Question:
For i = 1,...,s and j = 1,...,ni , let Xij be independent with Xi,j having distribution Fi , where Fi is
an arbitrary distribution with mean i and finite variances 2 that vary for each Fi......

Robustness of F- statistic under unequal variances
(A separate Excel working is attached for the development of Rejection probabilities and it graph)
The F-statistic that we consider in this exercise is nothing but the ratio of "Mean Between Sum of Squares" and "Mean Within Sum of Squares". If this ratio is sufficiently large, we reject the null hypothesis. The distribution of this ratio is derived based on the fact that its denominator and numerator follow independent Chi-square distributions. Again the assumption of chi-square distribution requires the assumption that the samples are taken from Normal distribution with almost similar variances.
In this exercise we are going to verify how this F-statistic is robust when the assumption of equal variances is violated. To establish this fact we make use of a hypothetical population with the following structure.
Groups Sample size Mean Standard Deviation
1 10 55 10
2 14 80 10
3 16 62 10

The above data consists of three groups with considerably different means (Group means are not equal) and with equal standard deviation. Thus one would expect to reject the ...

Solution Summary

Basic large sample theory is examined for distributions. Finite variances are analyzed.

Basic Statistics using Excel and Eviews. ... 40 mean 1,261.0250 sample variance 467,539.6147 sample standard deviation ... order and then delete the 5 largest and 5 ...

... space not only requires identifying three basic users: Early ...Theory Description Theory Application/Example. ... 6. In the second phase, the largest number of ...

... with Stock 1, you might get very large or very ... 4. We have four basic graphs in statistics: the bar ... shape of the distribution (is the sample symmetrical, skewed ...

... Consider this example: ... New South Wales, Department of Education and Training, 2006 A basic introduction to ... A toddler has a large knob puzzle with a simple bear ...

... This indicates a large number of hospitals and other ... be described in terms of some basic variables such ...SAMPLE Respondents will be coming from different groups ...

... Why? Some examples of organizational theories include: Classical, Neoclassical ... His theory had four basic principles: 1 ... of factors that yielded large increases in ...

... care and social costs views place the larger measure of ... The Duty to Comply The most basic moral duty that ... If the label on a bottle, for example, indicates only ...

... simple elements of mathematics, rules of logical syntax are the basic elements of ... to examine a small number of variables across a large sample of units ...

... not include the cost of the pollution it creates, especially in large cities ... Give a business or political example of the prisoner's dilemma from the field of ...

... are based on animism, which is a basic theory that all ... which is further divided into a large number of ... For example, there is no evidence that the concept ...