![In a genetic inheritance study discussed by
Margolin[1988],samples of individuals from several
ethnic groups were taken. Blood samples
were collected from each individual and several variables
measured.
Here, we want to test the hypothesis that the median of
blood samples for Native Americans is the same as that
for Caucasians against the alternative hypothesis that the
median of the blood samples for Native Americans is less
than that for Caucasians.](https://image.slidesharecdn.com/group-16-130810115729-phpapp02/75/Wilcoxon-Rank-Sum-Test-10-2048.jpg){kind=icon}
Uploaded bySahil Jain
Wilcoxon Rank-Sum Test
The document describes the Wilcoxon Rank-Sum Test, a non-parametric statistical hypothesis test used to assess whether one of two independent samples of observations tends to have larger values than the other when normality cannot be assumed. It provides details on running the test, including ranking the combined observations and computing the test statistic to determine if it is less than or equal to the critical value, rejecting the null hypothesis. An example applies the test to compare the nicotine content of two cigarette brands, finding no significant difference between their medians.
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Introduction to the Wilcoxon Rank-Sum Test presented by Sahil Jain from IIIT-Delhi.
Explains the conditions for using the Wilcoxon Rank-Sum Test, especially for non-parametric data.
Describes the process of selecting samples and ranking the combined observations.
Discusses how to make decisions based on the test statistic U and critical values under different hypotheses.
Presents a practical example testing the nicotine content in two cigarette brands at a 0.05 significance level.
Defines null and alternative hypotheses, sample sizes, and critical region for the previous example.
Details the ranking of data, computation of test statistics, and the decision made regarding the null hypothesis.
Describes a genetic inheritance study and hypotheses regarding blood samples of ethnic groups.
Indicates the sample sizes for the two groups involved in the genetic inheritance study.
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Wilcoxon Rank-Sum Test
- 1.
- 2. » Generally usedwhen normality assumption for the sample does not hold and sample size is small » Non-parametric statistical hypothesis test for assessing whether one of two samples of independent observations tends to have larger values than the other.
- 3. » Select arandom sample from each of the populations » Let n1 and n2 be the number of observations in the smaller and larger sample respectively » Arrange the combined n1+n2 observations in ascending order and substitute a rank of 1, 2… to the n1 + n2 observations » In the case of ties, we assign the conflicting observations with their mean ranks
- 5. » Our decisionis based on the value of the test statistic U(the random variable for u) » For one-tail test: u1 or u2 » For two-tail test: u= min(u1, u2) » Null hypothesis will be rejected whenever the appropriate statistic U1, U2 or U assumes a value less than or equal to the desired critical value. Test Statistic ≤ Critical Value H0 H1 Compute µ1 < µ2 u1 µ1=µ2 µ1 > µ2 u2 µ1 ≠ µ2 u
- 6. Brand A 2.14.0 6.3 5.4 4.8 3.7 6.1 3.3 Brand B 4.1 0.6 3.1 2.5 4.0 6.2 1.6 2.2 1.9 5.4 The nicotine content of two brands of cigarette, measured in mg, was found to be as given the table. Test the hypothesis, at 0.05 level of significance, that the median nicotine content of two brands are equal against the alternative that they are unequal.
- 7. » H0 :µ1 = µ2 » H1 : µ1 ≠ µ2 » α = 0.05 » n1 =8 » n2 =10 » Critical Region: µ ≤ 17 (From Table) » Computation Steps: Arranging observations in ascending order and assigning ranks from 1 to 18.
- 9. DATA RANKS BRAND 0.61 B 1.6 2 B 1.9 3 B 2.1 4 A 2.2 5 B 2.5 6 B 3.1 7 B 3.3 8 A 3.7 9 A 4.0 10.5 A 4.0 10.5 B 4.1 12 B 4.8 13 A 5.4 14.5 A 5.4 14.5 B 6.1 16 A 6.2 17 B 6.3 18 A • w1 = 4+8+9+10.5+13+14.5+16+18 = 93 • w2 = 1+2+3+5+6+7+10.5+12+14.5+17 = 78 • Therefore, u1 = 93-((8*9)/2) = 57 • u2 = 78-((10*11)/2) = 23 • Min(u1, u2) = 23 ( not ≤ 17) Decision: Don't reject Null Hypothesis H0 and conclude that there is no significant difference in median nicotine contents of two brands of cigarettes at 0.05 significance level.
- 10. In a geneticinheritance study discussed by Margolin[1988],samples of individuals from several ethnic groups were taken. Blood samples were collected from each individual and several variables measured. Here, we want to test the hypothesis that the median of blood samples for Native Americans is the same as that for Caucasians against the alternative hypothesis that the median of the blood samples for Native Americans is less than that for Caucasians.
- 11.