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December 16th, 2013, 09:39 PM   #1
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Help. Correlation Coefficient

I have three sets of data as below. A is subjective data. B and C are parameter values predicting A.

A=[ 0.56 0.93 0.59 0.12 -0.92 -1.28];
B=[2.48 2.65 2.74 1.80 1.99 2.12];
C=[ 1.61 1.82 1.98 1.57 1.78 1.97];

To find a parameter predicting A more accurately, I computed correlation coefficients between A and B, and between A and C. The results are as below.

A versus B: r=0.6673, p-value: 0.1476
A versus C: r=-0.2679, p-value: 0.6077

As would be noticed, B and C has a very similar trend, but one yields a positive correlation coefficient with A and there other yields a negative correlation. Considering the p-values are relatively high, maybe I can conclude that the correlation coefficients are not meaningful at any confidence level above 85 %. However, I wonder if there is any other interpretation or reason for such an obvious difference in the correlation coefficient.

Next question is what the minimum data point is relevant for the correlation coefficient calculation. In A, B, and C, the first three values are from Experiment I and the rest of the values are from Experiment II. The only difference between the two experiments is a measurement position. I assume that three data points are not sufficient for the correlation coefficient calculations, so I combined them. If three data points are OK for the correlation coefficient calculation, I would calculate it separately for Experiment I and II.

Last question is if there is other statistical (or mathematical) tool to find a better parameter in this case. Please note that the absolute difference (e.g., RMS) should not be a good tool.

Thank you.
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December 21st, 2013, 08:25 PM   #2
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Re: Help. Correlation Coefficient

Hey honeysyd.

For Q1 you need to tell us what hypothesis tests you are doing. I'm assuming that it is testing p = 0.

For Q2 you should setup the appropriate hypothesis tests.

For Q3 you need to consider how both measurement position and error factors into the data. If you have enough data for different positions you can fit a regression model and check to see whether they have an effect on the coefficients for that factor. You can do a hypothesis test on the coefficients.
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January 9th, 2014, 06:03 PM   #3
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Re: Help. Correlation Coefficient

I am sorry for the delayed post.

For Q1 and Q2, I do not understand why hypothesis is necessary in this case. Again, I would like to find which parameter (either B or c) is a best predictor of the subjective results (A) by performing a correlation coefficient test.

For Q3, if I have only 3 data points, is it OK to execute a correlation coefficient?

I am sorry. My mathematical knowledge does not seem to be good enough to understand your comments. I would appreciate it if you could be more kind to explain.
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January 9th, 2014, 06:23 PM   #4
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Re: Help. Correlation Coefficient

For Q1 are you trying to show whether a correlation exists between the data?

If so you are testing whether the correlation is equal or unequal to 0. To test this you need to construct a hypothesis test and get a p-value (or a probability value) that corresponds to the probability of p = 0 given your test statistic and sample distribution.

The simple explanation is this: you have a sample and you calculate a test statistic (your correlation value) which also has a distribution. You choose what values of the test-statistic you are testing for and then add these probabilities up to get your p-value. Once you have your p-value you compare it to a confidence level and if it is less than that value you reject the hypothesis that it belongs to.

The simplest example is the sample mean which is approximately normally distributed for any large sample size.

By testing p = 0, if you fail to reject then you have found evidence that your two variables are not correlated. If you have evidence to reject this, then you have evidence that correlation exists between your two variables.

Hypothesis testing is basic statistics and in order to understand statistics you need to understand hypothesis testing.

The easiest way to test correlation is to use a simple linear regression model where you use a t-distribution test statistic for the distribution of your correlation value. Basically you will get an interval for the hypothesis p = 0 and if your correlation value that you calculated is outside this value then you reject null hypothesis and conclude that both values are correlated.

How much do you know about hypothesis testing?
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