Scientific Measurement

Transcription

1 Scientific Measurement SPA4103 Dr. Alston J Misquitta Lecture 2 - Graph Plotting

2 Graph plotting is important to experimental practice: It allows you to spot mistakes! One point is anomalous Consider remeasuring point Check equipment Measure close to/around anomaly Do not discard data unless you are convinced it really is experimental problem - it could be real physics! Real example of bias 2

3 Plotting helps identify 'features': Choose to take more data around peak as this helps determine peak position better Identify relationships eg: linear behaviour, exponential, quadratic etc. 3

4 Finding features * First do a rough scan. * If you see something unusual, do a fine scan in the neighbourhood of the anomaly. Is there a peak here? Or is this an anomaly? This strategy is particularly useful when you need to find a peak or an edge but you do not know where these are located. Often, you can estimate the location where you need experimental data based on theoretical ideas. In this case, it probably is a peak! But adding additional data can cause a feature to vanish. A rough scan followed by a fine scan (in a small region) can save a lot of time! 4

5 Plots allow comparison with theory can perhaps refute one theory only data can do this! * How small must the uncertainties be to be sure of the signal? * What about the other bumps? Why do we ignore them? 5

6 Rules of Graph Plotting 1. Always plot uncertainty on your measurement! ALWAYS! 2. Preference: use a solid circle to mark data point can use o + but easy to confuse error bars 3. If value is 13.6 ± 0.2 then draw point at 13.6 and vertical line from Errors can be asymmetric eg: i.e. draw line errors often on ordinate and abcissa - not always If errors too small to draw you could multiply by 2 or 10 for presentation. * State this clearly in the figure or caption. 6

7 FIG. 11. Cross second virial coefficient B 12 T for methane-water. The symbols are experimental data as follows: squares: Ref. 76; stars: Ref. 75; diamonds: Ref. 74; filled triangles: Ref. 77; and open triangles: Ref. 78. The lines are from our calculations using the respective PESs except the one labeled Polynomial which is from a fit to the experimental virial as a function of temperature obtained in Ref. 77. Forget these and you will lose marks! Axis labels Units Legend Axis values Caption Figure Number 7

8 Interlude Graphs can be intentionally deceptive! 8

9 Sometimes we suppress the zero Makes details more visible Be aware that it can overemphasise dips and troughs FTSE year history has 30% gain, not 300% above! 9

10 Global warming out of control! Average monthly temperatures in New Haven, CT. Plot just the first half of the year and it looks bad. 10

11 Global warming stopped!!! Problems with this graph: * Atmospheric temperatures only. * I.e. show only part of the science. * Very short-term trend selected. * I.e. choose your data to prove your point. Mail on Sunday (2012)

12 End of Interlude! 12

13 Try to define linear variables - easier to spot linear behaviour For pendulum: T =2 s L g then plot T 2 =4 2 L g For refractive index: n = A + B 2 plot n vs

14 For exponential relationships e.g. radioactive decay rate: N = N 0 e t/ linearise by taking logarithms: log 10 N =log 10 N 0 t log10 e log 10 e = plot on log-lin paper label each decade 14

15 Moore s Law : An example of a semi-log plot. 15

16 Pitfalls of extrapolation 16

17 Same data shown on logarithmic and linear scales - data are same in both plots! Notice error bars look different in both plots In fact they are the same in both! 17

18 For power laws: taking logarithms: V = ki 3 2 log 10 V =log 10 k log 10 I plot on log-log paper: Nowadays use computers to plot They switch lin/log axes simply! PhysPlot will do this too 18

19 What do we expect in a good graph? Good use of the graph sheet. All points in the graph sheet - and not on the axes! Axis labels and units. A caption that describes what has been plotted. The ChiSq and the number of degrees of freedom (n.d.f.). Fitted data like the slope and intercept. Error bars! A legend if multiple data sets are present. 19