Significant figures in Results and Confidence Intervals

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SUMMARY

The discussion centers on the appropriate number of significant figures to express confidence intervals in lab reports, particularly in the format of "something ± something." The participant, Sam, emphasizes that rounding the values can affect the accuracy of the confidence interval, potentially shifting or altering its width. The consensus indicates that while un-rounded confidence intervals may better reflect the true mean, the decision to round is ultimately based on conventions and the need to avoid false precision. There is no universally correct answer, as it varies by context and standards used.

PREREQUISITES
  • Understanding of confidence intervals and their calculation.
  • Familiarity with statistical significance and normal distribution.
  • Knowledge of significant figures and their implications in reporting data.
  • Experience with lab report formatting and conventions in scientific writing.
NEXT STEPS
  • Research the conventions for reporting confidence intervals in scientific literature.
  • Learn about the implications of rounding in statistical reporting.
  • Explore the impact of sample size on confidence interval accuracy.
  • Study the differences between frequentist and Bayesian interpretations of confidence intervals.
USEFUL FOR

This discussion is beneficial for physicists, statisticians, and researchers involved in data analysis and reporting, particularly those who need to present confidence intervals in their findings.

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

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