This document consists of three modules concerned with aspects of statistics. The first provides knowledge of the effect of imperfect correlation and random error on differences between means, and the reasons for the necessity of random allocation of objects to experimental and control conditions in scientific experimentation. The second unit shows how to: 1) Use frequency distributions and histograms to summarize data; 2) Calculate means, medians, and modes as measures of central location; 3) Decide which measures of central location may be most appropriate in a given instance; and 4) Calculate and interpret percentiles. The third module is designed to enable the student to: 1) discuss how approximation is pervasive in statistics; 2) compare "structural" and "mathematical" approximations to probability models; 3) describe and recognize a hypergeometric probability distribution and an experiment in which it holds; 4) recognize when hypergeometric probabilities can be approximated adequately by binomial, normal, or Poisson probabilities; 5) recognize when binomial probabilities can be approximated adequately by normal or Poisson probabilities; 6) recognize when the normal approximation to binomial probabilities requires the continuity correction to be adequate; and 7) calculate with a calculator or computer hypergeometric or binomial probabilities exactly or approximately. Exercises and tests, with answers, are provided in all three units. (MP)
The CAUSE Research Group is supported in part by a member initiative grant from the American Statistical Association’s Section on Statistics and Data Science Education