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Here's the example: "Can you give me a real-life example of three events, A, B, C, where A and B are correlated, B and C are correlated, but A and C are uncorr

Here's the example: "Can you give me a real-life example of three events, A, B, C, where A and B are correlated, B and C are correlated, but A and C are uncorrelated." Claude 3.5 gets it correct for me ¯\_(ツ)_/¯

Faaak 2y ago
Can you paste the response for us that can't use the model easily?
- phaedryx 2y ago
  Here's what Claude gave me: A real-life example of three events A, B, and C where A and B are correlated, B and C are correlated, but A and C are uncorrelated could be: A: Ice cream sales B: Temperature C: Energy consumption for air conditioning Let's break this down: A and B correlation: Ice cream sales (A) and temperature (B) are positively correlated. As temperature rises, people tend to buy more ice cream. B and C correlation: Temperature (B) and energy consumption for air conditioning (C) are positively correlated. As temperature increases, people use more air conditioning, leading to higher energy consumption. A and C uncorrelated: Ice cream sales (A) and energy consumption for air conditioning (C) are not directly correlated. While both increase with temperature, there's no direct causal relationship between them.
  - chairmanmow 2y ago
    If the purpose of ice cream and air conditioning is to make the user feel cooler, then wouldn't it be logical to say the more ice cream they eat the less air conditioning they'd use and vice versa? That seems like a causal relationship to me that's being glossed over, but maybe I'm missing something.
    - card_zero 2y ago
      I think the way to construct these is: find (a) such that all kinds of things can cause it, choose (b) as one of the causes of (a), choose (c) as something else also caused by (b) but also having all kinds of other potential causes different from those of (a). So this example isn't good, because when people are eating most ice cream, people are using most air con, both being mainly caused by hot weather. (Unless as you point out we're looking at one individual who wants a solution to feeling hot and doesn't need to do both things together.)
audessuscest 2y ago
same > Certainly. Here's a real-life example of three events A, B, and C that demonstrate the correlation pattern you've described: A: Ice cream sales B: Temperature C: Sunscreen sales Explanation: 1. A and B are correlated: Ice cream sales (A) tend to increase as temperature (B) rises. People are more likely to buy ice cream on hot days, creating a positive correlation between these two events. 2. B and C are correlated: Temperature (B) and sunscreen sales (C) are also positively correlated. As the temperature increases, people are more likely to spend time outdoors and therefore buy more sunscreen to protect their skin. 3. A and C are uncorrelated: However, ice cream sales (A) and sunscreen sales (C) are not directly correlated. While both may increase during warmer weather, there isn't a direct causal relationship between the two. People don't necessarily buy more ice cream because they're buying sunscreen, or vice versa. This example demonstrates how two events can be indirectly related through a third event (in this case, temperature) without having a direct correlation with each other. Would you like me to elaborate on this example or provide additional information about correlation?
- audessuscest 2y ago
  another: Here's another example of three events A, B, and C that follow the correlation pattern you described: A: Coffee consumption B: Work productivity C: Typing speed Explanation: 1. A and B are correlated: Coffee consumption (A) and work productivity (B) often show a positive correlation. Many people drink coffee to increase alertness and focus, which can lead to improved productivity at work. 2. B and C are correlated: Work productivity (B) and typing speed (C) are generally positively correlated. As people become more productive, they often type faster to keep up with their increased output. 3. A and C are uncorrelated: However, coffee consumption (A) and typing speed (C) are not directly correlated. While coffee might indirectly influence typing speed through increased productivity, there's no direct causal relationship between drinking coffee and typing faster. This example shows how work productivity acts as an intermediary factor, connecting coffee consumption and typing speed without them being directly correlated. Would you like me to provide another example or explain any part of this in more detail?
  - user_7832 2y ago
goatlover 2y ago
Correlation isn’t causation, unless you’re a Humean about constant correlation, to this point in time. Would be humoirous if an LLM gave a similar response.
diggan 2y ago
So does GPT4o, unless I'm missing something very obvious: https://chatgpt.com/share/0a9d3674-0d79-4891-8045-f70376fbc721 https://chatgpt.com/share/0a9d3674-0d79-4891-8045-f70376fbc7... Events: A: Ice cream sales B: Temperature C: Incidence of sunburn Correlations: A and B are correlated: Ice cream sales (A) and temperature (B) are positively correlated. As the temperature increases, ice cream sales tend to increase because people are more likely to buy ice cream to cool down. B and C are correlated: Temperature (B) and incidence of sunburn (C) are positively correlated. Higher temperatures often mean sunnier weather, which increases the likelihood of people getting sunburned if they spend time outside without proper sun protection. A and C are uncorrelated: Ice cream sales (A) and incidence of sunburn (C) are uncorrelated directly. While both are influenced by temperature, one does not cause the other. People can buy ice cream without getting sunburned, and people can get sunburned without buying ice cream.
- hnlandfr 2y ago
  That looks wrong! As Slashdot never got tired of mentioning, correlation != causation. So A and C are still correlated, a causal relationship is not relevant.
samatman 2y ago
The replies to this show that it isn't just language models which struggle with the difference between correlation and causality! Here's the (logically valid but with fictional soundness) example I came up with: > The Elbonian people (A) are disproportionately tall (B). > Tall people (B) are disproportionately successful at basketball (C). > Elbonians (A) are disproportionately unsuccessful at basketball (¬C), because they don't play it. Edit: in context, I consider a negative correlation to adequately demonstrate the principle, which is that it is invalid to apply implication across a pair of correlations. But if you would prefer, we can substitute this third clause: > Elbonians (A) are precisely as successful at basketball as the rest of the general population, because despite their natural height, they have no cultural tradition of play, and therefore, tend not to do so. Your call.
- Ukv 2y ago
  > Elbonians (A) are disproportionately unsuccessful at basketball (¬C) Is that not a correlation? A negative correlation, but not uncorrelated. Though, I think you could tweak it such that they are only unsuccessful to the extent that it exactly cancels out benefit gained from height.

Faaak 2y ago

Can you paste the response for us that can't use the model easily?

phaedryx 2y ago
Here's what Claude gave me: A real-life example of three events A, B, and C where A and B are correlated, B and C are correlated, but A and C are uncorrelated could be: A: Ice cream sales B: Temperature C: Energy consumption for air conditioning Let's break this down: A and B correlation: Ice cream sales (A) and temperature (B) are positively correlated. As temperature rises, people tend to buy more ice cream. B and C correlation: Temperature (B) and energy consumption for air conditioning (C) are positively correlated. As temperature increases, people use more air conditioning, leading to higher energy consumption. A and C uncorrelated: Ice cream sales (A) and energy consumption for air conditioning (C) are not directly correlated. While both increase with temperature, there's no direct causal relationship between them.
- chairmanmow 2y ago
  If the purpose of ice cream and air conditioning is to make the user feel cooler, then wouldn't it be logical to say the more ice cream they eat the less air conditioning they'd use and vice versa? That seems like a causal relationship to me that's being glossed over, but maybe I'm missing something.
  - card_zero 2y ago
    I think the way to construct these is: find (a) such that all kinds of things can cause it, choose (b) as one of the causes of (a), choose (c) as something else also caused by (b) but also having all kinds of other potential causes different from those of (a). So this example isn't good, because when people are eating most ice cream, people are using most air con, both being mainly caused by hot weather. (Unless as you point out we're looking at one individual who wants a solution to feeling hot and doesn't need to do both things together.)

audessuscest 2y ago

same > Certainly. Here's a real-life example of three events A, B, and C that demonstrate the correlation pattern you've described: A: Ice cream sales B: Temperature C: Sunscreen sales Explanation: 1. A and B are correlated: Ice cream sales (A) tend to increase as temperature (B) rises. People are more likely to buy ice cream on hot days, creating a positive correlation between these two events. 2. B and C are correlated: Temperature (B) and sunscreen sales (C) are also positively correlated. As the temperature increases, people are more likely to spend time outdoors and therefore buy more sunscreen to protect their skin. 3. A and C are uncorrelated: However, ice cream sales (A) and sunscreen sales (C) are not directly correlated. While both may increase during warmer weather, there isn't a direct causal relationship between the two. People don't necessarily buy more ice cream because they're buying sunscreen, or vice versa. This example demonstrates how two events can be indirectly related through a third event (in this case, temperature) without having a direct correlation with each other. Would you like me to elaborate on this example or provide additional information about correlation?

audessuscest 2y ago
another: Here's another example of three events A, B, and C that follow the correlation pattern you described: A: Coffee consumption B: Work productivity C: Typing speed Explanation: 1. A and B are correlated: Coffee consumption (A) and work productivity (B) often show a positive correlation. Many people drink coffee to increase alertness and focus, which can lead to improved productivity at work. 2. B and C are correlated: Work productivity (B) and typing speed (C) are generally positively correlated. As people become more productive, they often type faster to keep up with their increased output. 3. A and C are uncorrelated: However, coffee consumption (A) and typing speed (C) are not directly correlated. While coffee might indirectly influence typing speed through increased productivity, there's no direct causal relationship between drinking coffee and typing faster. This example shows how work productivity acts as an intermediary factor, connecting coffee consumption and typing speed without them being directly correlated. Would you like me to provide another example or explain any part of this in more detail?
- user_7832 2y ago

goatlover 2y ago

Correlation isn’t causation, unless you’re a Humean about constant correlation, to this point in time. Would be humoirous if an LLM gave a similar response.

diggan 2y ago

So does GPT4o, unless I'm missing something very obvious: https://chatgpt.com/share/0a9d3674-0d79-4891-8045-f70376fbc721 https://chatgpt.com/share/0a9d3674-0d79-4891-8045-f70376fbc7... Events: A: Ice cream sales B: Temperature C: Incidence of sunburn Correlations: A and B are correlated: Ice cream sales (A) and temperature (B) are positively correlated. As the temperature increases, ice cream sales tend to increase because people are more likely to buy ice cream to cool down. B and C are correlated: Temperature (B) and incidence of sunburn (C) are positively correlated. Higher temperatures often mean sunnier weather, which increases the likelihood of people getting sunburned if they spend time outside without proper sun protection. A and C are uncorrelated: Ice cream sales (A) and incidence of sunburn (C) are uncorrelated directly. While both are influenced by temperature, one does not cause the other. People can buy ice cream without getting sunburned, and people can get sunburned without buying ice cream.

hnlandfr 2y ago
That looks wrong! As Slashdot never got tired of mentioning, correlation != causation. So A and C are still correlated, a causal relationship is not relevant.

samatman 2y ago

The replies to this show that it isn't just language models which struggle with the difference between correlation and causality! Here's the (logically valid but with fictional soundness) example I came up with: > The Elbonian people (A) are disproportionately tall (B). > Tall people (B) are disproportionately successful at basketball (C). > Elbonians (A) are disproportionately unsuccessful at basketball (¬C), because they don't play it. Edit: in context, I consider a negative correlation to adequately demonstrate the principle, which is that it is invalid to apply implication across a pair of correlations. But if you would prefer, we can substitute this third clause: > Elbonians (A) are precisely as successful at basketball as the rest of the general population, because despite their natural height, they have no cultural tradition of play, and therefore, tend not to do so. Your call.

Ukv 2y ago
> Elbonians (A) are disproportionately unsuccessful at basketball (¬C) Is that not a correlation? A negative correlation, but not uncorrelated. Though, I think you could tweak it such that they are only unsuccessful to the extent that it exactly cancels out benefit gained from height.