Fishers test

statistics in nursing

1. NON PARAMETRIC TEST : FISHER’S TEST PRINCY FRANCIS M I st Yr MSc (N)

2. 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

3. 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 .

4. About the inventor – RONALD FISHER

5. 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.

6. the "lady tasting tea" experiment

7. 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.

8. SPECIFICATION SMALL SAMPLE SIZE FREQUENCY SHOULD BE LESS THAN 5 2 X 2 TABLE

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.