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What's the best method to see if there's a strong correlation between two types of ratings on a product level (product $1, 2, \dots, n$) where each product has ratings of type '$a$' and '$b$'?

For the paired averages of ratings (of type $a$ and $b$) on a product level, would it be biasing my results if I filter out products with small number of ratings per type of rating, or low standard error in either average of ratings, or a combination of both?

Which would be best: Pearson's or Spearman's?

What's the most valid way to observe a potential existence of a relationship?

Also, would said method allow for more explanatory factor variables, like product type?

The overall goal is to see if there is a correlated (or non-random) relationship between the two averages on a product level (since they're what's surfaced on the marketplace).

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