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Statistics Review

Statistics Review. ChE 475 Fall 2013 Dr. Fletcher. 1. Repeated Data Points. Use t-test based on measured st dev ( s ). measured mean. true mean. Gaussian Distribution. 68.27% of distribution lies within one  95.45% of distribution lies within two 

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Statistics Review

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  1. Statistics Review ChE 475 Fall 2013 Dr. Fletcher

  2. 1. Repeated Data Points • Use t-test based on measured stdev (s) measured mean true mean

  3. Gaussian Distribution • 68.27% of distribution lies within one  • 95.45% of distribution lies within two  • 99.73% of distribution lies within three  • t-test is used when we do not have enough data points 68.27% 98.45% 99.73%

  4. 2. Comparing averages of measuredvariables New formula: Larger |T|: More likely different Step 1 For this example, Step 2 r = nx1+nx2-2 At a given confidence level (e.g. 95% or a=0.05), there is a difference if: Step 3 2-tail

  5. 3. Linear Regression • y = mx + b • Fit m and b, get r2 • Find confidence intervals for m and b • m = 3.56  0.02, etc. • Use standard error and t-statistic • Excel add-on (or Igor) • Find confidence intervals for line • Use standard error around mean • Narrow waisted curves around line • Depends on n • Meaning: How many ways can I draw a line through data • Find prediction band for line • Meaning: Where are the bounds of where the data lie

  6. 3. Linear Regression(Confidence Interval) • Confidence Interval • Prediction Band

  7. Example

  8. Confidence Intervals and Prediction Bands • What good is the confidence interval for a line? • Shows how many ways the line can fit the points • Let’s you state the confidence region for any predicted point • r2 still helps determine how good the fit is • What good is the prediction band? • Shows where the data should lie • Helps identify outlying data points to consider discarding

  9. Example 8.786 If the X value is 8.0, what is the predicted value of Y, and what is the confidence interval for that value of Y? Y(8.0) = 0.51617 + 0.922918.0 = 7.8995 UC(8) = 8.786, so (8.786-7.8995) =  0.89

  10. Rules for Statistics Quiz • Closed book, closed online notes • You can bring one 8.5  11 paper with equations and notes (one-sided) • You can use Excel and Igor • Expected time: 15 minutes • Maximum time: 30 minutes • 20 points

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