Significant figures in Results and Confidence Intervals

In summary, a user on the physicsforum is unsure about how many significant figures to express a confidence interval to when reporting it in a lab report. They also question the accuracy of the interval depending on rounding and the rationale behind rounding. They ask for clarification and rephrase their question.
  • #1
magin
6
0
Hello physicsforum people,

I'm not sure how many significant figures I should express a confidence interval to. I have confidence intervals for means that I need to express in a lab report, which I am going to do in the something ± something fashion. (I have assumed a normal distribution of the deviations of each measurement about the true mean, although it is not the calculation of the confidence intervals I have a problem with)

The resultant something ± something else confidence interval should be accurate to arbitrary precision shouldn't it? (neglecting the fact that you would have used a finite precision computer to calculate it)

If I were to round the bit left of the ± sign, I would shift the interval and if I round the bit to the right, I would narrow/broaden the interval. I am figuring that when making 95% confidence intervals in general, if you leave them un-rounded they will have a probability of containing the true mean closer to 95%, which is what I want, correct?

So why would someone round one, other than to the precision at which the computer can calculate it? I know the rationale behind rounding is to avoid false precision, but when you are explicitly stating precision, I do not believe this is a problem.

Thanks,
Sam
 
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  • #2
come on people, surely this is an easy question to answer. Can I rephrase it in a better way?
 
  • #3
No, it's not an "easy" question because it depends entirely upon what conventions you want to use. There simply is NO correct answer.
 

Related to Significant figures in Results and Confidence Intervals

1. What are significant figures and why are they important in scientific results?

Significant figures, also known as significant digits, are the digits in a number that are reliable and accurate. They are important in scientific results because they indicate the precision and accuracy of the measurement or calculation. They help scientists communicate the level of uncertainty in their data and ensure that the reported results are consistent and comparable.

2. How do you determine the number of significant figures in a measurement?

The general rule for determining significant figures is to count all non-zero digits and any zeros between non-zero digits. For example, the measurement 0.0078 has two significant figures (7 and 8), while 400 has one significant figure. However, there are specific rules for different types of numbers, such as exact numbers and numbers with decimal points, that should also be followed when determining significant figures.

3. Can significant figures be manipulated in calculations?

Yes, significant figures can be manipulated in calculations, but the result should be rounded to the same number of significant figures as the measurement with the least number of significant figures. For example, if you are multiplying 3.45 by 2.1, the result should be rounded to two significant figures, giving a result of 7.2. This ensures that the final result is not more precise than the original measurements.

4. What is the purpose of confidence intervals in scientific results?

Confidence intervals are a statistical measure that indicates the range of values within which the true value of a population is likely to fall. They are important in scientific results because they provide a measure of uncertainty and allow scientists to make conclusions about the population based on a sample of data. They also help to assess the reliability and validity of the results.

5. How are confidence intervals calculated and interpreted?

Confidence intervals are typically calculated using statistical methods such as t-distributions or z-distributions. They are interpreted as a range of values with a level of confidence, typically 95%, that the true value of the population falls within that range. For example, a confidence interval of 10 ± 2 means that there is a 95% chance that the true value of the population lies between 8 and 12. The smaller the confidence interval, the more precise the estimate of the population value.

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