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. Subtract the 1996 mean from the 2006 mean to find the discrepancy. The discrepancy (D) is the best measure of the disagreement between experiment and theory or between two experimiental values.

7. Find the ratio of D to SE in order to determine whether the discrepancy is significant. If the ratio is greater than 2, the discrepancy is significant at the 95% confidence level. Can you state with 95% confidence that the global surface temperature in 2006 was different than the temperature in 1996?

8. Even though this is real data, it is a simplified analysis. Discuss briefly any possible shortcomings it may have. What kind of statement would you feel justified in making based on this data and analysis?