Can l use chi-square test in this scenario ?

  • Context: Undergrad 
  • Thread starter Thread starter Nyasha
  • Start date Start date
  • Tags Tags
    Test
Click For Summary

Discussion Overview

The discussion revolves around the application of statistical tests, specifically the chi-square test, in evaluating the performance of camera parts based on measurement data. Participants explore the nature of the measurements, the appropriateness of different statistical tests, and the implications of their findings.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant proposes using a chi-square test to determine if variations in camera part performance are due to random error or faults.
  • Another participant emphasizes the need to clarify how performance is measured, distinguishing between numerical, categorical, and ranking scale measurements.
  • A participant mentions measuring counts per pixel and questions whether "variance" is used technically or synonymously with "difference."
  • There is a discussion about comparing means and variances of distributions from measurements taken with different parts, with one participant suggesting a t-test for mean comparisons.
  • Another participant points out the low number of measurements (five) and suggests that an ANOVA might not be appropriate, cautioning about the assumptions of normality and equal variances.
  • One participant expresses intent to use a single factor ANOVA test after considering the discussion.

Areas of Agreement / Disagreement

Participants express differing views on the appropriate statistical tests to use, with some advocating for the chi-square test and others suggesting a t-test or ANOVA. There is no consensus on the best approach due to varying interpretations of the data and statistical assumptions.

Contextual Notes

Participants highlight limitations related to the small sample size and the need for careful consideration of statistical assumptions, such as normality and equal variances, before applying certain tests.

Nyasha
Messages
127
Reaction score
0
I am testing a certain part on a camera. So l was thinking of taking a set of measurements and then change that part and take another set of measurements.After having those two sets of data l wanted to do a chi-square test in order to see if variations in how the two parts perform is due to random error or a fault somewhere.
 
Physics news on Phys.org
I think you must explain how you intend to measure the performance. Some measurements of performance are numerical ( like 600.3 pixels per inch) Some are categorical (such as "bad", "good", "better", "best".) Some measures, like ranking scales (0,1,2,...10) combine aspects of numerical and categorical measures.
 
Stephen Tashi said:
I think you must explain how you intend to measure the performance. Some measurements of performance are numerical ( like 600.3 pixels per inch) Some are categorical (such as "bad", "good", "better", "best".) Some measures, like ranking scales (0,1,2,...10) combine aspects of numerical and categorical measures.

I will be measuring counts per pixel. So l want to know if the variance is due to random in nature, or it is due to something wrong with the part l am changing.
 
Nyasha said:
I will be measuring counts per pixel. So l want to know if the variance is due to random in nature, or it is due to something wrong with the part l am changing.

I can't tell if you are using the word "variance" in the technical sense or whether you are using it as a synonym for "difference". I also don't know what "counts per pixel" represents. Let's say you take several measurements with part A in the camera and you get 5 numbers x1,x2..x5. Then you replace part A by part B and take 5 similar measurements y1,y2,..y5. One typical question is "Is the mean of the distribution from which the x's are drawn equal to the mean of the distribution from which the y's are drawn?" A different question is "Is the variance of the distribution from which the x's are draw equal to the variance of the distribution from which the y's are drawn?"

Yet another situation is to have paired observations. Say you take a photo of subject 1 with part A in the camera and get measurement x1. Then you replace part A with part B and get measurement y1. You do this for 5 different subjects.

If you want statistical advice, you must state you situation precisely.
 
Stephen Tashi said:
"Is the mean of the distribution from which the x's are drawn equal to the mean of the distribution from which the y's are drawn?" A different question is "Is the variance of the distribution from which the x's are draw equal to the variance of the distribution from which the y's are drawn?"

This is exactly what l am looking for. After testing a part and replacing it with another l want to know if the mean distributions of the 7 parts are equal. In other words this tells me that changing the part on my camera doesn't affect its performance. Hopefully that is the conclusion l want to get.
 
Nyasha said:
l want to know if the mean distributions of the 7 parts are equal..

Are there 7 parts? - or should you have written "7 measurements"?

Assuming you meant "7 measurements", the usual test for a difference in means would be a "T-test", not a chi-square test.

You didn't say how you intended to apply the chi-square statistic. There are many different ways of doing that. I can't think of one that would apply in this situation.
 
Stephen Tashi said:
Are there 7 parts? - or should you have written "7 measurements"?

Assuming you meant "7 measurements", the usual test for a difference in means would be a "T-test", not a chi-square test.

You didn't say how you intended to apply the chi-square statistic. There are many different ways of doing that. I can't think of one that would apply in this situation.


They are 7 parts each with 5 measurements. I want to compare 7 sets of data at the end of the day, and see if they are the same.

Doesn't the t-test work in a situation you have a Gaussian distribution ?
 
Nyasha said:
They are 7 parts each with 5 measurements. I want to compare 7 sets of data at the end of the day, and see if they are the same.

Doesn't the t-test work in a situation you have a Gaussian distribution ?

Hey Nyasha.

For frequentist statistics, five measurements is not that much. I was going to recommend an ANOVA but I don't think it would be a good idea given low number of measurements.

I did a quick search and the topic of this paper seems relevant:

http://www.stat.purdue.edu/~dasgupta/publications/tr94-19c.pdf

You can do an ANOVA, but if you do check the underlying statistics for other assumptions like equal variances, and especially normality checks. The thing though as hinted above, is that the normality check is using five values which is not what I would place much faith in. Unless you know or have a good argument why a normal distribution is a good underlying model, I would not use a frequentist ANOVA.
 
chiro said:
Hey Nyasha.

For frequentist statistics, five measurements is not that much. I was going to recommend an ANOVA but I don't think it would be a good idea given low number of measurements.

I did a quick search and the topic of this paper seems relevant:

http://www.stat.purdue.edu/~dasgupta/publications/tr94-19c.pdf

You can do an ANOVA, but if you do check the underlying statistics for other assumptions like equal variances, and especially normality checks. The thing though as hinted above, is that the normality check is using five values which is not what I would place much faith in. Unless you know or have a good argument why a normal distribution is a good underlying model, I would not use a frequentist ANOVA.


I was just reading about a single factor ANOVA test. I think l will go for that one.
 

Similar threads

Undergrad Does Returning Marbles After Each Draw Affect Chi-square Test Results?
  • · Replies 8 ·
Replies
8
Views
2K
Undergrad Online sourses to learn chi square test of homogeneity
  • · Replies 2 ·
Replies
2
Views
2K
High School Chi-squared test stat choosing a critical value
  • · Replies 5 ·
Replies
5
Views
4K
Graduate Can a Chi2 test be used on uniform p test results?
  • · Replies 4 ·
Replies
4
Views
1K
Undergrad About chi-squared and r-squared test for fitting data
  • · Replies 5 ·
Replies
5
Views
9K
Undergrad Data Analaysis -- How to choose the best statistical model to use?
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad How to do a chi squared test on a linear fit
  • · Replies 2 ·
Replies
2
Views
4K
Graduate What is a Chi-Squared Test Against Weighted Mean?
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Do outliers exist in categorical data and how can they be detected?
  • · Replies 6 ·
Replies
6
Views
5K
Graduate Interpreting Chi Squared .... backward
  • · Replies 20 ·
Replies
20
Views
4K