Reduced chi square for few data points

Click For Summary
SUMMARY

The discussion centers on fitting a straight line to a dataset consisting of 8 points with associated errors, specifically using reduced chi-squared analysis. The dataset includes x-values ranging from 1 to 8, y-values representing measurements, and y-errors reflecting Poisson errors. The user reports a reduced chi-squared value of 0.02, indicating a poor fit relative to the error margins. Participants emphasize the importance of understanding the origins of the error values and the potential impact of systematic errors on the analysis.

PREREQUISITES
  • Understanding of linear regression and curve fitting techniques
  • Familiarity with reduced chi-squared statistics
  • Knowledge of error propagation and Poisson statistics
  • Experience with data visualization tools for plotting datasets
NEXT STEPS
  • Investigate methods for improving linear fit accuracy in datasets with large error margins
  • Learn about systematic errors and their effects on statistical analysis
  • Explore advanced fitting techniques using tools like SciPy's curve_fit
  • Study the implications of reduced chi-squared values in model evaluation
USEFUL FOR

Researchers, data analysts, and statisticians involved in data fitting and error analysis, particularly those working with small datasets and seeking to understand the implications of statistical measures like reduced chi-squared.

Malamala
Messages
348
Reaction score
28
Hello! I need to make a straight line fit to 8 points, with errors on them. The data is like this ##x = [1,2,3,4,5,6,7,8]##, ##y=[377.488 691.191 , 1030.319, 1428.801, 1753.884, 2113.065 , 2398.642, 2797.664]##, ##y_{err}=[97.145, 131.452, 160.492, 188.997, 209.397, 229.840, 244.879, 264.464]##. The problem is that the errorbars (which are basically Poisson errors) are a lot bigger than the spread of the data. Hence I end up with a reduced chi-squared of 0.02. Is there anything I can do? The values of the fits are reasonable (given theoretical arguments), but I am not sure what to make out of this small reduced chi-square.
 
Physics news on Phys.org
Did you make a plot ?
Tell us how the data were obtained and what they represent. Especially the ##y_{err}##.
And how can you obtain such unbelievably accurate estimates of ##y_{err}##. Billions of observations, or just mindless copying calculation results ?
Are you aware of the role of systematic errors ?

BvU said:
How are the other threads going ? Long forgotten ?
I'd like to know if you understood the help given in earlier threads, or just lost interest and never reacted any more. I don't mind repeating things, but it should have a reasonable purpose.
 
Last edited:

Similar threads

Graduate How to set up and interpret Chi^2 test results for my data?
  • · Replies 11 ·
Replies
11
Views
3K
Undergrad Small Reduced Chi Squared interpretation
  • · Replies 5 ·
Replies
5
Views
5K
Graduate Chi squared test for data with error
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Error on non-linearity in a linear fit
  • · Replies 8 ·
Replies
8
Views
2K
What is the correct formula for the reduced Chi square?
  • · Replies 3 ·
Replies
3
Views
4K
Undergrad About chi-squared and r-squared test for fitting data
  • · Replies 5 ·
Replies
5
Views
9K
Undergrad Error bars, Chi square distribution
  • · Replies 1 ·
Replies
1
Views
4K
Undergrad Linear fit on the difference of data points
  • · Replies 26 ·
Replies
26
Views
3K
Undergrad Chi-squared fit with errors on both x and y
  • · Replies 8 ·
Replies
8
Views
7K
High School Chi-squared test stat choosing a critical value
  • · Replies 5 ·
Replies
5
Views
4K