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I'm stuck on the following issue. I want to find simple examples from everyday life where it's clear that a categorical and a quantitative variable are not connected by a cause-and-effect relationship.

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    $\begingroup$ A flip of a coin and the roll of two dice $\endgroup$ Commented Feb 6 at 0:01

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Some examples:

  • The name of a soccer team and daily temperature.
  • Card faces and the speed of drivers nearby.
  • School type in New York and number of monthly books sold in Texas.

The example from a coin flip and dice roll by Demetri also works.

Edit

Your comment is a much more complicated question than your original post suggested. For a good exploration of causal reasoning, I recommend Robert Long's post here about the usage of DAGs, which are graphical techniques for positing the causal forces behind variables. Note that causality can never be known for certain, it can only be inferred. This book also does a good job of explaining causality, though I admit that I haven't finished it yet.

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  • $\begingroup$ Thank you for your response. I would like some examples where it's clear that there is an association between the categorical and quantitative variables. For example, let's say we have data showing that there is an association between gender and income. Gender may not fully explain the differences in income, but it is certainly one of the factors influencing the "income" variable. In this example, we cannot rule out the causal relationship between the two variables. Are there clearer examples where there will be an association but the causal relationship can be logically excluded? $\endgroup$
    – gmathr
    Commented Feb 6 at 7:09
  • $\begingroup$ See edit to my original answer. $\endgroup$ Commented Feb 6 at 7:32
  • $\begingroup$ @gmathr Maybe you can change the title of your question so that it is more clear for CV users what you were looking for. $\endgroup$
    – BenP
    Commented Feb 6 at 9:18
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A nice example is the following. In the Netherlands (maybe in other countries as well?) children are sometimes told that storks bring new babies. These birds arrive in the Netherlands during spring time when they come back from southern regions, like Africa, where they spent winter. It happened to be the case that until about 1975 most children were born during spring time, as the following graph from Statistics Netherlands shows:

enter image description here

The green line showing most babies are born in the period from "maart" to "mei" meaning "march" and "may", so in spring time. Statistics Netherlands argue that people often plan the birth of their child to happen in spring. After 1975, new methods of contraception, especially the birth control pill, became popular. People still plan their babies to be born in spring, but that does not always work well, because when stopping using the pill, say, it can take a while before getting pregnant, and that can be a reason that after 1975 most babies are born later. The blue lines in the graph show this.

In short, there is (or was) an association between storks coming and the number of new born babies, which is not causal, as far as I know.

See the link Births per month, Statistics Netherlands, which is in Dutch though

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  • $\begingroup$ Nice example! Thank you! $\endgroup$
    – gmathr
    Commented Feb 6 at 9:17
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    $\begingroup$ If you feel Bens answer satisfies your query, please accept his answer by clicking the checkmark next to it. @gmathr $\endgroup$ Commented Feb 6 at 9:20
  • $\begingroup$ How could we precisely name the categorical variable in this example? $\endgroup$
    – gmathr
    Commented Feb 6 at 9:51
  • $\begingroup$ Return of the storks? $\endgroup$
    – BenP
    Commented Feb 6 at 9:56

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