• The fundamental premise of statistics is, "You could be wrong." The "you" in this premise could be a person of power, who might not like being doubted. Ubi dubium ibi libertas.
• Being an academic scientist is like running your own business...

• Three formalizations of central tendency and variability (not in textbook).
• The algebra of mean and variance: Standardized scores. (AA Ch. 2-3)

Examples of graphs shown in class. These three show how power increases as sample size increases. Click to enlarge.

Example of power of omnibus test in oneway ANOVA. Click to enlarge.

Example of power of test of correlation. Click to enlarge.

• Transforming to normality. Effects of linear or non-linear transformations on mean and variance.
• Rank-order methods:
  • Summed rank (Wilcoxon) test
  • ANOVA on rank-transformed data
• Monte-Carlo methods:
  • when form of population is specified by model - Monte Carlo sampling
  • when form of population is not hypothesized - the randomization technique

Binomial distribution (not in textbook):

• Population has two nominal categories, sampling distribution is binomial.
• Hypothesis testing; power; confidence intervals.
• When N is large: normal and Poisson approximations to binomial.

• Continuous chi-square distribution approximates discrete Pearson chi-square distribution when cell prob's are not extreme.
• Goodness of fit tests and tests of independent attributes.

• Textbook Box 17-1, pp. 620-621.
• Knowledge or Certainty by J. Bronowski. Notes of my visit to Göttingen.