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Comparing Two Proportions

Comparing Two Proportions. chapter 22 -Assumptions and conditions for comparing two proportions -Running a confidence interval and a significance test.

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Comparing Two Proportions

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  1. Comparing Two Proportions chapter 22 -Assumptions and conditions for comparing two proportions -Running a confidence interval and a significance test

  2. A presidential candidate fears he has a problem with women voters. His campaign staff plans to run a poll to assess the situation. They’ll randomly sample 300 men and 300 women, asking if they have a favorable impression of the candidate. 177 men and 159 women respond that they have a positive impression of the candidate. Is there a gender gap? How can we show the difference between the samples is indicative of the population? That its not just normal variation from a random sample?

  3. A presidential candidate fears he has a problem with women voters. His campaign staff plans to run a poll to assess the situation. They’ll randomly sample 300 men and 300 women, asking if they have a favorable impression of the candidate. 177 men and 159 women respond that they have a positive impression of the candidate. Is there a gender gap? Assumptions and Conditions: Independence Assumption Randomization condition (SRS, independent responses) 10% condition The 2 groups must be independent (if not SE is not valid) Success / Failure condition (check each group separately here)

  4. A presidential candidate fears he has a problem with women voters. His campaign staff plans to run a poll to assess the situation. They’ll randomly sample 300 men and 300 women, asking if they have a favorable impression of the candidate. 177 men and 159 women respond that they have a positive impression of the candidate. Is there a gender gap? The observed difference is: 177/300 – 159/300 = .06 Confidence Interval (never pool) SE: : ME: Interval:

  5. A presidential candidate fears he has a problem with women voters. His campaign staff plans to run a poll to assess the situation. They’ll randomly sample 300 men and 300 women, asking if they have a favorable impression of the candidate. 177 men and 159 women respond that they have a positive impression of the candidate. Is there a gender gap? The observed difference is: 177/300 – 159/300 = .06 Hypothesis Test (pool the data for better SE) Ho: Ha: : SE: ME: Z: P:

  6. Comparing Two Proportions Use the Lesson check on the web page to record your answers to the following questions.

  7. A study published in the Archives of General Psychiatry in March 2001 examined the impact of depression on a patient’s ability to survive cardiac disease. Researchers identified 450 people with cardiac disease, evaluated them for depression , and followed the group for 4 years. Of the 361 patients with no depression, 67 died. Of the 89 patients with minor or major depression, 26 died. Among people who suffer from cardiac disease, are depressed patients more likely to die than non-depressed ones?

  8. A study published in the Archives of General Psychiatry in March 2001 examined the impact of depression on a patient’s ability to survive cardiac disease. Researchers identified 450 people with cardiac disease, evaluated them for depression , and followed the group for 4 years. Of the 361 patients with no depression, 67 died. Of the 89 patients with minor or major depression, 26 died. Among people who suffer from cardiac disease, are depressed patients more likely to die than non-depressed ones? a) What kind of design was used to collect these data?

  9. A study published in the Archives of General Psychiatry in March 2001 examined the impact of depression on a patient’s ability to survive cardiac disease. Researchers identified 450 people with cardiac disease, evaluated them for depression , and followed the group for 4 years. Of the 361 patients with no depression, 67 died. Of the 89 patients with minor or major depression, 26 died. Among people who suffer from cardiac disease, are depressed patients more likely to die than non-depressed ones? b) Construct a 95% confidence interval, use the calculator for basic operations only (+ - x / ).

  10. A study published in the Archives of General Psychiatry in March 2001 examined the impact of depression on a patient’s ability to survive cardiac disease. Researchers identified 450 people with cardiac disease, evaluated them for depression , and followed the group for 4 years. Of the 361 patients with no depression, 67 died. Of the 89 patients with minor or major depression, 26 died. Among people who suffer from cardiac disease, are depressed patients more likely to die than non-depressed ones? c) Explain in context the confidence interval.

  11. A study published in the Archives of General Psychiatry in March 2001 examined the impact of depression on a patient’s ability to survive cardiac disease. Researchers identified 450 people with cardiac disease, evaluated them for depression , and followed the group for 4 years. Of the 361 patients with no depression, 67 died. Of the 89 patients with minor or major depression, 26 died. Among people who suffer from cardiac disease, are depressed patients more likely to die than non-depressed ones? d) Write appropriate hypothesis.

  12. A study published in the Archives of General Psychiatry in March 2001 examined the impact of depression on a patient’s ability to survive cardiac disease. Researchers identified 450 people with cardiac disease, evaluated them for depression , and followed the group for 4 years. Of the 361 patients with no depression, 67 died. Of the 89 patients with minor or major depression, 26 died. Among people who suffer from cardiac disease, are depressed patients more likely to die than non-depressed ones? e) Are the assumptions and conditions necessary for inference satisfied? Assumptions and Conditions: 1- Independence Assumption Randomization condition (SRS, independent responses) 10% condition The 2 groups must be independent (if not SE is not valid) Success / Failure condition (check each group separate here)

  13. A study published in the Archives of General Psychiatry in March 2001 examined the impact of depression on a patient’s ability to survive cardiac disease. Researchers identified 450 people with cardiac disease, evaluated them for depression , and followed the group for 4 years. Of the 361 patients with no depression, 67 died. Of the 89 patients with minor or major depression, 26 died. Among people who suffer from cardiac disease, are depressed patients more likely to die than non-depressed ones? f) Test the hypothesis and state your conclusion. Only use the calculator for basic operations (use the formulas, why would you pool this?)

  14. A study published in the Archives of General Psychiatry in March 2001 examined the impact of depression on a patient’s ability to survive cardiac disease. Researchers identified 450 people with cardiac disease, evaluated them for depression , and followed the group for 4 years. Of the 361 patients with no depression, 67 died. Of the 89 patients with minor or major depression, 26 died. Among people who suffer from cardiac disease, are depressed patients more likely to die than non-depressed ones? g) Explain in this context what your P-value means.

  15. A study published in the Archives of General Psychiatry in March 2001 examined the impact of depression on a patient’s ability to survive cardiac disease. Researchers identified 450 people with cardiac disease, evaluated them for depression , and followed the group for 4 years. Of the 361 patients with no depression, 67 died. Of the 89 patients with minor or major depression, 26 died. Among people who suffer from cardiac disease, are depressed patients more likely to die than non-depressed ones? h) If your conclusion is actually incorrect, which type of error did you commit?

  16. End of JV lecture

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