unit-iiinonparametrictestsbsrm-221019091259-e57b4925.pptx

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1. Unit- III Non- Parametric tests Wilcoxon Rank Sum Test Ravinandan A P 1 Mann- Whitney U test Kruskal- Wallis test Friedman Test Ravinandan A P Assistant Professor, Department of Pharmacy Practice, Sree Siddaganga College of Pharmacy In association with Siddaganga Hospital, Tumkur- 02

2. Level of significance (Non- parametric data)- 1. 2. 3. 4. Wilcoxan’s signed rank test Wilcoxan rank sum test Mann Whitney U test Kruskal -Wallis test (one way ANOVA) 5. Friedman Test Ravinandan A P 2

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4. Why non- parametric methods? • Certain statistical tests like the t- test require assumptions of the distribution of the study variables in the population –t- test requires the underlying assumption of a normal distribution –Such tests are known as parametric tests • There are situations when it is obvious that the study variable cannot be normally distributed, e.g., # of hospital admissions per person per year # of surgical operations per person Ravinandan A P 4

5. The study variable generates data which are scores & so should be treated as a categorical variable with data measured on ordinal scale –E.g., scoring system for degree of skin reaction to a chemical agent: 1: intense skin reaction 2: less intense reaction 3: No reaction For such type of data, the assumption required for parametric tests seem invalid => non- parametric methods should be used •Aka distribution- free tests, because they make no assumption about the underlying distribution of the study variables Ravinandan A P 5

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7. Ravinandan A P 7 Advantages of Non-Parametric tests Distribution free & hence no assumption about the population is required. When sample size is small it is simple to & understand & easy to apply. It is less time consuming & for significant result no further work is necessary Applicable to all type of data Helpful to researchers collecting pilot study or researchers working with a rare disease Make fewer assumptions than classical procedures. the medical

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11. Ravinandan A P 11 Wilcoxon test. Used to test whether or not the difference between two paired population medians is zero. The null assumption is that it is, i.e. the two medians are equal. Variables can be either metric or ordinal. Distributions any shape, but the differences should be distributed symmetrically. This is the non-parametric equivalent of the matched-pairs t test.

12. WILCOXON SIGNED RANK TEST For the comparison of two treatments in a paired design, a more sensitive non-parametric test is Wilcoxon signed rank test Ex: paired data obtained from bioavailability experiment: Time to Peak concentration Ravinandan A P 12

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14. WILCOXON SIGNED RANK TEST Subject Time to Peak Difference A B B- A 1 2.5 3.5 1 2 3 4 1 3 1.25 2.5 1.25 4 1.75 2 0.25 5 3.5 3.5 6 2.5 4 1.5 7 1.75 1.5 - 0.25 8 2.25 2.5 0.25 9 3.5 3 - 0.5 10 2.5 3 0.5 11 2 3.5 1.5 12 3.5 4 0.5 Ravinandan A P 14

15. Ranks with +ve Sign Ranks with - Ve sign 2 2 2 5 5 5 7.5 7.5 9 10.5 10.5 59 7 If the Smaller Rank sum is Less than or Equal to the table value , the comparative groups are different at the Indicated level of significance At 5% and 1% For N= 11 table Value = 13 at 5% - Level Cal value < Table Value Difference is Significant Ravinandan A P

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17. WILCOXON RANK SUM TEST The wilcoxon signed rank test for non- parametric test for the comparison of paired sample If two treatments are to compared, where the observations have been obtained from two independent groups, the non-parametric wilcoxon rank sum test or Mann – whitney U-test is alternative for Pooled t- test Ravinandan A P 17

18. 18 Wilcoxon rank sum test (aka Mann- Whitney U test) Non- parametric equivalent of parametric t-test for 2 independent samples (unpaired t- test) Suppose the waiting time (in days) for cataract surgery at two eye clinics are as follows: Patients at clinic A (nA=18) 12, 12, 22, 3, 14, 4, 2, 7, 2 Patients at clinic B (nB=15) 0, 9, 11, 7, 11, 10 1, 5, 15, 7, 42, 13, 8, 35, 21, 4, 9, 6, 2, 10, 11, 16, 18, 6,

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20. Amount Amount Rank(old) Rank(New) Dissolved Dissolved 53 58 3 11 61 55 14 5.5 57 67 9 21 50 62 1 15.5 63 55 17 5.5 62 64 15.5 18.5 54 66 4 20 59 59 2 12.5 59 68 12.5 12 57 57 9 9 64 69 18.5 23 56 7 105.5 160.5 Z = (| T - N1(N1+N2+1)/2 |) / (sqrt(N1N2(N1+N2+1)/12) T= Sum of the ranks for the smaller sample size N1 = Size of sample1 11 N2 = Size of sample2 12 Ravinandan A P 20

21. Ravinandan A P 21 Mann- Whitney test Used to test whether or not the difference between two independent population medians is zero. The null assumption is that it is, i.e. the two medians are equal. Variables can be either metric or ordinal. No requirement as to shape of the distributions, but they need to be similar. This is the non-parametric equivalent of the two-sample t test.

22. Ravinandan A P 22 Kruskal- Wallis test. Used to test whether the medians of three of more independent groups are the same. Variables can be either ordinal or metric. Distributions any shape, but all need to be similar. This non-parametric test is an extension of the Mann- Whitney test.

23. Ravinandan A P 23 Friedman Test The Friedman test is a non- parametric statistical test developed by Milton Friedman. Similar to the parametric repeated measures ANOVA, it is used to detect differences in treatments across multiple test attempts. The procedure involves ranking each row (or block ) together, then considering the values of ranks by columns. Applicable to complete block designs.

24. Ravinandan A P 24 Friedman Test The Friedman test is a non-parametric alternative to ANOVA with repeated measures. No normality assumption is required. The test is similar to the Kruskal-Wallis Test. We will use the terminology from Kruskal-Wallis Test and Two Factor ANOVA without Replication.

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28. Ravinandan A P 28 Non- parametric vs. parametric methods Advantages: Do not requires the assumption needed for parametric tests. Therefore useful for data which are markedly skewed Good for data generated from small samples. For such small samples, parametric tests are not recommended unless the nature of population distribution is known Good for observations which are scores, i.e. measured on ordinal scale Quick and easy to apply and yet compare quite well with parametric methods

29. Ravinandan A P 29 Non- parametric vs. parametric methods Disadvantages Not suitable for estimation purposes as confidence intervals are difficult to construct No equivalent methods for more complicated parametric methods like testing for interactions in ANOVA models Not quite as statistically efficient as parametric methods if the assumptions needed for the parametric methods have been met

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