Susan Bailey, PhDSpring 2010

Lecture 6

Stages of a StudyFormulate the Research Question

May or may not test a hypothesisReview the LiteratureChoose/Design Measures and InstrumentsIdentify the Sampling FrameObtain IRB ApprovalConduct the SamplingCollect DataProcess DataAnalyze DataReport Results

Learning ObjectivesUnderstand the theory behind statistical testing

Recognize a few types of statistical testsConfidence intervalsZ scoreT-testChi-squareF score

Understand the importance of statistical power

Statistical Inference

Sample Generalize

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 statisticsPopulation Parameters Sample Statistics

µ X barσ sN n

Relevance

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

More TermsNull hypothesis - shows no relationship - we

want to be able to reject thisAlternative hypothesis - want to say that this is

statistically likelyAlpha (α) - probability that we incorrectly

reject the null hypothesis (want to minimize this) - usually 0.05

One-tailed test - relationship is in one directionTwo-tailed test - relationship can be in either

direction

Normal Distribution

One tail – p = 0.025Two tail - p = 0.05

One tail – p = 0.05Two tail – p = 0.10

α =1-0.95 α = 1 – 0.975

α =0.05α = 0.025

-1.96 -1.64 0.00 1.64 1.96

α=0.50 α=1-0.50

Confidence IntervalProbability-based margin of error around a sample

statistic as an estimate of a population parameterpoint 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/ nThis is the confidence interval for µThe tighter the interval, the more precise the

estimateWidth of the interval is directly related to n

Standardized ValuesAlso called test statisticsBased on a probability-based distribution of

standard scoresZ - when sample n is ≥ 30t - 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

Other Test StatisticsChi-square (χ2) - for categorical outcomesF - for Analysis of Variance (ANOVA) when

have a continuous outcome and more than two samples being compared

Statistical PowerGoal is to maximize the power to detect effects and

reject the null hypothesisα = 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)

Statistical PowerDepends 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 µUse formula of confidence interval to solve for n

µ ± Z (σ/ n ) so margin of error (E) = Z (σ/ n ) son = ((Z σ)/E)2

Also statistical packages that do power analysis