Global Surface Temperature Data Analysis Activity
written by John Welch and Douglas Brown, Cabrillo College Physics Dept.
Read An Introduction to Error Analysis. Keep this document handy--you will want to refer to it often in lab!
1. Open the Excel spreadsheet GlobalTempData.xls. This contains data gathered by NASA on global surface temperature from 1996-2006. Note that the numbers given aren't absolute temperatures, but just relative temperatures from some baseline value. We are going to try to determine whether this data shows that global surface temperatures in 2006 were higher than those in 1996.
2. Find the mean relative temperature for the years 1996 and 2006 using Excel's AVERAGE function. The mean (M) is the best estimate of the "true" value. Clearly label the mean (and all statistics) in an adjacent cell.
3. Find the standard deviations of the temperature measurements using Excel's STDEV function. The standard deviation (SD) is the best estimate of the uncertainty (also called error, scatter, reproducibility or noise) of an individual measurement.
4. Find the standard errors of the mean temperatures by dividing SD by the square root of the number of measurements (Excel SQRT function). The standard error (SE) is the best estimate of the uncertainty of a mean value.
5. Write each of your experimental results (1996 and 2006) in the form M +/- SE.
6. Make sketches of 2 bell-shaped curves on one graph. The first should be centered on the Mean value for 1996. On this curve, put marks near the tails that are 2 Standard Errors from the Mean, one on each side. Do the same for the 2006 data. Do the two curves overlap?
7. If two bell shaped curves don't overlap at the width of 2 Standard Errors, then we are 95% sure that the difference between them is not due to random chance. If they do overlap (the SE marks cross each other), then we aren't 95% sure and we say that 'maybe this is just do to random chance.' Are you 95% sure that the tempuratures in 1996 and 2006 are different from each other?
8. Even though this is real data, the way we chose to compare temperatures might not have been the most sophisticated. Discuss briefly any possible problems with the way we chose to look at the situation. If a newspaper reporter asked you to tell them about the results, how would you phrase it to them?