Methods of Research in Public Health MPH 606

1. Methods of Research in Public HealthMPH 606 Susan Bailey, PhD Spring 2010 Lecture 6

2. Stages of a Study • Formulate the Research Question • May or may not test a hypothesis • Review the Literature • Choose/Design Measures and Instruments • Identify the Sampling Frame • Obtain IRB Approval • Conduct the Sampling • Collect Data • Process Data • Analyze Data • Report Results

3. Inferential Statistics

4. Learning Objectives • Understand the theory behind statistical testing • Recognize a few types of statistical tests • Confidence intervals • Z score • T-test • Chi-square • F score • Understand the importance of statistical power

5. Statistical Inference Sample Generalize

6. Probability and Statistical Inference • Probabilities - numbers that reflect the likelihood that a particular event will occur • Statistical inference - making generalizations or inferences about unknown population parameters based on sample statistics Population ParametersSample Statistics µ X bar σ s N n

7. Relevance • We want to be 95% confident that our sample statistic is a correct estimate of our population parameter

8. More Terms • Null hypothesis - shows no relationship - we want to be able to reject this • Alternative hypothesis - want to say that this is statistically likely • Alpha (α) - probability that we incorrectly reject the null hypothesis (want to minimize this) - usually 0.05 • One-tailed test - relationship is in one direction • Two-tailed test - relationship can be in either direction

9. Normal Distribution One tail – p = 0.025 Two tail - p = 0.05 One tail – p = 0.05 Two tail – p = 0.10 α=0.50 α=1-0.50 α =1-0.95 α = 1 – 0.975 α =0.05 α = 0.025 -1.96-1.640.001.641.96

10. Confidence Interval • Probability-based margin of error around a sample statistic as an estimate of a population parameter point estimate ± margin of error • Margin of error includes a standard value associated with an α level based on a probability distribution Mean ± (standard value) s/ n • This is the confidence interval for µ • The tighter the interval, the more precise the estimate • Width of the interval is directly related to n

11. Standardized Values • Also called test statistics • Based on a probability-based distribution of standard scores • Z - when sample n is ≥ 30 • t - when sample n is < 30 • For example, if α is 0.05 relevant Z is 1.96, can then say that we’re 95% confident that our estimate of the parameter is within the interval surrounding the sample statistic

12. Other Test Statistics • Chi-square (χ2) - for categorical outcomes • F - for Analysis of Variance (ANOVA) when have a continuous outcome and more than two samples being compared

13. Statistical Power • Goal is to maximize the power to detect effects and reject the null hypothesis α = p (Type I error) = p (reject a null hypothesis that is really correct) β = p (Type II error) = p (don’t reject a null hypothesis that is really incorrect) Power = 1 - β = p (reject a null hypothesis that is really incorrect) • Standard is 80% power (20% chance of making a Type II error - missing a true result)

14. Statistical Power • Depends on: • Sample size (n) • Desired level of significance (α) • Effect size (expected strength of a relationship or magnitude of difference between comparison groups) • Determined based on clinical or practical criteris • Power analysis - simple example for CI of µ • Use formula of confidence interval to solve for n µ ± Z (σ/ n ) so margin of error (E) = Z (σ/ n ) so n = ((Z σ)/E)2 • Also statistical packages that do power analysis