Relationship Between Two Continuous Variables - University of Strathclyde
While a categorical variable is essentially a non-numerical factor that has been assigned a number (e.g. gender, if boys are given the number 2 and girls 1, these numbers don’t signify any kind of order between the two), continuous variables are ordered and the distance between the numbers is fixed (in contrast to ordinal variables where the distance between the numbers is not fixed). A typical example of a continuous variable is weight. Five kilos are more than 4 kilos, and the difference between 4 and 5 kilos is the same as that between 2 and 3 kilos, i.e. 1 kilo
While a categorical variable is essentially a non-numerical factor that has been assigned a number (e.g. gender, if boys are given the number 2 and girls 1, these numbers don’t signify any kind of order between the two), continuous variables are ordered and the distance between the numbers is fixed (in contrast to ordinal variables where the distance between the numbers is not fixed). A typical example of a continuous variable is weight. Five kilos are more than 4 kilos, and the difference between 4 and 5 kilos is the same as that between 2 and 3 kilos, i.e. 1 kilo
Correlation is the concept of association between one measure and another. It requires a population, e.g., of pupils and two scores from each member, e.g., maths and English score.
The correlation basically tells us the extent to which the two variables co-vary or move in tandem with one another.
In statistical terms the relationship between variables is denoted by the correlation coefficient, which is a number between 0 and 1.0. Pearson’s r is the most common; the main ideas discussed here are similar for all correlation coefficients.
- If there is no relationship between the variables under investigation (or between the predicted values and the actual values), then the correlation coefficient is 0, or non-existent.
- As the strength of the relationship between the variables increases, so does the value of the correlation coefficient, with a value of 1 showing a perfect relationship. (As mentioned, in variables studied in educational research, or generally in social sciences, it is highly unlikely that such perfect correlations are found.)
Causation or causality in statistical terms means that variable A isn’t just correlated with variable B, but that it actually produces a change in B.
When conducting a correlation analysis, it is important to remember that we cannot claim that a relationship between variables is a “cause and effect” one. All we can say is that the two variables occur together, that changes in one is accompanied by systematic changes in the other. Causal inferences are made based on underlying theories and knowledge.
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