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Kurtosis: The extent to which the peak of the unimodal probability distribution or the frequency distribution departs from its shape of the normal distribution, by either being more pointed (like leptokurtic)or flatter ( like platykurtic). Commonly measured for a probability distribution as
where 4 is the fourth central moment of distribution, and 2 is its variance.
(consequent functions of sample moments are used for frequency distributions.)
For the normal distribution this index takes the value three and often index is redefined as the value above minus three so that the normal distribution would contain the value zero.
(Other distributions with the zero kurtosis are known as mesokurtic.) For the distribution which is leptokurtic the index is positive and for the platykurtic curves it is negative. It is shown in the figure
Multiple comparison tests : Procedures for detailed examination of the differences between a set of means, generally after a general hypothesis that they are all equal has been rej
we are testing : Ho: µ=40 versus Ha: µ>40 (a= 0.01) Suppose that the test statistic is z0=2.75 based on a sample size of n=25. Assume that data are normal with mean mu and standa
Likelihood is the probability of a set of observations provided the value of some parameter or the set of parameters. For instance, the likelihood of the random sample of n observ
Hazard plotting is based on the hazard function of a distribution, this procedure gives estimates of distribution parameters, the proportion of units failing by the given time per
Observational study is the study in which the objective is to discover cause-and-effect relationships but in which it is not feasible to use the controlled experimentation, in th
Historical controls : The group of patients treated in the past with the standard therapy, taken in use as the control group for evaluating the new treatment on the present patient
The approach of controlling the error rate in an exploratory analysis where number of hypotheses are tested, but where the strict control which is provided by multiple comparison p
Normal approximation : Normal distributions which approximate other distributions; such as, a normal distribution with the mean np and variance np(1 - p) which acts as an approxima
The graphic representation of the alternatives in a decision making problem which summarizes all the possibilities foreseen by the decision maker. For instance, suppose we are give
The Null Hypothesis - H0: β 1 = 0 i.e. there is homoscedasticity errors and no heteroscedasticity exists The Alternative Hypothesis - H1: β 1 ≠ 0 i.e. there is no homoscedasti
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