If you look in different statistics textbooks, you are likely to find different-looking but equivalent formulas for computing a correlation coefficient. In this section, we present several formulas that you may encounter. The most common formula for computing a product-moment correlation coefficient r is given below.
Product-moment correlation coefficient. The correlation r between two variables is:. Population correlation coefficient. The formula below uses sample means and sample standard deviations to compute a sample correlation coefficient r from sample data.
Sample correlation coefficient. The interpretation of the sample correlation coefficient depends on how the sample data are collected. A nonlinear curve may show a positive or a negative relationship. The slope of a curve showing a nonlinear relationship may be estimated by computing the slope between two points on the curve.
The slope at any point on such a curve equals the slope of a line drawn tangent to the curve at that point.
The slope of a line describes a lot about the linear relationship between two variables. If the slope is positive, then there is a positive linear relationship, i. If the slope is 0, then as one increases, the other remains constant.
Common Examples of Positive Correlations. The more time you spend running on a treadmill, the more calories you will burn.
Taller people have larger shoe sizes and shorter people have smaller shoe sizes. Correlational studies are quite common in psychology, particularly because some things are impossible to recreate or research in a lab setting. Instead of performing an experiment , researchers may collect data from participants to look at relationships that may exist between different variables. From the data and analysis they collect, researchers can then make inferences and predictions about the nature of the relationships between different variables.
Correlation strength is measured from The correlation coefficient, often expressed as r , indicates a measure of the direction and strength of a relationship between two variables. A correlation of Scattergrams also called scatter charts, scatter plots, or scatter diagrams are used to plot variables on a chart see example above to observe the associations or relationships between them.
The horizontal axis represents one variable, and the vertical axis represents the other. Each point on the plot is a different measurement. From those measurements, a trend line can be calculated.
The correlation coefficient is the slope of that line. When the correlation is weak r is close to zero , the line is hard to distinguish. When the correlation is strong r is close to 1 , the line will be more apparent. A zero correlation suggests that the correlation statistic did not indicate a relationship between the two variables.
It's important to note that this does not mean that there is not a relationship at all; it simply means that there is not a linear relationship. Correlations can be confusing, and many people equate positive with strong and negative with weak. A relationship between two variables can be negative, but that doesn't mean that the relationship isn't strong.
A weak positive correlation would indicate that while both variables tend to go up in response to one another, the relationship is not very strong. A strong negative correlation, on the other hand, would indicate a strong connection between the two variables, but that one goes up whenever the other one goes down.
Of course, correlation does not equal causation. A correlation of The sample correlation coefficient, denoted r, The magnitude of the correlation coefficient indicates the strength of the association. A zero correlation exists when there is no relationship between two variables.
For example there is no relationship between the amount of tea drunk and level of intelligence. A negative correlation can indicate a strong relationship or a weak relationship.
A correlation of -1 indicates a near perfect relationship along a straight line, which is the strongest relationship possible.
0コメント