Correlation using t-test and correlation coefficient - What is the correct result?

[jefnik3201028]

Hello Guys,
Thanks for all your comments. Here is the data set :

Set A Set B
0.107 0.13
0.111 0.12
0.118 0.11
0.103 0.14
0.11 0.09
0.118 0.1
0.093 0.06
0.104 0.11
0.107 0.07
0.108 0.09
0.113 0.05
0.127 0.04
0.134 0.06
0.11 0.08
0.12 0.08
0.13 0.18
0.108 0.16
0.115 0.26
0.137 0.17
0.119 0.27

When I said same sample, what I actually mean was paired sample. One location was measured by 2 different measuring equipment. The objective was to verify if we can use both equipments and produce the same results so we run a simple linear regression, with r value @ only 0.15 which suggest that there is poor correlation. I suspect the problem here is that the 2 sets have unequal variances.
By the way, the data is about roughness measurements.

Expecting your valuable inputs.

[Bev D]

you shouldn't use the paired t test for repeated measurements of the same thing. This is a gage study. BUT this isn't the problem with your data.

as suggested you should always plot your data - that will tell you the answer; the statistical analysis merely confirms what you see. Doing the statistical analyssi without looking at the plot of the data leaves you blind to the answer.

You cannot use your 2 instruments interchangeably - they give you very different results. THe difference in the standard deviation of the 2 data sets is real and critical to understanding that the devices are NOT interchangable. I cannot tell which one is correct.

the attached spreadsheet shows you the data plotted on a square scatter plot. the X axis is the first measurement and the Y axis is the second measurement.

[Steve Prevette]

In Reply to Parent Post by jefnik3201028

Hello Guys,
Thanks for all your comments. Here is the data set :

Set A Set B
0.107 0.13
0.111 0.12
0.118 0.11
0.103 0.14
0.11 0.09
0.118 0.1
0.093 0.06
0.104 0.11
0.107 0.07
0.108 0.09
0.113 0.05
0.127 0.04
0.134 0.06
0.11 0.08
0.12 0.08
0.13 0.18
0.108 0.16
0.115 0.26
0.137 0.17
0.119 0.27

I'd say just looking at the data there are problems. Note the .113 versus .05 and .134 versus .06. The first method gives a reading twice the second method. But then it flip flops on the last reading - 0.119 versus 0.27 - the second is more than twice the first. It looks like the first half of the data compare fairly well, but the second half is all over the place.

[Jim Wynne]

In Reply to Parent Post by Steve Prevette

I'd say just looking at the data there are problems.

Yes. I think this is one of those case where just looking at the number is enough, and rigorous statistical analysis is unnecessary. As my father used to say, you can't make chicken salad out of chicken poop, only he didn't say "poop."

[jefnik3201028]

Hello Bev D,
Appreciate your very useful input. I did X-Y plot by using the linear regression charting and by looking at the plot, the r coefficient was quite low so we know that there is poor correlation between the 2 machines.
Measurement B was coming from a machine which is giving us a very erratic reading so we're verifying if it was really a machine issue of sample issue.
I guess if the 2 groups have equal variance then the result of the paired t-test should still be applicable.
Another fatal error here is, instead of measuring product samples, the calibration standards should have been used.
You know guys, I was just asked to help analyze the data, I was not part of the plan on how they will do data collection.
Anyway thanks for the effort Bev D, appreciate it.

[Miner]

I recommend a linearity study on both gages using master references.

Reviewing Bev D's analysis, one of the gages shows variation while the other does not. Which one is correct depends on whether the parts that you measured exhibit variation or not. You cannot tell at this point.

[jefnik3201028]

Hello Miner,
I guess that's the best approach.

Thanks for cove members who makes useful inputs.

To others,
At this age and time, no one will deal with you when you say "by just looking at the data" so eventhough its obvious and someone needs an analysis then we need to find one that fits, right ? Hope people stops making sarcastic comments......
I seldom go to this forum and I still meet people this kind of comments instead of useful information.....

[Jim Wynne]

In Reply to Parent Post by jefnik3201028

To others,
At this age and time, no one will deal with you when you say "by just looking at the data" so eventhough its obvious and someone needs an analysis then we need to find one that fits, right ? Hope people stops making sarcastic comments......
I seldom go to this forum and I still meet people this kind of comments instead of useful information.....

I assume you were referring to me when you addressed your comment "to others." There was no sarcasm in my response; I was merely trying to point out the fact that if you take something that's obvious on its face, and put it through a grinder, you're not going to come up with anything you didn't already know. If you're in the position of having someone who's demanding a detailed analysis of something that doesn't need it, you should take the position of demonstrating to him, or them, why you already know what you need to know.