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# 8 - Standard deviation Improving the value of standard...

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1 Standard deviation Improving the value of standard deviation – Sometimes you may have a small set of results, but the same type of analysis has been done many times in the past on other samples – You can use standard deviations calculated from You can use standard deviations calculated from historical data to get lower confidence limits – This is referred to as "pooling" data 1 Pooled standard deviation Example. Refer to data sets "A" and "B" 2 Recall: Confidence limits A: 60.53, 60.53, 60.37, 60.37, 60.29, 60.29% B: 60.53, 60.37, 60.29 % – Calculate the 95% confidence intervals for the sets of results A and B above • This means that on repeated measurement you would This means that on repeated measurement, you would get a result within these ranges 95 times out of 100 Only 5% of the time would you get a result outside this range 3

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2 Recall:Confidence limits 4 Pooled standard deviation – A: 60.53, 60.53, 60.37, 60.37, 60.29, 60.29 % – Mean = ( x i )/ N = 362.38/6 = 60.40 % – Standard deviation (s) = ([ ( x i x ) 2 ]/ N -1) = (0.0598/5) = 0.01196 = 0.1093 = 0.11 % – 95% CI ( μ ) = x ± t*s / N 95% CI ( ) t s / = 60.40 ± 2.571*0.11 / 6 = 60.40 ± 0.2810/2.449 = 60.40 ± 0.11 % 5 Pooled standard deviation B: 60.53, 60.37, 60.29 % – Mean = ( x i )/ N = 181.19/3 = 60.40 % – Standard deviation (s) = ([ ( x i x ) 2 ]/ N -1) = (0.0299/2) = 0.01495 = 0.1222 = 0.12 % 95% CI ( μ ) = x ± t*s / N – 95% CI ( ) = / = 60.40 ± 4.303*0.12 / 3 = 60.40 ± 0.5258/1.732 = 60.40 ± 0.30 % 6