Statistics Review

Statistics Review ChE 475

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

2. Estimates of Error (d) for input variables(d’s are propagated tofind uncertainty) • Measured: • measure multiple times; obtain s; d≈ 2.5s • Could also use  from t statistic • Tabulated: • d ≈ 2.5 times last reported significant digit (with 1) • Manufacturer spec or calibration accuracy: • use given spec or accuracy data • Variable from regression (i.e. calibration curve): • d≈ 2.5*standard error (std error is stdev of residual) • Judgment for a variable: • use judgment for d

3. Propagation of Error (d) for calculated variables • Propagation of max error - brute force • Find range of input variables that gives max error • Propagation of max error – analytical • Partial derivatives for each input variable • Propagation of variance – analytical (not used much) • Propagation of variance - brute force (i.e., Monte Carlo simulation) • Easier than it looks

4. 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

4. Linear Regression(Confidence Interval) • Confidence Interval • Prediction Band

Example

In-Class Example • See Handout

Statistics Review