Science Strategy
In bivariate analysis, we use statistical techniques to discover how two variables relate to each other. Pearson's correlation provides a way to examine the strength of the relationship between two linearly related variables. If variables are linearly related, a scatter plot should generally look like a straight line. Correlation is a measure of how strongly two variables relate to one another, but it does not imply causality. For a valid Pearson's correlation, two assumptions must hold true: 1) the two variables must be numerical, and 2) the two variables must be continuous.
A corresponding coefficient called Pearson's coefficient or simply "r" is derived from a line of correlation. The r coefficient ranges from negative 1 to positive 1, reflecting both the direction and the strength of the relationship between two variables. An r of 1 denotes a perfect correlation, an r of -1 implies an inverse or reciprocal relationship, and a Pearson's r of 0 means there is no relationship between the two variables.
Lesson Outline
<ul> <li>Bivariate analysis: statistical techniques to discover how two variables relate to each other</li> <li>Pearson's correlation: examines the strength of the relationship between two linearly related variables</li> <ul> <li>Scatter plot should generally look like a straight line for linearly related variables</li> <li>Measures the strength of the relationship, not causality or association</li> <li>Valid Pearson's correlation requires two assumptions:</li> <ul> <li>1) The two variables must be numerical</li> <li>2) The two variables must be continuous</li> </ul> </ul> <li>Pearson's coefficient (r): derived from a line of correlation, reflects direction and strength of the relationship between two variables</li> <ul> <li>Ranges from -1 to 1</li> <li>R of 1: perfect correlation</li> <li>R of -1: inverse or reciprocal relationship</li> <li>R of 0: no relationship between the two variables</li> </ul> <li>Running a Pearson's correlation</li> <ul> <li>Plot the two variables on two axes</li> <li>Use a basic statistical program to calculate the r-value or use the r formula</li> <li>Formula considers the means of the x and y variable sets, their variance, and their covariance</li> </ul> </ul>
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FAQs
A positive correlation indicates that when one variable increases, the other variable tends to increase as well, signaling a direct relationship between the two variables. An inverse relationship, on the other hand, signifies that when one variable increases, the other variable tends to decrease, indicating a negative correlation between the variables. In both instances, the strength of the relationship is determined by the correlation coefficient, which can range from -1 (perfect negative correlation) to +1 (perfect positive correlation).
A scatter plot is a graphical representation used to display the relationship between two variables. In correlation analysis, scatter plots help visualize the association between two variables by plotting data points on a horizontal and vertical axis, representing the values of those variables. If the points on a scatter plot appear to form a straight line, it implies a linear relationship between the variables. The scatter plot gives a visual overview of the strength and direction of the relationship while also allowing for the identification of any outliers.
Pearson's coefficient (r) reflects the strength and direction of a linear relationship between two continuous variables. It ranges from -1 to +1, where -1 indicates a perfect negative correlation, +1 indicates a perfect positive correlation, and 0 means no linear correlation. The closer the coefficient is to +1 or -1, the stronger the linear association between the variables. If the coefficient value is near zero, it implies that there is a weak or no linear relationship between the variables.
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