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RESEARCH METHODOLOGY & STATISTICS LECTURE 6B: CONFIDENCE INTERVALS Addictions Department MSc(Addictions) From sample to population… units population inference sample RESEARCH METHODS AND STATISTICS Sampling distributions and confidence intervals Sampling distributions population 6 mean sample Sampling distributions population 6 5 mean sample Sampling distributions population 5 6 mean sample 6 Sampling distributions population 4 6 7 5 6 7 8 5 6 7 8 9 sampling distribution sampling distribution of the mean sample Relationship between distributions population the distribution of the mean is normal even if the distribution of the variable is not mean mean sample mean sampling distribution Relationship between distributions population how precisely the population mean is estimated by the sample mean standard error deviation standard deviation sampling distribution √sample size sample 95% confidence interval for a mean population standard error mean mean mean mean -1.96 x s.e. sample mean +1.96 x s.e. 95% probability that sample mean is within 1.96 standard errors of the population mean 95% confidence interval for a mean population mean? mean mean mean -1.96 x s.e. sample mean +1.96 x s.e. 95% probability that population mean is within 1.96 standard errors of the sample mean 95% confidence interval for a mean population mean? mean mean mean -1.96 x s.d. √size sample mean +1.96 x s.d. √size 95% probability that population mean is within 1.96 standard errors of the sample mean Sampling and inference population mean? mean sample mean sampling distribution Interpreting confidence intervals • An example result: mean = 6.7, 95% CI = 2.7 – 8.9 • Does not indicate: “there is a 95% probability that the population mean lies between 2.7 and 8.9” • The population mean is unknown but it is a fixed number • The confidence interval varies between samples 1. Take multiple random, independent samples 2. For each, calculate 95% confidence interval 3. On average, 19/20 (95%) of the confidence intervals will overlap the true population mean COMPUTER EXERCISE Confidence intervals Creating confidence intervals http://tinyurl.com/oqwtguv Exercises 1. How does altering the sample size affect the confidence intervals calculated? 2. Select a Skewed Bimodal distribution. What happens to the confidence intervals with a large sample size (>30)? What happens when the sample size is <10? 3. Try creating different distributions to see how the confidence interval calculation is affected Modify Java settings 1. Go to the Java Control Panel (On Windows Click Start and then type Configure Java) 2. Click on the Security tab 3. Click on the Edit Site List button 4. Click the Add button 5. Type http://wise.cgu.edu 6. Click the Add button again 7. Click Continue and OK on the security window dialogue box
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