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Statistical Analysis Essentials: Hypothesis Testing, Sampling Methods, Bias, and More

Dive into key statistical concepts such as hypothesis testing, sampling methods, bias identification, distribution characteristics, measures of variation, probability distributions, and regression analysis.

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Statistical Analysis Essentials: Hypothesis Testing, Sampling Methods, Bias, and More

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  1. Review Lecture 51 Tue, Dec 13, 2005

  2. Chapter 1 • Sections 1.1 – 1.4. • Be familiar with the language and principles of hypothesis testing. • Given two explicit hypotheses, be able to calculate  and . • Given a value of the “test statistic,” be able to calculate the p-value. • Etc.

  3. Chapter 2 • Sections 2.1 – 2.8. • Know the characteristics of the different sampling methods: • Simple random sampling • Stratified sampling • Systematic sampling • Cluster sampling.

  4. Chapter 2 • Be familiar with the different types of bias: • Selection bias. • Response bias. • Non-response bias. • Experimenter bias. • Etc.

  5. Chapter 3 • Sections 3.1 – 3.5. • Know the difference between • An observational study and an experiment. • A prospective study and a retrospective study. • Be able to distinguish among explanatory, response, and confounding variables. • Be familiar with some methods of minimizing bias. • Etc.

  6. Chapter 4 • Sections 4.1 – 4.3.2, 4.4.1 – 4.4.2, 4.4.4, 4.5. • Be able to draw correctly • Pie charts • Bar graphs • Stem-and-leaf displays • Frequency plots • Histograms • Know which ones are appropriate for which kinds of data.

  7. Chapter 4 • Be familiar with the important characteristics of a distribution’s shape. • Etc.

  8. Chapter 5 • Sections 5.1 – 5.3. • Measures of center: • Mean • Median • Mode • Measures of variation • Range • Interquartile range

  9. Chapter 5 • Variance • Standard deviation • Be able to draw a boxplot. • Etc.

  10. Chapter 6 • Sections 6.1 – 6.4. • Be able to find a probability or percentile associated with a normal distribution. • Be able to find a probability or percentile associated with a uniform distribution. • Know and be able to apply the 68-95-99.7 Rule.

  11. Chapter 6 • Be able to draw a discrete probability distribution and find probabilities associated with it. • Etc.

  12. Chapter 7 • Section 7.5 – 7.5.1, 7.5.3. • Know what a random variable is. • Know the difference between discrete and continuous random variables. • Be able to calculate the mean, variance, and standard deviation of a discrete random variable from its probability distribution. • Etc.

  13. Chapter 8 • Sections 8.1 – 8.4. • Know what is meant by a sampling distribution of a statistic. • Be very familiar with the Central Limit Theorem for proportions, summarized on page 519. • Be very familiar with the Central Limit Theorem for means, summarized on pages 536 - 537. • Be able to recognize problems that call for the Central Limit Theorem and be able to apply it.

  14. Chapter 8 • Understand what bias and variability mean for a random variable. • Etc.

  15. Chapter 9 • Sections 9.1 – 9.4. • Know the sampling distribution of p^. • Know the criteria for when the sample size is large enough. • Be able to test a hypothesis concerning p. • Be able to calculate a confidence interval for p. • Know the 7 steps of hypothesis testing. • Etc.

  16. Chapter 10 • Sections 10.1 – 10.4. • Know the sampling distribution ofx. • Know the criteria for when the sample size is large enough. • Know how to decide whether to use the normal distribution or the t distribution. • Be able to test a hypothesis concerning. • Be able to calculate a confidence interval for .

  17. Chapter 10 • Be able to find p-values and percentiles for the t distribution. • Know the 7 steps of hypothesis testing. • Etc.

  18. Chapter 11 • Sections 11.1 – 11.5. • Know the difference between paired samples and independent samples. • Be able to test a hypothesis concerning paired differences. • Be able to test a hypothesis concerning the difference between two population proportions. • Be able to estimate the difference between two population proportions.

  19. Chapter 11 • Know when and how to use a pooled estimate of p. • Be able to test a hypothesis concerning the difference between two population means. • Be able to estimate the difference between two population means. • Know the criteria in all cases for using the normal distribution vs. the t distribution.

  20. Chapter 11 • Know when and how to use a pooled estimate of . • Etc.

  21. Chapter 13 • Sections 13.1 – 13.3, 13.7, 13.9. • Be able to draw a scatterplot of bivariate data. • Be familiar with the important characteristics: • Linear association. • Positive or negative association. • The strength of the association. • Know exactly what distinguishes the least squares regression line from all other lines.

  22. Chapter 13 • Be able to calculate the following: • The coefficients a and b of the regression line. • The residuals. • The predicted value of y, for a given value of x. • The residual sum of squares, SSE. • The regression sum of squares, SSR. • The total sum of squares, SST. • The correlation coefficient r. • The coefficient of determination r2.

  23. Chapter 13 • Be able to interpret the correlation coefficient. • Be able to interpret the coefficient of determination. • Be able to interpret the slope of the regression line. • Etc.

  24. Chapter 14 • Sections 14.1 – 14.5. • Be able to find chi-square probabilities and percentiles. • Be able to perform hypothesis tests for • Goodness of fit (univariate data) • Homogeneity (bivariate data) • Independence (bivariate data) • In all cases, be able to find the expected counts. • Etc.

  25. The TI-83 • Most of the calculations in Chapters 1 – 10 can be done on the TI-83. • You should be able to do them both on the TI-83 and by hand. • Most of the calculations in Chapters 11, 13, and 14 can be done on the TI-83. • Anything that can be done on the TI-83 in Chapters 11 - 14, you do not need to be able to do by hand.

  26. Formulas • You should know the necessary formulas from Chapters 1 – 10 and some miscellaneous formulas from Chapters 11 – 14. • The formulas that you do not need to know are listed on the Statistical Formulas sheet. • The standard normal table, the t tables, and the chi square tables will be provided.

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