By A. A. Walters (auth.)
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Extra resources for An Introduction to Econometrics
We now form the ratio F = estimate of variance between classes estimate of variance within classes or in algebra: F~o. 22) Now suppose we have a population where class does not matter; and let us take one sample after another from this population. For each sample we can calculate the value F, and so one can imagine the sampling frequency distribution ofF being formed. One can discover the chances of getting a value of F in excess of any particular value; thus one can measure the probability that, from a population where class does not matter, we can get a value ofF as high or higher than a given value.
Xya + (xa- x) 2 2 or I[( 1 2 2 - x1 -x-+~ -) + 2 2 ( )J 1 2 x +x 2 X2 - - - Now the value of xis obtained from the sample. And it is well known that the sum of squares of deviations from the mean will give a lower value than the sum of squares of deviations from any other value. The sensible approach seems to be, therefore, to calculate i[(x1- ~) 2 + (xa- ~) 2] and use this as a measure of the variance. This will not have the downward bias associated with the former measure. Unfortunately, we often do not know the value of ~ and so this course is rarely open to one.
3). We have assumed that the standard deviations of the two income distributors are the same, and that the same number is taken in all samples; thus the sampling distributions have the same variance and standard deviation. They differ only in location along the (sample average) income axis. e. hypothesis I) by rejecting it if the sample value falls outside the range £I,ooo ± 2 (standard error). For this means rejecting I when the sample average falls below L (below which lie 2! per cent of the distribution of I); but rejecting I means accepting II, which is much higlur than I.
An Introduction to Econometrics by A. A. Walters (auth.)