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Unit 3: Foundations for inference Lecture 4: Review / Synthesis Statistics 101 Thomas Leininger June 6, 2013 Announcements Announcements 1 A few details 2 Hypothesis testing Confidence intervals Review 3 Populations vs. sampling

  1. Unit 3: Foundations for inference Lecture 4: Review / Synthesis Statistics 101 Thomas Leininger June 6, 2013

  2. Announcements Announcements 1 A few details 2 Hypothesis testing Confidence intervals Review 3 Populations vs. sampling Sampling strategies Contingency tables Conditional probability Binomial distribution Hypothesis testing and confidence intervals Statistics 101 U3 - L4: Review / Synthesis Thomas Leininger

  3. Announcements Announcements MT tomorrow: you bring your cheat sheet & calculator, I will provide tables Project proposal due Tuesday Requested topics for today? Statistics 101 (Thomas Leininger) U3 - L4: Review / Synthesis June 6, 2013 2 / 17

  4. A few details Announcements 1 A few details 2 Hypothesis testing Confidence intervals Review 3 Populations vs. sampling Sampling strategies Contingency tables Conditional probability Binomial distribution Hypothesis testing and confidence intervals Statistics 101 U3 - L4: Review / Synthesis Thomas Leininger

  5. A few details Hypothesis testing Announcements 1 A few details 2 Hypothesis testing Confidence intervals Review 3 Populations vs. sampling Sampling strategies Contingency tables Conditional probability Binomial distribution Hypothesis testing and confidence intervals Statistics 101 U3 - L4: Review / Synthesis Thomas Leininger

  6. A few details Hypothesis testing What you need to know about HTs: Format for answering a hypothesis test question: Statistics 101 (Thomas Leininger) U3 - L4: Review / Synthesis June 6, 2013 3 / 17

  7. A few details Hypothesis testing What you need to know about HTs: Format for answering a hypothesis test question: State the null and alternative hypotheses 1 Statistics 101 (Thomas Leininger) U3 - L4: Review / Synthesis June 6, 2013 3 / 17

  8. A few details Hypothesis testing What you need to know about HTs: Format for answering a hypothesis test question: State the null and alternative hypotheses 1 Calculate the Z -statistic (and standard error) 2 Statistics 101 (Thomas Leininger) U3 - L4: Review / Synthesis June 6, 2013 3 / 17

  9. A few details Hypothesis testing What you need to know about HTs: Format for answering a hypothesis test question: State the null and alternative hypotheses 1 Calculate the Z -statistic (and standard error) 2 Calculate the p -value (double if two-sided hypothesis) 3 Statistics 101 (Thomas Leininger) U3 - L4: Review / Synthesis June 6, 2013 3 / 17

  10. A few details Hypothesis testing What you need to know about HTs: Format for answering a hypothesis test question: State the null and alternative hypotheses 1 Calculate the Z -statistic (and standard error) 2 Calculate the p -value (double if two-sided hypothesis) 3 Reject or fail to reject the null hypothesis 4 Statistics 101 (Thomas Leininger) U3 - L4: Review / Synthesis June 6, 2013 3 / 17

  11. A few details Hypothesis testing What you need to know about HTs: Format for answering a hypothesis test question: State the null and alternative hypotheses 1 Calculate the Z -statistic (and standard error) 2 Calculate the p -value (double if two-sided hypothesis) 3 Reject or fail to reject the null hypothesis 4 Interpret your decision in context of the problem 5 Statistics 101 (Thomas Leininger) U3 - L4: Review / Synthesis June 6, 2013 3 / 17

  12. A few details Confidence intervals Announcements 1 A few details 2 Hypothesis testing Confidence intervals Review 3 Populations vs. sampling Sampling strategies Contingency tables Conditional probability Binomial distribution Hypothesis testing and confidence intervals Statistics 101 U3 - L4: Review / Synthesis Thomas Leininger

  13. A few details Confidence intervals What you need to know about CIs: Format for answering a confidence interval question: Statistics 101 (Thomas Leininger) U3 - L4: Review / Synthesis June 6, 2013 4 / 17

  14. A few details Confidence intervals What you need to know about CIs: Format for answering a confidence interval question: Find and state the critical value ( z ⋆ ) 1 Statistics 101 (Thomas Leininger) U3 - L4: Review / Synthesis June 6, 2013 4 / 17

  15. A few details Confidence intervals What you need to know about CIs: Format for answering a confidence interval question: Find and state the critical value ( z ⋆ ) 1 Calculate the standard error 2 Statistics 101 (Thomas Leininger) U3 - L4: Review / Synthesis June 6, 2013 4 / 17

  16. A few details Confidence intervals What you need to know about CIs: Format for answering a confidence interval question: Find and state the critical value ( z ⋆ ) 1 Calculate the standard error 2 Calculate the confidence interval 3 Statistics 101 (Thomas Leininger) U3 - L4: Review / Synthesis June 6, 2013 4 / 17

  17. A few details Confidence intervals What you need to know about CIs: Format for answering a confidence interval question: Find and state the critical value ( z ⋆ ) 1 Calculate the standard error 2 Calculate the confidence interval 3 Interpret your confidence interval in context of the problem 4 Statistics 101 (Thomas Leininger) U3 - L4: Review / Synthesis June 6, 2013 4 / 17

  18. Review Announcements 1 A few details 2 Hypothesis testing Confidence intervals Review 3 Populations vs. sampling Sampling strategies Contingency tables Conditional probability Binomial distribution Hypothesis testing and confidence intervals Statistics 101 U3 - L4: Review / Synthesis Thomas Leininger

  19. Review Populations vs. sampling Announcements 1 A few details 2 Hypothesis testing Confidence intervals Review 3 Populations vs. sampling Sampling strategies Contingency tables Conditional probability Binomial distribution Hypothesis testing and confidence intervals Statistics 101 U3 - L4: Review / Synthesis Thomas Leininger

  20. Review Populations vs. sampling Populations vs. sampling Two statistics students at UCLA conducted an energy efficiency survey of graduate student apartments. There were seven university apartment buildings, and the students randomly selected three to be included in the study. In each building, they randomly chose 25 apartments. Statistics 101 (Thomas Leininger) U3 - L4: Review / Synthesis June 6, 2013 5 / 17

  21. Review Populations vs. sampling Populations vs. sampling Two statistics students at UCLA conducted an energy efficiency survey of graduate student apartments. There were seven university apartment buildings, and the students randomly selected three to be included in the study. In each building, they randomly chose 25 apartments. What population does their results actually apply to? (a) All graduate student apartments in the world. (b) All UCLA graduate student apartments in this group of seven buildings. (c) All UCLA graduate student apartments in the three sampled buildings. (d) All UCLA graduate student apartments that were sampled in the three buildings. Statistics 101 (Thomas Leininger) U3 - L4: Review / Synthesis June 6, 2013 5 / 17

  22. Review Populations vs. sampling Populations vs. sampling Two statistics students at UCLA conducted an energy efficiency survey of graduate student apartments. There were seven university apartment buildings, and the students randomly selected three to be included in the study. In each building, they randomly chose 25 apartments. What type of study is this? (a) an observational study using simple random sampling. (b) a double-blind experiment. (c) an observational study using cluster sampling. (d) an observational study using stratified sampling. Statistics 101 (Thomas Leininger) U3 - L4: Review / Synthesis June 6, 2013 5 / 17

  23. Review Sampling strategies Announcements 1 A few details 2 Hypothesis testing Confidence intervals Review 3 Populations vs. sampling Sampling strategies Contingency tables Conditional probability Binomial distribution Hypothesis testing and confidence intervals Statistics 101 U3 - L4: Review / Synthesis Thomas Leininger

  24. Review Sampling strategies What is the difference between stratified and cluster sampling? Why might we choose either of these methods over a simple random sam- ple? Statistics 101 (Thomas Leininger) U3 - L4: Review / Synthesis June 6, 2013 6 / 17

  25. Review Sampling strategies What is the difference between stratified and cluster sampling? Why might we choose either of these methods over a simple random sam- ple? Stratified: homogenous strata Cluster: heterogenous strata, but clusters are similar SRS is ideal, but To control for how various characteristics of the population are represented in the sample, we might choose stratified sampling Cluster sampling may be preferable for economical reasons Statistics 101 (Thomas Leininger) U3 - L4: Review / Synthesis June 6, 2013 6 / 17

  26. Review Contingency tables Announcements 1 A few details 2 Hypothesis testing Confidence intervals Review 3 Populations vs. sampling Sampling strategies Contingency tables Conditional probability Binomial distribution Hypothesis testing and confidence intervals Statistics 101 U3 - L4: Review / Synthesis Thomas Leininger

  27. Review Contingency tables Contingency tables Table from earlier describing agreement with parents’ policial views and view on legalizing marijuana: Parent Politics Legalize MJ No Yes Total No 11 40 51 Yes 36 78 114 Total 47 118 165 Statistics 101 (Thomas Leininger) U3 - L4: Review / Synthesis June 6, 2013 7 / 17

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