What Justifies Using a Single SD for All Measurements in a Dataset?

  • Context: Graduate 
  • Thread starter Thread starter Niles
  • Start date Start date
  • Tags Tags
    Uncertainties
Click For Summary
SUMMARY

The discussion centers on the justification for using a single standard deviation (SD) for all measurements in a dataset when individual measurements lack assigned SDs. The consensus is that if all measurements are derived from the same population with a constant SD, it is valid to apply the overall SD of the dataset to each individual measurement. This allows for the calculation of the width of the average using the formula SD/sqrt(N), where N represents the number of measurements.

PREREQUISITES
  • Understanding of standard deviation (SD) in statistics
  • Knowledge of the concept of population versus sample in data analysis
  • Familiarity with the formula for calculating the width of the average
  • Basic statistical analysis skills
NEXT STEPS
  • Research the implications of assuming a constant standard deviation across a dataset
  • Learn about the Central Limit Theorem and its relevance to standard deviation
  • Explore methods for estimating standard deviation in datasets without assigned SDs
  • Study the differences between population SD and sample SD in statistical analysis
USEFUL FOR

This discussion is beneficial for statisticians, data analysts, and researchers who need to understand the implications of using a single standard deviation for multiple measurements in datasets lacking individual SDs.

Niles
Messages
1,834
Reaction score
0
Hi

Ok, we all know that if a quantity T is measured N times, then all measurements have the same standard deviation (SD). Now, with this assumption one can derive the width of the average to get SD/sqrt(N).

I have often encountered a dataset D, where each measurement has been assigned no SD. Then one finds the SD for the whole dataset, and then the author uses SD/sqrt(N) to find the width of the average of D.

My question is: In these cases, then what justifies that SD found from the whole dataset D can be assumed to be valid for each single measurements, such that one can use SD/sqrt(N)?

I hope you understand.


Niles.
 
Physics news on Phys.org
"In these cases, then what justifies that SD found from the whole dataset D can be assumed to be valid for each single measurements"

The assumption that all the values in the data set come from the same population - one having a constant standard deviation.
 
Thanks, that makes sense.

Best wishes,
Niles.
 

Similar threads

Undergrad Error bars in Excel (standard deviation, standard error, percentage)
  • · Replies 4 ·
Replies
4
Views
3K
Graduate Monte Carlo to compute uncertainties, why report the mean and SD?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Propagation of Error when Taking the Average of Averages
  • · Replies 19 ·
Replies
19
Views
8K
Graduate Low value standard deviation bias
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad What is the significance of standard deviation for arbitrary distributions?
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Error propagation with averages and standard deviation
  • · Replies 33 ·
2
Replies
33
Views
55K
Undergrad What is the correct definition of measurement uncertainty?
  • · Replies 21 ·
Replies
21
Views
3K
Graduate Uncertainty on an asymmetry signal
  • · Replies 4 ·
Replies
4
Views
2K
High School Measurements - How can it be that precise?
  • · Replies 42 ·
2
Replies
42
Views
4K
Undergrad How to implement proper error estimation using MC
  • · Replies 3 ·
Replies
3
Views
3K