Biology 300

Readings in Zar (1999) Biostatistical Analysis, 4th edition (and other resources)

1. Introduction: Cats, statistics, and other stories.
   • None
   
   
2. Data description: Kinds of data, frequency tables, histograms, cumulative frequency distributions, mean, median, mode, range, standard deviation, variance.
   • Chapter 1 (all)
   • Chapter 3 intro, sections 3.1, 3.2 (ignore interpolation for tied observations), 3.4, 3.5
   • Chapter 4 intro, sections 4.1, 4.4, 4.5,4.6
   
   
3. Introduction to estimation: Samples and populations, population and sample histograms, distribution of sample means, standard error of the sample mean.
   • Chapter 2 (all)
   • Chapter 6 section 6.3 (ignore the normal distribution for now)
   
   
4. Introduction to hypothesis testing: Null vs alternate, statistical significance, statistical errors.
   • Chapter 6 section 6.4 (to end of page 83 only)
   • Notes on the correct interpretation of the P-value from the Prism Guide
   
   
5. Probability: Basic rules, mutually exclusive events, independence, probability trees.
   • Chapter 5 section 5.5, 5.6, 5.7
   • Zar doesn't explain probability trees but see the trees in Term 1 online notes
   
   
6. The Binomial distribution: Probabilities, estimating a binomial proportion, binomial test.
   • Chapter 24 intro, section 24.1, 24.3, 24.6 (ignore normal approximation for now)
   • See also my notes on the binomial distribution
   
   
7. Testing goodness of fit: Goodness of fit tests, the chi-square distribution, goodness of fit to binomial distribution, log-likelihood ratio (G).
   • Chapter 22 section 22.1, 22.2, 22.4, 22.5, 22.7
   • Chapter 24 section 24.5
   • Our rule of thumb will be: no expected frequencies less than 1 and no more than 20% less than 5
   
   
8. The Poisson distribution: Probabilities, goodness of fit to Poisson distribution.
   • Chapter 25 intro, section 25.1, 25.3
   • See also my notes on the Poisson distribution
   
   
9. Contingency tables: Tests of independence of two nominal variables, 2 × 2 tables, Fisher's exact test, chi-square test, general r × c tables, log-likelihood ratio.
   • Chapter 23 intro, section 23.1, 23.2, 23.7
   • Chapter 24 section 24.10 (don't worry about computing, just know what Fisher exact test is used for)
   
   
10. The Normal distribution: Probabilities under the normal curve, normal approximation to the binomial distribution.
    • Chapter 6 intro, section 6.1, 6.2, 6.3 (again)
    • Chapter 24 section 24.6 (normal approximation to binomial test only)
    
    
11. One-sample inference (normal case): Distribution of sample means, confidence intervals for the population mean, one- and two-tailed hypotheses, the t-distribution, distribution of sample variance, testing departures from normality.
    • Chapter 7 section 7.1, 7.2, 7.3, 7.4, 7.10, 7.11
    • Chapter 6 section 6.5
    • See the Prism Guide for a clear interpretation of the confidence interval for the mean.
    • See the Rice Virtual Lab for a Java tool to simulate the confidence interval for a population mean.
    
    
12. One-sample inference (non-normal case): Central Limit Theorem, normal approximation.
    • Zar does not have much on the Central Limit Theorem. The HyperStat Online Textbook has a reasonably good explanation. The Rice Virtual Lab has tools to simulate the Central Limit Theorem.
    • Zar uses a different formula to approximate a 95% confidence interval for a binomial proportion. You only need to know the formula presented in lecture (and provided on the formula sheet).
    
    
13. Two-sample inference: Confidence limits and tests for the difference between two variances, and two means, normal approximation, nonparametric alternatives (Mann-Whitney U-test).
    • Chapter 8 intro, section 8.5, 8.6, 8.1, 8.2, 8.9, 8.10 (to top of page 153 only), 8.11
    
    
14. Paired samples: Paired t-test, confidence limits for mean difference, nonparametric alternatives (Wilcoxon paired-sample test).
    • Chapter 9 intro, section 9.1, 9.2, 9.5
    
    
15. Notes on tests of significance: Significance vs importance, one vs two-tailed tests, testing many hypotheses).
    • Notes on statistical significance from the Prism Guide
    
    
16. Experimental design: Treatments and controls, experimental vs observational studies, beware the sample of convenience).
    • None
    
    
17. Introduction to multisample inference: The analysis of variance (ANOVA) for comparison of several treatment means, one-way ANOVA, random and fixed effects, homogeneity of variances, nonparametric alternatives (Kruskall-Wallis test)).
    • Chapter 10 intro, section 10.1, 10.2, 10.4
    
    
18. Multiple comparisons: The a posteriori comparison of means, Tukey test, Newman-Keuls test).
    • Chapter 11 intro, section 11.1, 11.2
    
    
19. Data transformations: Log, arcsine square root, and square root).
    • Chapter 13 intro, section 13.1, 13.2, 13.3
    
    
20. Linear regression: Bivariate data, scatterplots, dependent and independent variables, estimation and tests for slope and intercept, predicting values of Y, data transformation, comparing two slopes).
    • Chapter 17 intro, section 17.1, 17.2, 17.3, 17.4, 17.5 (first formula only; this formula makes sense only for fixed effects), 17.10,
    • We will additionally cover the topic of inverse prediction in random effects models (not in Zar).
    • The HyperStat Online Textbook has a section on the "regression effect" (regression toward the mean).
    
    
21. Correlation: Linear correlation coefficient, confidence intervals and tests, comparing correlation coefficients, nonparametric alternatives (rank correlation)), species are not independent observations.
    • Chapter 19 intro, 19.1, 19.2, 19.9
    
    
22. Introduction to experiments with more than one factor
    • Chapter 12 intro, section 12.1 (ignore formula details), figure 12.2