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ERIC Number: ED021317
Record Type: Non-Journal
Publication Date: 1967-Dec
Reference Count: N/A
Effects of Inapplicability of the Continuity Condition upon the Probability Distributions of Selected Statistics and their Implications for Research in Education. Final Report.
Sparks, Jack N.
Computer routines were devised to investigate the behavior of two statistics, the Student t and the Mann-Whitney U, under specific conditions. Certain of these conditions were violations of the underlying assumptions of the two tests. Both were computed for 5,000 pairs of samples sized 5, 10, and 20 from a rectangular, a normal and an exponential distribution. The scales of measurement were progressively changed from those as continuous as possible to those of 50 cells, 20 cells, l0 cells, 4 cells, 3 cells, and 2 cells. For the Mann-Whitney U statistic, ties were handled by (1) putting all tied members of sample number one before those in sample number two tied for the same position, (2) assigning members of a tie group the mean of the ranks for which they were tied, and (3) assigning each member of a tied group to a random number of the positions for which they were tied. Results for the Student t statistic varied little from the tabled results even for a dichotomous scale. The Mann-Whitney U statistic, however, was very heavily affected by discreteness. (Author/TT)
Publication Type: N/A
Education Level: N/A
Sponsor: Office of Education (DHEW), Washington, DC. Bureau of Research.
Authoring Institution: Pennsylvania State Univ., University Park.