# correlation

Correlation is something that scientists are often trying to show––is there a correlation between smoking and poor health or between napping and productivity? How about daily flossing and good grades?

Correlation derives from the Latin cor- 'together' and -relatio 'relation'––the word is all about things that go together. But beware: just because a study shows a correlation between two variables, it doesn't mean one necessarily causes the other. There is a significant correlation between going to high school and being a teenager, but that doesn't mean that going to high school causes you to be a teenager.

Definitions of correlation
1. noun
a reciprocal relation between two or more things
synonyms: correlativity
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type of:
reciprocality, reciprocity
a relation of mutual dependence or action or influence
2. noun
a statistical relation between two or more variables such that systematic changes in the value of one variable are accompanied by systematic changes in the other
synonyms: correlational statistics
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types:
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curvilinear correlation, nonlinear correlation, skew correlation
any correlation in which the rates of change of the variables is not constant
partial correlation
a correlation between two variables when the effects of one or more related variables are removed
direct correlation, positive correlation
a correlation in which large values of one variable are associated with large values of the other and small with small; the correlation coefficient is between 0 and +1
indirect correlation, negative correlation
a correlation in which large values of one variable are associated with small values of the other; the correlation coefficient is between 0 and -1
spurious correlation
a correlation between two variables (e.g., between the number of electric motors in the home and grades at school) that does not result from any direct relation between them (buying electric motors will not raise grades) but from their relation to other variables
first-order correlation
a partial correlation in which the effects of only one variable are removed (held constant)
type of:
statistics
a branch of applied mathematics concerned with the collection and interpretation of quantitative data and the use of probability theory to estimate population parameters
3. noun
a statistic representing how closely two variables co-vary; it can vary from -1 (perfect negative correlation) through 0 (no correlation) to +1 (perfect positive correlation)
“what is the correlation between those two variables?”
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Pearson product-moment correlation coefficient, product-moment correlation coefficient
the most commonly used method of computing a correlation coefficient between variables that are linearly related
multiple correlation coefficient
an estimate of the combined influence of two or more variables on the observed (dependent) variable
biserial correlation, biserial correlation coefficient
a correlation coefficient in which one variable is many-valued and the other is dichotomous
chance-half correlation, split-half correlation
a correlation coefficient calculated between scores on two halves of a test; taken as an indication of the reliability of the test
tetrachoric correlation, tetrachoric correlation coefficient
a correlation coefficient computed for two normally distributed variables that are both expressed as a dichotomy
type of:
parametric statistic
any statistic computed by procedures that assume the data were drawn from a particular distribution
Commonly confused words

#### correlation / corollary

A correlation is exactly what it sounds like: a co-relation, or relationship — like the correlation between early birds waking up and the sun rising. But corollary is more like a consequence, like the corollary of the rooster crowing because you smacked it in the beak. Both words love the math lab but can hang with the rest of us, too.