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By William Feller
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Extra info for An introduction to probability theory and its applications
055 is sufficiently strong to perhaps warrant a similar study with a larger group of students. ©2001 CRC Press LLC Comments. 1. 1 that small exper iments may never produ ce P-valu es indic ating stron g evide nce again st H0, an interesting effect may sometimes be suggested even with very small samples; this is encouraging given the current emphasis on small group work in teaching, where data concerning individuals in the group are often used for illustrative purposes. A teaching advantage of using such data from small groups is that in working through the arithmetic one is not bogged down as would be the case with larger data sets.
0462, not markedly different from that given by the Pitman test. However it is doubtful whether the distribution of sentence length is symmetric, and certainly doubt about whether it is normally distributed. There are good grounds for these doubts. Firstly, for a symmetric distribution the means and medians coincide and thus in a sample one expects them to be close. 17 so there is a recognizable difference between them. Inspecting the sample values shows that this difference is largely due to the influence on the mean of the value 108 which is 67 more than the median, whereas the minimum observed length is only 29 less than the median.
E. to data values below θ 0). We expect a near equal scatter of positive and negative ranks if θ0 is the true mean or median, implying that the sum of all positive ranks and the sum of all negative ranks should not differ greatly. A high sum of the positive (negative) ranks relative to that of the negative (positive) ranks implies θ0 is unlikely to be the population mean. We now apply a test that is mechanically equivalent to the Pitman test where signed ranks of deviations replace the signed deviations themselves.
An introduction to probability theory and its applications by William Feller