabulation of Malay vs non-Malay and Snoring status. Crosstab Snoring Status Yes No Total Malay Malay Count 43 27 70 % within Malay 61.4% 38.6% 100.0% Other Count 58 72 130 % within Malay 44.6% 55.4% 100.0% Total Count 101 99 200 % within Malay 50.5% 49.5% 100.0% p = 0.023 (Chi-Square test)