Fisher's exact test is a statistical significance test used in the analysis of contingency tables when sample sizes are small. It provides an exact p-value for a 2x2 contingency table, while the chi-squared test provides only an approximation. Fisher's exact test is valid for all sample sizes, while the chi-squared test relies on an approximation that is only valid for large sample sizes. Fisher's exact test calculates the exact probability of observing the data or one more extreme, given the null hypothesis, using a hypergeometric distribution.

1. z

2. z
NON PARAMETRIC
TEST : FISHER’S TEST
PRINCY FRANCIS M
Ist Yr MSc (N)

3. NON PARAMETRIC TEST
•Non parametric test is a class of statistical tests that
do not involve stringent assumptions about the
distribution of critical variables.
•They involve less restrictive assumptions about the
shape of the variables distribution than do parametric
tests.
•Non parametric test are sometimes called
distribution – free statistics

4. Fisher’s Exact test
When the total sample size is small (total N
of 30 or less) or when there are cells with
frequencies (5 or fewer), Fisher’s exact test
should be used to test the significance of
differences in proportions.

5. ABOUT THE INVENTOR –
RONALD FISHER

6. Significance of the deviation from a null
hypothesis (e.g., P-value) can be calculated
exactly, rather than relying on an approximation
that becomes exact in the limit as the sample size
grows to infinity, as with many statistical tests.

7. THE "LADY TASTING TEA" EXPERIMENT

8. The Fisher Exact test uses to obtain the probability of the
combination of the frequencies that are actually obtained.
It also involves the finding of the probability of every
possible combination which indicates more evidence of
association.

9. ASSUMPTIONS
•It is assumed that the sample that has been drawn from the population is
done by the process of random sampling.
•A directional hypothesis is assumed.
•It is assumed that the value of the first person or the unit of items that
are being sampled do not get affected by the value of the second
person or the other unit of item being sampled. This assumption of
the fisher exact test would be violated if the data is pooled or united.

10. ASSUMPTIONS CONT…
•In the fisher exact test, mutual exclusivity within the
observations is assumed.
•The dichotomous level of measurement of the variables is assumed

11. FISHER’S TEST FORMULA
•p= ( a + b ) ! ( c + d ) ! ( a + c ) ! ( b + d ) !
a ! b ! c ! d ! N !

12. EXAMPLE
•A sample of teenagers might be divided into male
and female on the one hand, and those that are
and are not currently studying for a statistics
exam on the other. Hypothesize, that the
proportion of studying individuals is higher among
the women than among the men, and to test
whether any difference of proportions that
observed is significant.

13. ADVANTAGES OF NONPARAMETRIC TEST
• Probability statements obtained from most nonparametric tests are
exact probabilities.
• If samples are of sizes as small as six, there is no alternative to
using a nonparametric test unless the nature of the population
distribution is precisely known.
• These are suitable tests for treating observations from samples
drawn from several different populations
• Tests are available to treat data that are inherently in ranks as well
as data whose seemingly numerical scores have only the strength of
ranks.
• Methods are available to treat data that are simply classificatory.
• These tests are much easier to learn and apply than parametric
tests.

14. DISADVANTAGES
If all the assumptions of the parametric test are in fact met in the data, and
if the measurement is of the required strength, then nonparametric tests are
wasteful of data.
There are nonparametric methods for testing interactions in the analysis of
variance.
Tables of critical values may not be easily available.
Nonparametric methods may lack power as compared with more
traditional approaches, especially when sample size is very small.

15. JOURNAL ABSTRACT
•Statistical notes for clinical researchers: Chi-squared
test and Fisher's exact test
The chi-squared test and Fisher's exact test can assess for
independence between two variables when the comparing groups are
independent and not correlated. The chi-squared test applies an
approximation assuming the sample is large, while the Fisher's exact
test runs an exact procedure especially for small-sized samples.
Fisher's exact test is practically applied only in analysis of small
samples but actually it is valid for all sample sizes.

16. •While the chi-squared test relies on an
approximation, Fisher's exact test is one of exact
tests. Especially when more than 20% of cells have
expected frequencies < 5, we need to use Fisher's
exact test because applying approximation method
is inadequate. Fisher's exact test assesses the null
hypothesis of independence applying
hypergeometric distribution of the numbers in the
cells of the table.

17. •Many packages provide the results of Fisher's exact test
for 2 × 2 contingency tables but not for bigger
contingency tables with more rows or columns. For
example, the SPSS statistical package automatically
provides an analytical result of Fisher's exact test as well
as chi-squared test only for 2 × 2 contingency tables. For
Fisher's exact test of bigger contingency tables, we can
use web pages providing such analyses. For example, the
web page ‘Social Science Statistics’
(http://www.socscistatistics.com/tests/chisquare2/Default2
.aspx) permits performance of Fisher exact test for up to 5
× 5 contingency tables.

18. UNDERSTANDING STATISTICAL TESTS IN
THE MEDICAL LITERATURE: WHICH
TEST SHOULD I USE?
• For two dichotomous or binary variables, one will be able to build a 2 × 2
table. If the data follow a normal distribution, the most common test will
be Chi-square test. It is used to compare the proportion of subjects in two
groups, and verify the independence of each other. For example, if a study
about a certain treatment obtains data that shows that it reduces mortality
more than placebo for a given disease, one would like to know if the
results are true or merely a coincidence. Therefore, we perform a Chi-
square test and obtain the p value. One limitation of the Chi-square testing
is that its distribution breaks down as the frequencies decrease. If in one of
the cells of your table there are five or less observations, the data is
considered skewed. In this case, you need to use Fisher’s exact test,
specifically designed for small samples.

19. ASSIGNMENT
Write an assignment on “Application of Fisher’s test in
Medical Field”.

20. REFERENCES
• Rao SSSP. Biostatistics. Third edition. New Delhi: Prentice
Hall India Pvt Ltd;2004.
• Polit FD , Beck Tc . Nursing research : principles and methods.
7th edition. 2004.
• Basvanthappa BT, Nursing research and statistics , 3rd edition.
Newdelhi: jaypeepublication , 2014
• Sharma KS. Nursing research & statistics. New Delhi: Elsevier
publishers, 2012.