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Power The Four Components to a Statistical Conclusion Sample size The number of units (e.g., people) accessible to study Effect size The salience of the program relative to the noise Alpha level The odds the observed result is due to chance Power The odds you’ll observe a treatment effect when it occurs The Four Components to a Statistical Conclusion Sample size Amount of information Effect size Salience of program Alpha level Willingness to risk Power Ability to see effect that’s there The Effect Size Is a ratio of... The Effect Size Is a ratio of... Signal Noise The Effect Size Is a ratio of... Signal Noise Difference between groups Standard error of the difference Given Values for Any Three, You Can Compute the Fourth. n = f(effect size, a, power) effect size = f(n, a, power) a = f(n, effect size, power) power = f(n, effect size, a) The Decision Matrix In reality What we conclude The Decision Matrix In reality Null true Alternative false In reality... • What • There is no real program effect There is no difference, gain • we conclude Our theory is wrong The Decision Matrix In reality Null true Alternative false In reality... • What • There is no real program effect There is no difference, gain • we conclude Our theory is wrong Accept null Reject alternative We say... • There is no real program effect • There is no difference, gain • Our theory is wrong The Decision Matrix In reality Null true Alternative false In reality... • What • There is no real program effect There is no difference, gain • we conclude Our theory is wrong Accept null 1- Reject alternative THE CONFIDENCE LEVEL We say... The odds of saying there is • There is no real no effect or gain when in program effect fact there is none • There is no difference, # of times out of 100 when gain there is no effect, we’ll say • Our theory is wrong there is none The Decision Matrix In reality Null true Alternative false In reality... • What • There is no real program effect There is no difference, gain • we conclude Our theory is wrong Reject null Accept alternative We say... • There is a real program effect • There is a difference, gain • Our theory is correct The Decision Matrix In reality Null true Alternative false In reality... • What • There is no real program effect There is no difference, gain • we conclude Our theory is wrong Reject null Accept alternative TYPE I ERROR We say... The odds of saying there is an effect or gain when in • There is a real program effect fact there is none • There is a difference, # of times out of 100 when gain there is no effect, we’ll say • Our theory is correct there is one The Decision Matrix Null false In reality Alternative true In reality... What • • There is a real program effect There is a difference, gain we conclude • Our theory is correct The Decision Matrix Null false In reality Alternative true In reality... • What • There is a real program effect There is a difference, gain • we conclude Our theory is correct Accept null Reject alternative We say... • There is no real program effect • There is no difference, gain • Our theory is wrong The Decision Matrix Null false In reality Alternative true In reality... • What • There is a real program effect There is a difference, gain • we conclude Our theory is correct Accept null Reject alternative TYPE II ERROR We say... The odds of saying there is • There is no real no effect or gain when in program effect fact there is one • There is no difference, # of times out of 100 when gain there is an effect, we’ll say • Our theory is wrong there is none The Decision Matrix Null false In reality Alternative true In reality... • What • There is a real program effect There is a difference, gain • we conclude Our theory is correct Reject null Accept alternative We say... • There is a real program effect • There is a difference, gain • Our theory is correct The Decision Matrix Null false In reality Alternative true In reality... • What • There is a real program effect There is a difference, gain • we conclude Our theory is correct Reject null 1- Accept alternative POWER We say... The odds of saying there is an effect or gain when in • There is a real program effect fact there is one • There is a difference, # of times out of 100 when gain there is an effect, we’ll say • Our theory is correct there is one The Decision Matrix Null false In reality Null true Alternative false Alternative true In reality... In reality... • • What • There is no real program effect There is no difference, gain • There is a real program effect There is a difference, gain • • we conclude Our theory is wrong Our theory is correct Accept null 1- Reject alternative THE CONFIDENCE LEVEL TYPE II ERROR We say... The odds of saying there is The odds of saying there is • There is no real no effect or gain when in no effect or gain when in program effect fact there is none fact there is one • There is no difference, # of times out of 100 when # of times out of 100 when gain there is no effect, we’ll say there is an effect, we’ll say • Our theory is wrong there is none there is none Reject null 1- Accept alternative TYPE I ERROR POWER We say... The odds of saying there is The odds of saying there is an effect or gain when in an effect or gain when in • There is a real program fact there is none fact there is one effect • There is a difference, # of times out of 100 when # of times out of 100 when gain there is no effect, we’ll say there is an effect, we’ll say • Our theory is correct there is one there is one The Decision Matrix Null false In reality Null true Alternative false Alternative true In reality... In reality... • • What • There is no real program effect There is no difference, gain • There is a real program effect There is a difference, gain • • we conclude Our theory is wrong Our theory is correct Accept null 1- Reject alternative THE CONFIDENCE LEVEL TYPE II ERROR We say... • There is no real program effect • There is no difference, gain • Our theory is wrong Reject null 1- Accept alternative TYPE I ERROR POWER We say... • There is a real program effect • There is a difference, gain • Our theory is correct The Decision Matrix Null false In reality Null true Alternative false Alternative true In reality... In reality... • • What • There is no real program effect There is no difference, gain • There is a real program effect There is a difference, gain • • we conclude Our theory is wrong Our theory is correct Accept null 1- Reject alternative THE CONFIDENCE LEVEL TYPE II ERROR We say... CORRECT • There is no real program effect • There is no difference, gain • Our theory is wrong Reject null 1- Accept alternative TYPE I ERROR POWER We say... • There is a real program CORRECT effect • There is a difference, gain • Our theory is correct The Decision Matrix Null false In reality Null true Alternative false Alternative true In reality... In reality... • • What • There is no real program effect There is no difference, gain • There is a real program effect There is a difference, gain • • we conclude Our theory is wrong Our theory is correct Accept null 1- Reject alternative THE CONFIDENCE LEVEL TYPE II ERROR We say... The odds of saying there is The odds of saying there is • If you try to increase power, you increase There is no real no effect or gain when in no effect or gain when in program effect fact there is none fact there is one • winding up the chance of times out of 100 when in the bottom when There is no difference, # of # of times out of 100 gain • there is no effect, we’ll say error. row and of none I Our theory is wrong there is Type there is an effect, we’ll say there is none Reject null 1- Accept alternative TYPE I ERROR POWER We say... The odds of saying there is The odds of saying there is an effect or gain when in an effect or gain when in • There is a real program fact there is none fact there is one effect • There is a difference, # of times out of 100 when # of times out of 100 when gain there is no effect, we’ll say there is an effect, we’ll say • Our theory is correct there is one there is one The Decision Matrix Null false In reality Null true Alternative false Alternative true In reality... If you try to • There is no real program effect • In reality... What There is a real program effect decrease Type I •• There is no is wrong gain difference, • • There is a difference, gain we conclude Our theory Our theory is correct errors, you Accept null 1- increase the Reject alternative THE CONFIDENCE LEVEL TYPE II ERROR chance of winding The odds of saying there is We say... The odds of saying there is There is top up •in theno real row no effect or gain when in no effect or gain when in program effect fact there is none fact there is one • There is Type II and of no difference, # of times out of 100 when # of times out of 100 when gain error. • Our theory is wrong there is no effect, we’ll say there is none there is an effect, we’ll say there is none Reject null 1- Accept alternative TYPE I ERROR POWER We say... The odds of saying there is The odds of saying there is an effect or gain when in an effect or gain when in • There is a real program fact there is none fact there is one effect • There is a difference, # of times out of 100 when # of times out of 100 when gain there is no effect, we’ll say there is an effect, we’ll say • Our theory is correct there is one there is one

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posted: | 9/1/2012 |

language: | English |

pages: | 23 |

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