Non parametric test

non parametric test introduction

1. Problem- ANOVA The haemoglobin level of three groups of children fed three different diets are given in the table. Test whether the means of these groups differ significantly

2. Group I Group II Group III 11.6 11.2 9.8 10.3 8.9 9.7 10.0 9.2 11.5 11.5 8.8 11.6 11.8 8.4 10.8 11.8 9.1 9.1 12.1 6.3 10.5 10.8 9.3 10 11.9 7.8 12.4 10,7 8.8 10.7 11.5 10.0 9.7

3. Number of subject 11 12 10 Total 124 107.5 106.1 Mean 11.27 8.96 10.61 Total no of subject 33 Grand Total 337.6 Common mean 10.23

4. Non Parametric test

5. Definition It is the mathematical procedures concerned with the treatment of standard statistical problem. when the assumption of normal are replaced with general assumption for the distribution function.

6. When to use non parametric test In experiments when the data is not normal. Sample size is so small All the tests involving the ranking of data are non parametric.

7. Nonparametric statistics, also known as distribution-free statistics . It may be applicable when the nature of the distributions are unknown . we are not willing to accept the assumptions necessary for the application of the usual statistical procedures. When to use non parametric test

8. some people believe that any kind of data, no matter what the distribution, can be correctly analyzed using nonparametric methods. Many believe that most nonparametric methods require that the distributions be C ontinuous S ymmetrical , and I ndependent When to use non parametric test

9. Data that are categorical or attribute measurements. These are also known as nominal observations (i.e., the observation is given a name). Thus , a person is observed to be a “male” or a “female” or “black,” “white,” or “yellow.”

10. The assignment of a number to such nominal data may be useful to differentiate the categories, perhaps for computer usage. For example, we could assign the number 1 to a male and 2 to a female , but this does not imply that a female is larger (or, for that matter, smaller) than a male.

11. Non parametric test “sophisticated” level of measurement involves data that can be ranked in order of magnitude . kinds of ordered data are known as ordinal measurements . Continuous variables are ordinal measurements

12. Ordinal measurement For example, patients receiving antidepressant medication, may be rated according to attributes such as “sociability .” A high score will be assigned to a patient performing well on this criterion . If the patient shows characteristics of “ withdrawal ,” a low score will result. Intermediary scores reflect various degrees of response. These are ordinal measurements.

13. A patient with a score of zero after one week of medication . A score of 3 after two weeks of medication can be said to have improved. D uring the period between one and two weeks of treatment . A score of 3 is better than a score of zero.

14. Many nonparametric tests are based on ranking data. The condition of the “depressed” patient is a continuum. The condition can vary from one extreme to another with infinitely small gradations, in theory. It is not possible practically to measure the subjective condition with its infinite subtleties, and therefore we substitute an ordered scale that approximates the condition of the patient.

15. if a score of 3 represents “marked improvement” in sociability, 2 represents “moderate improvement ,” and 1 represents “no improvement,” one usually cannot say that the difference between scores of 3 and 2 is equal in magnitude to the difference of 2 and 1. Yet the data analysis of such scores usually treats a difference between 3 and 2 as equivalent to a difference between 2 and 1.

16. Data derived from continuous distributions are particularly amenable to nonparametric methods when the distributions deviate greatly from normality. A marked disadvantage of the simpler nonparametric techniques is the lack of flexibility of the design and analysis . The sign test is probably the simplest of the nonparametric tests.

17. If the sample size is small [as 6] there is no alternative to use a non parametric test unless the nature of population distribution is precisely known. Easy to learn It is applicable when the observation are nominal, ordinal [ ranked ] , or measured imprecisely Advantage

18. It is suitable for treating samples made up of observations from different populations. The hypothesis tested by the non parametric test may be more appropriate for the research investigation. It can be applied easier than parametric tests. Advantage

19. It is used to modify the hypothesis rather than estimation. Test is about the median instead of the mean. Tables of critical values may not be easily available. Tests are not systematic. Disadvantage

20. Some non parametric tests When we have to test an assumption about the population distribution with a random sample from the population Binomial test- when data are in two categories and the sample size is small. Chi- square test – when the data are in discrete categories and the sample are sufficiently large. Kolmogorov – smirnov test – when the variable has a continuous distribution

21. When we have to test if two random samples are likely to have come from population with the same mean. Randomisation test- small samples when data measurement in a numerical scale Kolmogorov – smirnov test with weaker measurement Mann whitney U test- large samples when data represent weaker measurement. Median test Some non parametric tests

22. Some non parametric tests Kruskal – wallis test When more than two sample are considered when they all belong to same population. Fisher exact probability test It is used when scores from the independent random samples all fall into one or other of mutually exclusive classes.

23. Some non parametric tests When we have to find out the statistical significance of difference in matched pairs comparison. Mecnemar test Data are frequencies in different categories Sign test Data are on a variable with continuity but can be measured only in a gross way. Ranks within the pairs are used

24. Some non parametric tests Wilcoxon test Differences observed for the various matched pairs can be meaningfully ranked. Randomisation test When data measurement in a numerical scale and the sample size is sufficiently small

25. Some non parametric tests When we have to measure the correlation as the observations are ranked. Kendall’s tau Spearmann rho

26. Application When parametric tests are not satisfied If testing hypothesis does not have any distribution. In order to quickly analyse the data When unscaled data is available.

27. Assumptions Observations are independent Continuous variable It is applied appropriately to data measured in an ordinal scale.

28. Test procedure- General steps to carry out non parametric test Stating hypothesis The null and alternative hypothesis is stated. Setting significance level The alpha related significance level with null hypothesis is set. it is normally set as 5% and therefore the confidence level is 95 %

29. Selecting test Suitable statistic test is chosen It is done by considering T he number of sample, whether the sample is dependent or independent. Types of data. Calculating statistics The test statistics is then calculated. Comparing values Test procedure- General steps to carry out non parametric test

30. The value required to reject the null hypothesis is determined using the suitable table of critical values for the specified statistics. This value is compared with the critical values which enables us to find the difference based on a specific significance level. Then we can state whether the null hypothesis should be rejected or not. Making decision The results are explained and a conclusion is drawn. Test procedure- General steps to carry out non parametric test

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