Sample Size Determination

Transcription

1 Distributio of differece betwee sample meas Vijar Føebø Distributio of differece betwee two sample meas. Your variable is: ( x x ) Differece betwee sample meas The statistical test to be used would be: ( x x) Stadard deviatio Differece betwee sample meas The statistical test to be used would be: ( x x) Stadard deviatio What is the stadard deviatio i differeces betwee two sample meas? Differece betwee sample meas Distributio of differece betwee two sample meas SD: Differece betwee sample meas Distributio of differece betwee two group meas SD: The SD ca be maipulated by chagig

2 How may subjects (persos, rats or whatever) eed to be icluded i my study? Example used: Is there a differece i systolic blood pressure betwee persos bor i the midight su seaso compared to the midday darkess seaso? First importat questio you eed to address: What is the smallest blood pressure differece you thik it is ecessary to detect? Cliical relevace?? First importat questio you eed to address: What is the smallest blood pressure differece you thik it is ecessary to detect? Cliical relevace?? Let us choose 5 mmhg What is your hypothesis value? Origial research questio: Is there a differece i systolic blood pressure betwee persos bor i the midight su seaso compared to the midday darkess seaso? The hypothesis value is We must make sure that what we wat to show is ot compatible with the ull hypothesis. ie: > xsd

3 BUT, we are still acceptig a 5% chace of icorrectly cocludig that the ull hypothesis is ot a possible explaatio. We call this the α of power calculatios. Here α =.5 Type I error What if the real differece i the populatio is exactly 5 mmhg ad the sample size is of a size that 5 mmhg is foud exactly SDs from the ull hypothesis? But, remember: There will be a samplig distributio aroud 5 mmhg. 5 mmhg 5 mmhg We are acceptig a 5% chace of icorrectly cocludig that the ull hypothesis is a possible explaatio. THAT RISK IS TOO BIG We are here oly acceptig a % chace of icorrectly cocludig that the ull hypothesis is a possible explaatio. 5 mmhg 5 mmhg

4 BUT, we are still acceptig a % chace of icorrectly cocludig that the ull hypothesis is a possible explaatio. We call this the β of power calculatios. Here β =.(Risk of type II error) This is also called a power of.8 or 8% How do we fid the cut-off poit for %? How do we fid the cut-off poit for %? Areas of the Normal Curve () () Area (3) Area (3) betwee Area betwee Area the Mea beyod the Mea beyod () () z ad z z z ad z z We eed.96 SDs to take care of a α of.5. We eed aother.84 SDs to take care of a β of.. Our target of differece i systolic blood pressure eeds to be =.8 SDs away from the ull hypothesis value. The sample size determiatio equatio thus = 8. mmhg The sample size determiatio equatio thus is either kow from previous studies, or you must make a guess = 8. mmhg

5 The sample size determiatio equatio thus is either kow from previous studies, or you must make a guess = 8. mmhg ad are most ofte equal ad are the oly ukow compoets of the equatio Rearraged the equatio the =. 8 5 m m H g If we say = 5 tha we eed 4 persos i each group. For categorical data where the outcome is measured by risks ad rates, the priciple of reasoig is the same Books you ca read Statistics i small doses WM Castle, Churchill Livigstoe ISBN Statistical First Aid RP Hirsch, RK Riegelma, Blackwell Scietific Publicatios ISBN Essetials of medical statistics BR Kirkwood, Blackwell Scietific Publicatios ISBN Statistical packages you ca use Microsoft Excel Epi-Ifo STATA SPSS SAS