# Can l use chi-square test in this scenario ?

1. Jun 14, 2012

### Nyasha

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.

2. Jun 14, 2012

### Stephen Tashi

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.

3. Jun 14, 2012

### Nyasha

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.

4. Jun 14, 2012

### Stephen Tashi

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.

5. Jun 15, 2012

### Nyasha

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.

6. Jun 15, 2012

### Stephen Tashi

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.

7. Jun 15, 2012

### Nyasha

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 ?

8. Jun 15, 2012

### chiro

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.

9. Jun 15, 2012

### Nyasha

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