K300, Prof. Kruschke K300 Statistics, Prof. Kruschke

Exam 3: Sample Questions
Updated Tuesday 3/08/2005

Be sure to
  • write your name and ID on every page
  • write clearly
  • annotate your computations -- an unannotated sequence of numbers and derivations that mysteriously ends up with the correct numerical answer will not be given full credit
  • answer every part of every question.
    1. Effect size.
      • Consider a figure like those shown in class, that has four distributions: The null population in the top left, the null sampling distribution in the top right, the alternative population in the bottom left, and the alternative sampling distribution in the bottom right. Be able to mark and identify the population means, standard deviation, and the effect size.
      • What is the technical definition of effect size?
      • A treatment is applied to three people, and their three scores are -1, 1 and 3. Assuming the null hypothesis mean is zero, what is the estimated effect size of the treatment?
      • Suppose a sample has a mean of 1.0 and a stdev (using N-1) of 2.0, and a sample size of 500. Assuming the null hypothesis mean is zero, what is the estimated effect size?
    2. Power.
      • Consider a figure like those shown in class, that has four distributions: The null population in the top left, the null sampling distribution in the top right, the alternative population in the bottom left, and the alternative sampling distribution in the bottom right. Be able to mark and identify the critical values and area that represents power.
      • What is the technical definition of statistical power?
      • What are the three realistic ways to increase the power of an experiment?
      • If an experiment has a sample size of 1,000 and the result is "significant," what must we be careful about when interpreting the conclusion?
      • If an experiment has a sample size of 4 and the result is "not significant," what must we be careful about when interpreting the conclusion?
    3. Computation of t-test (for a single mean).
      Suppose we apply a treatment to a sample of five people. The null hypothesis is no change, i.e., normally distributed scores with mean zero. The actual changes for the five people are 0, 0, 4, 8 and 8.
      Formulas: t = ( M - μ0 ) / [ S / sqrt(N) ]. S = sqrt( [1/(N-1)] Σi ( xi - M )2 ).
      • What is the best estimate of the population standard deviation? (Compute the actual value.) Is that larger or smaller than the standard deviation of the scores in the sample itself?
      • What is the value of t for the sample?
      • Can the null hypothesis be rejected at the .05 significance level? Be sure to state what the df value is, and what the critical t value is. (A table of critical t values will be displayed in class at test time.)
      • What is the estimated effect size? What must we be careful about when interpreting the conclusion of the significance test?
    4. Concepts of t-test (for a single mean).
      • The table of critical t values was generated by sampling from a normal population distribution. What happens to the critical values if the population is uniform (not normal)?
      • The table of critical t values was generated by sampling from a normal population distribution. What happens to the critical values if the population is severely skewed (not normal)?
      • The table of critical t values was generated by sampling from a normal population distribution. What happens to the critical values if the population is severely bimodal (not normal)?
      • Suppose we do an experiment and get sample scores of 1, 1, 1, 9, 9, and 9. The sample t value is therefore 2.80 (honest), and according to the t table the critical value is 2.57 (honest). Should we reject the null hypothesis?