Basic Large Sample Theory
Not what you're looking for?
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......
Purchase this Solution
Solution Summary
Basic large sample theory is examined for distributions. Finite variances are analyzed.
Solution Preview
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 ...
Purchase this Solution
Free BrainMass Quizzes
Terms and Definitions for Statistics
This quiz covers basic terms and definitions of statistics.
Measures of Central Tendency
Tests knowledge of the three main measures of central tendency, including some simple calculation questions.
Measures of Central Tendency
This quiz evaluates the students understanding of the measures of central tendency seen in statistics. This quiz is specifically designed to incorporate the measures of central tendency as they relate to psychological research.
Know Your Statistical Concepts
Each question is a choice-summary multiple choice question that presents you with a statistical concept and then 4 numbered statements. You must decide which (if any) of the numbered statements is/are true as they relate to the statistical concept.