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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 ;-)

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  • $\begingroup$ possible duplicate of Can I use the correlation between two variables when observations on each variable are autocorrelated? $\endgroup$ Commented Jun 8, 2015 at 14:44
  • $\begingroup$ @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. $\endgroup$ Commented Jun 9, 2015 at 8:54
  • $\begingroup$ 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"? $\endgroup$ Commented Jun 9, 2015 at 12:10
  • $\begingroup$ @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. $\endgroup$ Commented Jun 9, 2015 at 12:18
  • $\begingroup$ 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? $\endgroup$ Commented Jun 9, 2015 at 12:23

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You cannot, correlation is a one-to-one match between two variables, with the same person providing both values for 2 separate variables

Gloria

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  • $\begingroup$ Thank you for the answer and welcome to Cross Validated (CV for short)! I am afraid, that both cases has that one-to-one match. My question is about something more subtle: about the assumption, that in Pearson's correlation test all cases must be independent. The more my data are time series, the less this assumption is satisfied. $\endgroup$ Commented Jul 30, 2014 at 16:31

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