# What would you call the relationship between variables that show a correlation but no causal relationship?

Take say height and weight of people.

There is a positive correlation here but no causal relationship here.

Height doesn't cause weight.

Take as another example the number of icecreams bought and number of cold drinks bought in a park over a number of days. There is a positive correlation as days where more icecreams are bought there are more cold drinks bought also. They share a common causal relationship which is temperature. How would you describe this relationship ?

Another example would be marks in students' mock exam and final exam. There is a strong correlation as students who did well in their mock exam are likely to do well in the final. The mock result doesn't cause the final result. They share a hidden variable. Both are caused by how hard working and determined the student is.

• In a sense, height might be thought to cause weight (one of several reasons that adults tend to be heavier than babies is that they grow taller) to a greater degree than weight causing height. Commented Jun 27, 2020 at 17:41

You already named it, it’s just correlation. There may, but doesn’t have to be, a casual relationship if the events are correlated.

Actually, as to "what would you call the relationship between variables that show a correlation but no causal relationship?", many names have been applied per this article: 10 Correlations That Are Not Causations, however, not all examples have associated names, so here is my extracted list, starting with, to quote:

Take the Hawthorne Works in Cicero, Ill. In a series of experiments from 1924-1932, researchers studied the worker productivity effects associated with altering the Illinois factory's environment,... observed increases in productivity flagged almost as soon as the researchers left the works, indicating that the workers' knowledge of the experiment, not the researchers' changes, had fueled the boost. Researchers still call this phenomenon the Hawthorne Effect.

Next:

The sophomore slump, too, typically arises from a too-good first year. Performance swings tend to even out in the long run, a phenomenon statisticians call regression toward the mean. In sports, this averaging out is aided by the opposition, which adjusts to counter the new player's successful skill set.

Also:

Statisticians call this the gambler's fallacy, aka the Monte Carlo fallacy, after a particularly illustrative example occurring in that famed Monaco resort town. During the summer of 1913, bettors watched in increasing amazement as a casino's roulette wheel landed on black 26 times in a row. Inflamed by the certainty that red was "due," the punters kept plunking down their chips. The casino made a mint...

Next, I referred to as sample selection bias:

Randomized controlled trials are the gold standard in statistics, but sometimes -- in epidemiology, for example -- ethical and practical considerations force researchers to analyze available cases. Unfortunately, such observational studies risk bias, hidden variables and, worst of all, a study group that might not reflect the population as a whole.

And, data mining per the comment:

Big data -- the process of looking for patterns in data sets so large they resist traditional methods of analysis...It's a rule that's drummed into most researchers in their first stats class: When encountering a sea of data, resist the urge to go on a fishing expedition.

And last:

While it's true that no vaccine is 100 percent harmless, the belief in this causal link arises mainly from natural parental concern, burdened by confusion, fueled by anecdotal evidence and influenced by confirmation bias...