MATH 502 APPLIED STATISTICS

Course Syllabus

Topic 1. Controlled Experiments

1. Randomized, double blinded controls (the Salk vaccine field trial)

2. Bias and confounding

3. Historical controls

Topic 2. Observational Studies

1. Examples of confounding variables in real observational studies.

2. Simpson's paradox.

Topic 3. Data Histograms and Cross-Sectional Data.

1. Reading and drawing histograms

2. The density scale

3. Controlling for a potentially confounding variable

4. Cross-Tabulation

Topic 4. The Average, Root Mean Square, and Standard Deviation Their definition, computation, interpretation, and relationship with the histogram. Their sensitivity to extreme values and alternate resistant measures of central tendency and spread in the presence of severe skewness.

Topic 5. The Normal Approximation of Data.

1. Finding areas under the normal curve

2. The normal approximation for data

3. Percentiles

4. Percentiles and the normal curve

Topic 6. The Gauss Model for Measurement Error

Topic 7. Correlation

1. Scatterplots for bivariate data; scatterplots of data with elliptical contours

2. The Correlation Coefficient

3. Symmetry, scale and location invariance of the correlation coefficient

4. Sensitivity to extreme bivariate values' inappropriateness for nonlinear associations

5. Fallacies due to ecological correlations

6. Association is not causation

Topic 8. Regression

1. Interpretation of the regression line as a smoother of the graph of averages

2. Calculating and interpreting the regression coefficient

3. The regression effect and the regression fallacy

4. The nonsymmetry of regression - there are two regression lines

5. Root mean squared error for regression

6. Use of the normal approximation to compute conditional densities

Topic 9. Probability

1. Interpretation of probability as relative frequency

2. Conditional probabilities

3. The multiplication rule

4. Independence

Topic 10. The Law of Averages

1. What the Law of Averages says and what it does not say.

2. Box Models

Topic 11. Expected Value (EV) Standard Error (SE), and the Normal Approximation for the Probability Histogram

1. Definitions and interpretations

2. Computations for the EV and SE of the sum of the draws from a box model.

3. Simplified computations for classifying and counting (the binomial model)

4. Probability histograms

5. The normal approximation for sums (the central limit theorem)

6. The scope of the normal approximation

Topic 12. Sample Surveys

1. Historical look at polling and its failure to predict

2. Nonsampling errors or biases in polling

3. Simple random samples, stratified samples and cluster samples.

4. Chance errors in sampling

5. A close look at the Gallop poll

Topic 13. The Accuracy of Percentages

1. Confidence intervals for percentages

2. Interpretation and misinterpretations of confidence intervals

3. Assumptions underlying the estimation of a percentage

Topic 14. The Accuracy of Averages

1. The sample average

2. Confidence intervals for averages

3. Assumptions underlying the estimation of an average

Topic 15. Tests of Significance

1. Null and alternative hypotheses

2. Test statistics and significance levels and their interpretation

3. The z-test and the t-test

Topic 16. More Tests for Averages

1. The standard error for a difference

2. Comparing two sample averages: confidence intervals and tests

3. Examination of the assumptions

Topic 17. The Chi-squared Test

1. The structure of a Chi-squared Test

2. Testing independence and homogeneity

Topic 18. A Closer Look at Tests of Significance

1. Was the result significant?

2. Data snooping

3. Was the result Important?

4. Does the difference prove the point?

5. The role of the model

6. Conclusion

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