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

[jefnik3201028]

Hello guys,
Its been a while since I wrote in this forum but I've been reading a lot on those threads.
Well I need the experts help here.
I usually does not encounter this problem but time and again this issue comes up. I have 2 sets of data, same sample measurement, the sample size is 20. Here are the details :
Mean 1=0.1146 Mean2 =0.1185
SD 1=0.011038 SD2 = 0.0636

t-test for dependent sample result showed, p>0.05 which suggest the 2 sets are not significantly different which I can not accept.
Is this result distorted because of the SD problem ? I remember that an f-test should be performed to test equality of variances, do you think that that is the reason for this?

Therefore for this case I ignored the result of the t-test and referred to the linear regression coefficient of r as basis for the correlation.

Need the expert's input if the approach is correct.

Thanks,
Jefnik

[Bev D]

please post the raw data - it will allow us to truly help you.
adn if you can elaborate more on what the data is and what it represents. what question are you trying to answer with this test? why can't you accept the answer...

[Geoff Withnell]

In Reply to Parent Post by jefnik3201028

Hello guys,
Its been a while since I wrote in this forum but I've been reading a lot on those threads.
Well I need the experts help here.
I usually does not encounter this problem but time and again this issue comes up. I have 2 sets of data, same sample measurement, the sample size is 20. Here are the details :
Mean 1=0.1146 Mean2 =0.1185
SD 1=0.011038 SD2 = 0.0636

t-test for dependent sample result showed, p>0.05 which suggest the 2 sets are not significantly different which I can not accept.
Is this result distorted because of the SD problem ? I remember that an f-test should be performed to test equality of variances, do you think that that is the reason for this?

Therefore for this case I ignored the result of the t-test and referred to the linear regression coefficient of r as basis for the correlation.

Need the expert's input if the approach is correct.

Thanks,
Jefnik

Without seeing the data, just the summary data, I suspect that the problem is that while the means and variances MAY be different, they are not ENOUGH different for a sample of 20 to reliably distinguish between them. I will bet if you plot both samples as histograms, and lay one over the other, you will see that they are very similar. When dealing with two populations such as we have here, with means separated by only a fraction of a standard deviation, a fairly large sample is usually required to show the separation, unless the SDs are very different. Not mathematically rigorous, but it often helps to look at the data visually to diagnose a problem.

Geoff Withnell

[amanbhai]

In Reply to Parent Post by Geoff Withnell

Without seeing the data, just the summary data, I suspect that the problem is that while the means and variances MAY be different, they are not ENOUGH different for a sample of 20 to reliably distinguish between them. I will bet if you plot both samples as histograms, and lay one over the other, you will see that they are very similar. When dealing with two populations such as we have here, with means separated by only a fraction of a standard deviation, a fairly large sample is usually required to show the separation, unless the SDs are very different. Not mathematically rigorous, but it often helps to look at the data visually to diagnose a problem.

Geoff Withnell

Offcourse the sample size in many cases maybe important.
but Do we determine ourself the sample size? or the population size?

[Bev D]

In Reply to Parent Post by amanbhai

Offcourse the sample size in many cases maybe important.
but Do we determine ourself the sample size? or the population size?

we never determine the appropriate sample size, but we should calculate it (in this case, the definition of the words matter): the system from which we are sampling determines the sample size. The process's standard deviation and homogeneneity of data determines what sample size and sampling scheme is necessarry to make accurate estimates. We can choose how accurate we wish to be and how much difference we wish to detect. This will enable us to calculate what sample size is necessarry to meet our wishes.

Population size is mostly an irrelevent question in the practical world (unless very small)

[Dave Strouse]

jefnik3201028,

Please excuse if you have thought this through, but are you sure you are using the right test?

You state that you did the t-test for dependent samples. This is a paired test. It is a restriction on randomization. Perhaps this is appropriate for your data, maybe not.

What is your pairing mechanism?

The test statistic in the independent test is the t-distributed difference in means. The test statistic for the dependent test is the t-distribution of the differences between paired observations. Completely different results may well obtain from the same data tested in both ways.

As suggested earlier, an explanation of what the data is and the data itself would allow folks here to be more helpful.

[Bev D]

In Reply to Parent Post by Dave Strouse

jefnik3201028,



You state that you did the t-test for dependent samples.

actually he stated that he had "2 sets of data, same sample measurement". he didnt' explicitly say he dependent data although it is a viable interpretation. My first thought was that he was doing a measuremetn repeatability study (for which a paired t test isn't appropriate and certainly a grouped t test not appropriate) but I'm only interpreting vague words.

Hence my and everyone else's request for more information and the raw data.

I guess we have to wait until he wakes up

[Dave Strouse]

Bev,

Agree that getting the data is key, but from the OP's note

"t-test for dependent sample result showed, p>0.05 which suggest the 2 sets are not significantly different which I can not accept."

can only be interpreted to mean that he ran the "dependent" or "paired" t-test analysis.

My question was exactly as you stated.."Was the data dependent (paired)? OP does not say how the test was run and data collected, so the dependent analysis may not be right. Or it might. With out understanding what was done, we can only guess.


Dave