美国麻省理工大学：《航空航天学讲义》教学资源（讲义，英文版）12 lecturedatareduction1

Data reduction It's poetic 16.621 March 18.2003

Data Reduction “It’s Poetic” 16.621 March 18, 2003

Introduction A primary goal of your efforts in this course w be to gather empirical data so as to prove(or disprove) your hypothesis Typically the data that you gather will not directly satisfy this goal Rather, it will be necessary to reduce the data, to put it into an appropriate form, so that you can draw valid conclusions In our discussion today we will examine some typical methods for processing empirical data Caution-garbage in/garbage out still applies

Introduction • A primary goal of your efforts in this course will be to gather empirical data so as to prove (or disprove) your hypothesis • Typically the data that you gather will not directly satisfy this goal • Rather, it will be necessary to “reduce” the data, to put it into an appropriate form, so that you can draw valid conclusions • In our discussion today we will examine some typical methods for processing empirical data • Caution-garbage in/garbage out still applies

Hiawatha designs an experiment Maurice. kendall From The american statistician Vol.13,No.5,1959,pp23-24 Verses 1 through 6

Hiawatha Designs an Experiment by Maurice G. Kendall From The American Statistician Vol. 13, No. 5, 1959, pp 23-24 Verses 1 through 6

Deyst's 1662X Project I have performed a very simple experiment The hypothesis was: my driving route distance, from West Garage to my driveway in arlington, is eight miles On a number of trips i recorded the mileage as indicated by the odometer of my automobile I now wish to reduce the data and draw some conclusions

Deyst’s 16.62X Project • I have performed a very simple experiment • The hypothesis was: my driving route distance, from West Garage to my driveway in Arlington, is eight miles • On a number of trips I recorded the mileage, as indicated by the odometer of my automobile • I now wish to reduce the data and draw some conclusions

Experimental Project(cont My experimental procedure was: at the exit from West Garage I zeroed my trip odometer and when i reached my driveway at home i recorded the odometer reading On each of ten trips i took the same route home

Experimental Project (cont.) • My experimental procedure was: at the exit from West Garage I zeroed my trip odometer and when I reached my driveway at home I recorded the odometer reading • On each of ten trips I took the same route home

Error sources Random errors Odometer readout resolution Odometer mechanical variations Route path variations ire Slippage Systematic errors Bias in the odometer readings Odometer scale factor error Tire diameter decreases due to wear

Error Sources Random errors Odometer readout resolution Odometer mechanical variations Route path variations Tire slippage Systematic errors Bias in the odometer readings Odometer scale factor error Tire diameter decreases due to wear

Error Sources(cont The resolution I achieved in reading the odometer was within t 025 miles The best knowledge I have about the other random errors is that they were all in the range of±.10 miles i zeroed the odometer at the beginning of each trip so any bias in the measurements is small (i. e about t.005 miles)

Error Sources (cont.) • The resolution I achieved in reading the odometer was within ±.025 miles • The best knowledge I have about the other random errors is that they were all in the range of ±.10 miles • I zeroed the odometer at the beginning of each trip so any bias in the measurements is small (i.e. about ± .005 miles)

Error Sources(cont) I did a scale factor calibration by driving 28 miles. according to mileage markers on Interstate 95. and in both directions i recorded 27. 425 miles on my odometer Thus the scale factor is 27425 odometer indicted miles SF 980 28 actual miles And any error in the scale factor due to readout resolution is 025 SE ×9 ±0006

Error Sources (cont.) • I did a scale factor calibration by driving 28 miles, according to mileage markers on Interstate 95, and in both directions I recorded 27.425 miles on my odometer • Thus, the scale factor is 27.425 odometer indicted miles S.F. = = .980 28 actual miles • And any error in the scale factor due to readout resolution is .025 e ≅ ±.0006 SF = ± 28⋅ 2

Recorded data Trip Mileage S.F. Corrected Number Reading Mileage reading 7.8257.985 7.8508.010 7.8758.036 79008061 78508010 7.8257985 7.8758036 7.8508.010 78758036 10 78257985

Recorded Data Trip Number Mileage Reading S.F. Corrected Mileage reading 1 7.825 7.985 2 7.850 8.010 3 7.875 8.036 4 7.900 8.061 5 7.850 8.010 6 7.825 7.985 7 7.875 8.036 8 7.850 8.010 9 7.875 8.036 10 7.825 7.985

Mileage Data Analysis My system model is that the route distance Is constant To minimize the effect of random errors take the sample mean(average)of the data to obtain an estimate d=8.015 miles

Mileage Data Analysis • My system model is that the route distance is constant • To minimize the effect of random errors take the sample mean (average) of the data to obtain an estimate n dˆ = 1 ∑ di = 8.015 miles n i =1