Graph uncertainty analysis question

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Discussion Overview

The discussion centers on the analysis of data points with associated uncertainty values, specifically regarding the mathematical determination of maximum and minimum slopes for a linear plot of these points. Participants explore tools and methodologies for conducting such analyses, including software options and relevant literature.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Homework-related

Main Points Raised

  • One participant inquires about the possibility of mathematically determining the maximum and minimum slopes of a linear plot given data points with uncertainties.
  • Another participant confirms that it is possible and suggests consulting graphical analysis textbooks for further details.
  • A different participant mentions using Sigmaplot for error analysis of slopes and notes its capabilities for limited non-linear analysis.
  • One participant requests guidance on using Sigmaplot, expressing confusion about the program.
  • Another participant suggests that Excel can perform the necessary calculations but emphasizes that familiarity with statistics is required for effective use.
  • This participant also mentions that the concept of MAX/MIN slope is not commonly presented in data analysis methods and recommends looking into least squares residual analysis related to linear regression.
  • Several references to textbooks on statistical analysis and data evaluation are provided as resources for further understanding.

Areas of Agreement / Disagreement

Participants express varying levels of familiarity with the tools and methods discussed, and while some agree on the feasibility of the analysis, there is no consensus on the specific methodologies or tools to be used.

Contextual Notes

Limitations include the lack of clarity on the specific methods for determining MAX/MIN slopes and the varying levels of expertise among participants regarding the software mentioned. The discussion also reflects differing opinions on the relevance of certain statistical methods.

Who May Find This Useful

This discussion may be useful for individuals interested in data analysis, particularly in the context of scientific research involving uncertainty in measurements, as well as those seeking software recommendations for statistical analysis.

silver-rose
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Suppose you have a set of data points with uncertainty values for each of them. For simplifications, assume it is a linear plot. Is it possible to mathematically find out the MAX/MIN slopes of the linear plot of the data points?

Is there a program that can do such analysis for you?

thanks in advance
 
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The answer to your first question is "yes". Consult a graphical analysis, data analysis textbook for details.

Of the many programs out there, I have used Sigmaplot to give error analysis of slopes. I believe that the latest version also does some limited non-linear analysis provided you input a mathematical function to model.
 
hmmm, can you refer me to some instructions/ provide some direction, because i am quite lost with that new program. thanks
 
Excel can do this calculation for you. The Excel program is not a tutorial, however. It is best used by someone with some familiarity of statistics and data analysis. Use the "help" pull down menu and type in "Regression Analysis".

Your OP referred to MAX/MIN slope through some data points which I have never seen presented as a method to analyze data. I am familiar with least squares residual analysis as it relates to linear regression analysis. As a chemist, my suggestion would be to look at an undergraduate Analytical Chemistry text and refer to the chapter dealing with the evaluation of analytical data. My book is "Fundamentals of Analytical Chemistry", Chapter 3, by Skoog and West, 4th edition, Philadelphia: Saunders College Publishing (1982).
This type of data analysis is useful to most other branches of science such as Biology, Physics, Sociology, Public Health Administration, Political Science, etc... All of these disciplines have their own applications for this type of Statistical Analysis. A discussion of the underlying statistics of linear regression can be found at:

"Statistical Methods in Research and Production", 4th ed., O.L. Davies and P.L. Goldsmith, Eds., Chapter 7, New York: Hafner Publishing Co. (1972).

"Introduction to Statistical Analysis", W.J. Dixon and F.J. Massey, Jr., 3rd edition, New York: McGraw-Hill (1969).

You should be able to find newer editions of books titled "Introduction to Statistics (or Statistical Analysis)" at the bookstore or you might find these examples at your local University Library.
 

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