Calculating Delta Values: Paired t Test

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Discussion Overview

The discussion revolves around the appropriate method for pairing results in a paired t-test to calculate delta values related to pollution measurements taken in September and April. Participants explore different approaches to pairing data and the implications of those choices for statistical analysis.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant questions whether to pair results as downstream - upstream for both months or to compare upstream and downstream values separately for each month.
  • Another participant asks for clarification on the quantity being tested and how the chosen pairing relates to that quantity.
  • A different participant raises a concern about the interpretation of pollution values, suggesting there may be a typo regarding whether pollution is increasing or decreasing.
  • A later reply emphasizes that only deltas for the same day are relevant, arguing that comparing values from different months may not be appropriate and suggesting a one-tailed t-test with a specific null hypothesis.

Areas of Agreement / Disagreement

Participants express differing opinions on the appropriate method for pairing results and the relevance of comparing data from different months. No consensus is reached on the best approach.

Contextual Notes

Participants do not clarify certain assumptions regarding the data or the specific statistical methods to be employed, leaving some steps in the analysis unresolved.

lamlam1
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upload_2019-3-10_21-59-57.png


Using paired t test, how should I pair these results?
To calculate the delta values, should I use: downstream - upstream for both sep and apr ?
or upstream (sep) - upstream (apr) and downstream (sep) - downstream (apr) ?

Thanks
 

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What is the quantity that you want to test and which pairing gives you that quantity?
 
How do you get a net pollution value? Is there a typo on increasing pollution? Shouldn't it be lowering pollution?
 
lamlam1 said:
View attachment 240043

Using paired t test, how should I pair these results?
To calculate the delta values, should I use: downstream - upstream for both sep and apr ?
or upstream (sep) - upstream (apr) and downstream (sep) - downstream (apr) ?

Thanks

Only the delta for the same day makes sense as the concern is an upper limit of 4 mg/L increase. Not sure why comparing April and Sep as two populations is relevant, seems to me a one tailed t-test on the delta with a null hypothesis that the mean of the delta >4 would be the relevant test
 
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