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Mann Whitney test is a distribution free test which is used as an alternative to the Student's t-test for assessing that whether the two populations have the same median. The test statistic U is calculated from comparing each pair of the values, that is one from each group, scoring these pairs 1 or 0 depending upon whether the first group observation is higher or lower than the from the second group and summing the resulting scores over all the pairs. In the case of no ties then the following g case could be seen here n is the number of observations in the smaller group and W is the rank sum statistic associated with the Wilcoxon's rank sum test. The two tests are hence equivalent. Tables giving critical values of test statistic are available, and for the moderate and large sample sizes, a normal approximation can be taken in use.
Prevented fraction is a measure which can be used to attribute the protection against the disease directly to an intervention. The measure can given by the proportion of disease w
Probability weighting is the procedure of attaching weights equal to inverse of the probability of being selected, to each respondent's record in the sample survey. These weights
Hazard function : The risk which an individual experiences an event in a small time interval, given that the individual has survived up to the starting of the interval. It is th
Johnson''s Job Sequencing for n jobs and 2 machines
1) Let N1(t) and N2(t) be independent Poisson processes with rates, ?1 and ?2, respectively. Let N (t) = N1(t) + N2(t). a) What is the distribution of the time till the next epoch
Banach's match-box problem : The person carries two boxes of matches, one in his left and one in his right pocket. At first they comprise N number of matches each. When the person
A family of the probability distributions of the form given as here θ is the parameter and a, b, c, d are the known functions. It includes the gamma distribution, normal dis
The theorem relating structure of the likelihood to the concept of the sufficient statistic. Officially the necessary and sufficient condition which a statistic S be sufficient for
This term is sometimes used for the data collected in those longitudinal studies in which more than the single response variable is recorded for each subject on each occasion. For
A term usually used for unobserved individual heterogeneity. Such variation is of main concern in the medical statistics particularly in the analysis of the survival times where ha
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