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Comparing Two Populations

Comparing Two Populations. Chapter 9 Gonick Anthony Timpson Geog 3000 Feb 21 st , 2010. What are we doing?. How do we test questions like: Does taking aspirin reduce the risk of heart attack Does this pesticide increase our crop yield D o men and women make the same wage for the same job

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Comparing Two Populations

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  1. Comparing Two Populations Chapter 9 Gonick Anthony Timpson Geog 3000 Feb 21st, 2010

  2. What are we doing? • How do we test questions like: • Does taking aspirin reduce the risk of heart attack • Does this pesticide increase our crop yield • Do men and women make the same wage for the same job • To test these questions we compare two independent random samples taken from each population

  3. Comparing Success rates • In the example of Aspirin and heart attack rate • A large sample (20,000 subjects) • Two groups, placebo and aspirin • Compare directly the rates of heart attack in both groups • P-hat1 = x1/n1 and P-hat2 = x2/n2 • Where x = the number of successes in each trial n = the total sample size P-hat = rate of heart attack in sample group

  4. Comparing Success rates • The observed difference between the two is .0217-.0126= .0091 • The observed difference in risk is • .0217/.0126 = 1.72, meaning those who do not take aspirin are 1.72 times more likely to have a heart attack

  5. Sampling Distribution for P-hat1 - P-hat2 • For large samples P-hat1 - P-hat2 is ~ normally distributed • Remember these equations we will use the results to calculate confidence intervals on the next page • Z= ((P-hat1 - P-hat2) – (p1-p2))/σ (P-hat1 - P-hat2) • σ(P-hat1 - P-hat2) = Sqrt(σ2(P-hat1 ) + σ2(P-hat2 ))

  6. Confidence Intervals for p1-p2 • Standard Error • SE(P-hat1 - P-hat2)= Sqrt(((P-hat1)(1- P-hat1)/n1) + (P-hat2)(1- P-hat2)/n2)) • For the aspirin test the value SE = .0175 • Confidence Interval • The range of values we can expect to see with an expected confidence level, (95% for this test) • use the difference between placebo and aspirin .0091,the z value 1.96 (95% confidence) and the SE .0175 to calculate the expected range in heart attack reduction • Expected rate of heart attack reduction with daily aspirin intake, = (.0091 +- (1.96)(.0175)) * 100%

  7. Hypothesis Testing • Ho= 0Null Hypothesis, aspirin has no effect • Ha not = 0 Test hypothesis, aspirin has an effect • Where Z = Std dev from Ho = P-hat1 - P-hat2/ SE(P-hat1 - P-hat2)= .0091/.00175 = 5.20 • Ho = 0 • Ha = 5.20 • Aspirin definitely has an effect on heart attack rates

  8. Summary • This is one example of comparisons between two populations • There are countless other examples, each work in the same way utilizing the same principles to achieve the same goal • The end product is a range of values which can be expected given a selected confidence level and sufficient sample size

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