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Introduction to Biostatistics (PUBHLTH 540) Hypothesis Testing

Introduction to Biostatistics (PUBHLTH 540) Hypothesis Testing. General Idea How unusual is the result? Test statistics Type I error (alpha level) p-value Type II error (beta level) Power=1-beta. Introduction to Biostatistics (PUBHLTH 540) Hypothesis Testing-General Idea.

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Introduction to Biostatistics (PUBHLTH 540) Hypothesis Testing

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  1. Introduction to Biostatistics (PUBHLTH 540)Hypothesis Testing • General Idea • How unusual is the result? • Test statistics • Type I error (alpha level) • p-value • Type II error (beta level) • Power=1-beta

  2. Introduction to Biostatistics (PUBHLTH 540)Hypothesis Testing-General Idea • Total cholesterol (mg/dl) is measured on a simple random sample of 32 women over the age of 60. Is there evidence that mean cholesterol is different in women of this age group as compared with women under age 50? • Estimate of TC: (see ejs09b540p36.sas) • Plot histogram of SRS of n=32 from women <50. (see ejs09b540p37.sas) Result is very unusual relative to what we’d expect from sampling. Conclude the mean is differnet. 244

  3. Introduction to Biostatistics (PUBHLTH 540)Hypothesis Testing-General Idea • Histogram of distribution of sample means/standardized value- • need to know mean and variance of TC for women < 50. • use Z if variance is known, t if variance is estimated • for women < 50: 244

  4. Introduction to Biostatistics (PUBHLTH 540)Hypothesis Testing-General Idea • Histogram of distribution of sample means • or … histogram of standardized values of the difference of the sample mean from the mean TC for women < 50 • need to know mean and variance of TC for women < 50. • use Z if variance is known, t if variance is estimated • for women < 50: 244

  5. Introduction to Biostatistics (PUBHLTH 540)Hypothesis Testing-General Idea 244

  6. Introduction to Biostatistics (PUBHLTH 540)Hypothesis Testing-General Idea z=8.08

  7. Introduction to Biostatistics (PUBHLTH 540)Hypothesis Testing-General Idea z=8.32 z=8.3

  8. Introduction to Biostatistics (PUBHLTH 540)Hypothesis Testing-General Idea • Is the result ‘unusual’? • Decide a level of ‘unusualness’ • usually set at values so that 5% of time, sample mean would be further away • If in either direction, then 2.5% on either side, and test is called ‘2-sided’ • If unusual is important only in one direction (drug lowers cholesterol), then put all 5% on one side • Null hypothesis is ‘usual’ or commonly accepted position. • Alternative hypothesis is what you want to ‘prove’

  9. Figure 1. Histogram of sample means of n=32 for tc from Population of N=93 10 Percent 5 0 170 173 176 179 182 185 188 191 194 197 200 203 206 209 212 215 218 221 224 227 230 233 236 239 242 245 mn_samp Source: ejs09b540p37.sas 10/27/2009 by ejs Introduction to Biostatistics (PUBHLTH 540)Hypothesis Testing-General Idea Null Hypothesis:

  10. Figure 1. Histogram of sample means of n=32 for tc from Population of N=93 10 Percent 5 0 170 173 176 179 182 185 188 191 194 197 200 203 206 209 212 215 218 221 224 227 230 233 236 239 242 245 mn_samp Source: ejs09b540p37.sas 10/27/2009 by ejs Introduction to Biostatistics (PUBHLTH 540)Hypothesis Testing-General Idea AlternativeHypothesis

  11. Figure 1. Histogram of sample means of n=32 for tc from Population of N=93 10 Percent 5 0 170 173 176 179 182 185 188 191 194 197 200 203 206 209 212 215 218 221 224 227 230 233 236 239 242 245 mn_samp Source: ejs09b540p37.sas 10/27/2009 by ejs Introduction to Biostatistics (PUBHLTH 540)Hypothesis Testing-General Idea 2-sided test Unusual Unusual

  12. Figure 1. Histogram of sample means of n=32 for tc from Population of N=93 10 Percent 5 0 170 173 176 179 182 185 188 191 194 197 200 203 206 209 212 215 218 221 224 227 230 233 236 239 242 245 mn_samp Source: ejs09b540p37.sas 10/27/2009 by ejs Introduction to Biostatistics (PUBHLTH 540)Hypothesis Testing-General Idea 1-sided test Unusual

  13. Figure 1. Histogram of sample means of n=32 for tc from Population of N=93 10 Percent 5 0 170 173 176 179 182 185 188 191 194 197 200 203 206 209 212 215 218 221 224 227 230 233 236 239 242 245 mn_samp Source: ejs09b540p37.sas 10/27/2009 by ejs Introduction to Biostatistics (PUBHLTH 540)Hypothesis Testing-General Idea 2-sided test Unusual Unusual

  14. Figure 1. Histogram of sample means of n=32 for tc from Population of N=93 10 Percent 5 0 170 173 176 179 182 185 188 191 194 197 200 203 206 209 212 215 218 221 224 227 230 233 236 239 242 245 mn_samp Source: ejs09b540p37.sas 10/27/2009 by ejs Introduction to Biostatistics (PUBHLTH 540)Hypothesis Testing-General Idea 1-sided test Unusual

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