Psyc_315_-_Winter_2010_-_Class_18

Psyc_315_-_Winter_2010_-_Class_18 - Calculating Statistical...

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Calculating Statistical Power Examples 1 2 Example 1 • The mean of a population (M 2 ) is 200, with a standard error of the mean of 6. • The mean of a sample ( Μ 1 ) is 208. • Significance Level, α =0.05, 1-tailed. • Step 1: Μ 1 =208, SD M =6, Μ 2 =200 • Step 2: 5% significance level, one tailed, the Z-score of the cutoff would be +1.64 and convert to raw score (Note: Use H0 mean). ( ) 1 2 2 200 (1.64)(6) M M M M Z rearranged M M Z SD SD - = = + = + 2 Crit 3 Answer for Example 1 A Z of +1.64 is a raw score of 209.84 Step 3: Find Z score from same point, but on sample distribution (Note: Use H1 mean) Z = (209.84 - 208) / 6 = 0.31 Step 4: Look up % in normal curve table b For a z-score of 0.31, the area beyond = 38%. – So the power of the study is 38% and β {chance of Type II Error}= 1-0.38= 0.62 (62%).
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4 Example 2 • In a planned study, the population of a town is known to have a mean of 500 and a standard deviation of 100. • The researchers will give the experimental treatment to 60 people, and predict that the mean of those 60 will be 540. • They will use an α =0.05. • What is the power of this study, and what is the beta? 2 Crit 2 Crit 2 Crit 2 Crit 2 Crit ( ) 1 2 2 M M M M Z rearranged M M Z SD SD - = = + 2 Crit 5 Answer to Example 2 1. Gather info Mean of distribution is 500 Predicted mean of the sample is 540 Standard Error = 100/ 60=12.91 2. Raw-score cutoff point. M=M 2 +Z(SD M )=(1.64)(12.91)+500 A Z of 1.64 (5% significance level) will give a raw mean score of 521.17 3. Z score from same point, but on sample distribution Z=(521.17-540)/12.94 A raw mean of 521.17 will give a z-score of -1.46 4. Using normal curve table, figure probability of getting a mean more extreme than the z score: Power = 93% (that is, 43% between mean and Z of -1.46, and 50% above mean). β =1-0.93 = 7%. 6 Example 3 • Ex: A boutique wants to know whether background music affects sales. (The music could induce a mood that incites clients to buy more. The music could be considered noisy, and therefore a deterrent to sales). • For similarly-sized stores, mean revenue:
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Psyc_315_-_Winter_2010_-_Class_18 - Calculating Statistical...

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