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I have here a data-set containing river flow rates for two separate river catchments, A and B.

There are exactly 365 values for river flow rate for both A and B.

Therefore, am I correct in assuming that each value is for each day of the year (there are 365 days in a year).

Therefore, am I working with three variables here?

  1. Day (range from 1 to 365)
  2. Flow rate for river A
  3. Flow rate for river B

In order to test for significance, should I use an independent sample t-test to compare both means?

Ferdi
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Erstwhistle
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    You say you want to test for significance. But what significance? What result are you interested in testing? That the mean flow of river A and B are the same/different? That there is an effect that impacts both the flow of river A and B for every day (e.g. rain on a certain day increases both flow in A and B)? Think of what you want to know beforehand. – Jan Oct 15 '18 at 14:07
  • The goal is to examine if flow in A and B is different – Erstwhistle Oct 15 '18 at 14:11
  • From a hydrological point of view testing two catchments for the same mean is dubious. Even adjusted for say area and rainfall, two catchments aren't expected to have the same mean "flow rate" (whatever that means: discharge? velocity?). But you can always summarize each catchment's data and look at cross-correlation. If the catchments are nearby and roughly similar in size their response patterns in time may be similar (given the same weather and climate). – Nick Cox Oct 15 '18 at 16:01
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    My answer is relevant per @Jan 's comment: [Which stats tests to use?](https://stats.stackexchange.com/questions/125498/which-stats-tests-to-use-bee-flight-activity-quantified-during-an-eclipse) – Alexis Oct 15 '18 at 17:40

2 Answers2

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We'll never be sure, but perhaps it is the day of the year. You could plot both rates of flow against what you think is the day of the year variable, and see if there's any dependence / cyclicity.

It's unclear what you mean by "test for significance" - significance of what? In any case, if the flow rate has a strong time dependence, then an independent sample t-test would be a poor choice to test for a difference of means as the samples would not only be cross-correlated, they would perhaps also be autocorrelated, which would violate the t-test assumptions as I understand them.

If the first variable does turn out to be time, you should think about modelling the flow rates per day of the year, then testing for significant differences among the two series in terms of level, correlation, etc.

Nick Cox
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adityar
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  • Ignoring the third time variable, which I 'invented', the dataset came with only two variables, flow rates for A and B. Is it possible to perform correlation analysis on these two variables, one on x axis, one on y? – Erstwhistle Oct 15 '18 at 14:05
  • Of course, I don't see why that'd be a problem. – adityar Oct 15 '18 at 14:07
  • I'd just like help with which correlation method is most appropriate for the data (i.e. Spearman, Pearson, Kendal), looking at this graph, https://i.imgur.com/QsjJALH.png, – Erstwhistle Oct 15 '18 at 14:10
  • The distributions of the flow rates are skewed. Could you also post what these look like against your first variable, the index, which you think is time? – adityar Oct 15 '18 at 14:12
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    Besides, the variables are clearly not i.i.d. - if the 'x' variable is low, I'm reasonably certain that the 'y' variable is as well. – adityar Oct 15 '18 at 14:16
  • I just want to do two things with this data. 1) Perform correlation analysis using best method 2) Assessing the significance of this using p-values. How should I do this? – Erstwhistle Oct 15 '18 at 14:19
  • My suggestion is, look at the way the two series behave over time, which you said might be the other variable. If there's a strong time dependance, model the time series using something that looks like $flow\_rate = f(t) + \epsilon_t$ where $f(t)$ - the trend, could be a spline. You could have a look at the errors around this trend and see if the trend other series falls within its errors. The methods that you named (spearman, etc.) _**all**_ make assumptions like i.i.d.-ness or exchangeability. I don't think any out-of-the-box test exists that'd give you p-values specific to your question. – adityar Oct 15 '18 at 14:30
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    @Erstwhistle "I just want to do two things with this data. **1) Perform correlation analysis**" You are not appreciating that "correlation analysis" or even "correlation analysis between $x$ and $y$" is actually quite *vague*. Please see the link I just posted in the comment to your original question, I think it will help you to hone in on your question of interest. – Alexis Oct 15 '18 at 17:42
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Since you have time series data ... you might want to look at Correlation of non-stationary time series ....particularly my response ... strongly suggesting that ordinary correlation coefficients are not interpretable. One needs to assess the significance GIVEN that the series are auto-correlated.

Ferdi
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IrishStat
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