the estimate and uncertainty for experiment 1 is .15+-.01 and the .12+-.01 for experiment 2. Is the discrepancy between these two data sets significant? Why?
I would say yes, the discrepancy is probably significant, because the measurements should agree to within less than three standard deviations if they were measuring the same thing. These measurements differ by three standard deviations.
can you explain what you mean by three standard deviations? thanks
To determine if the discrepancy between two data sets is significant, we need to compare their uncertainties and assess the overlap between their estimates. In this case, we have the estimate and uncertainty as 0.15±0.01 for experiment 1 and 0.12±0.01 for experiment 2.
1. Assessing the overlap:
- Take the upper bound of experiment 1's estimate and subtract the lower bound of experiment 2's estimate: (0.15 + 0.01) - (0.12 - 0.01) = 0.03.
- Check if the difference is within the sum of the uncertainties of both estimates: 0.01 + 0.01 = 0.02.
2. Comparing the uncertainties:
- The uncertainties for experiment 1 and 2 are both ±0.01.
Now, if the difference between the two estimates (0.03) is larger than the combined uncertainties (0.02), then the discrepancy would be considered significant. In this case, since 0.03 is indeed greater than 0.02, there is a significant discrepancy between the two data sets.
In summary, the discrepancy between the two data sets is significant as the difference between their estimates exceeds the sum of their uncertainties.