# How to test for Pearson correlation when one variable is arbitratily fixed for number of cases?

I have 4 groups of different respondents, each group surveyed on four different dates (points of time). All respondents have answered a psychological questionnaire related to their perception of death (Perception of Death Questionnaire, PDQ). I also have a sample of popular newspapers that have circulated on and before those four points of time. I built a death-presentation index (DPI) from the information gathered from the newspapers (text mining). This index was computed for each time the participants were surveyed, namely 4 times.

Each participant had his own PDQ level. He also had one of 4 DPI index values that matched the day he took part in the experiment.

I want to test whether PDQ and DPI are correlated with each-other.

My current insight into the problem follows:

One case = one date

I can average all answers to PDQ given at each day, and get 4-cases sample with columns PDQ and DPI.

AFAIK I can't use classical correlation significance even if I had more than 4 of days: effectively my sample will be time series, where cases are not mutually independent. Calculating Pearson's correlation coefficient will be OK, but for testing its significance I will need a different set of statistical tests (like VECM).

One case = one participant

I could treat the sample as it is - as a sample of respondents. Each respondent has day of participation, and so I can pair it with the associated value of DPI.

Then I can calculate Pearson's correlation coefficient. Since I have the same number of respondents for each group, I believe that the correlation coefficient will have exactly the same value as in "One case = one date" case. But can I test for it significance??

My guts tell me, that from the same reasons as above, I cannot. But the more I think about it, the less I know why exactly. Please, help ;-)

• Commented Jun 8, 2015 at 14:44
• @ssdecontrol yes, it is close but I don't think it is a duplicate. Too bad, that the question you reference does not have a constructive answer. I need(ed) statistical significance. Commented Jun 9, 2015 at 8:54
• It's not at all clear what you mean by "fixed on date." And by "statistical significance" do you mean "a statistical test of the null hypothesis that the correlation is zero"? Commented Jun 9, 2015 at 12:10
• @ssdecontrol I wanted to test for the causality between coverage of death-related topics on popular press and perception of death by the respondents. We decided that we cannot measure reliably how many death-related news materials did the participant consumed, so we calculated a DPI index for each of the 4 dates the survey took place. So we had a fixed-by-date DPI that had only 4 distinct values and the PDQ with distinct values for each participant. Commented Jun 9, 2015 at 12:18
• Okay, but I still don't know what you mean by "fixed by date". Is it that the "date" index is a real world date, so that "day 1, participant 1" is not the same date as "day 1, participant 2"? Why not normalize "date" to "days since death" or something? Commented Jun 9, 2015 at 12:23