positive correlation

(noun)

A relationship between two variables such that as one increases or decreases the other does the same. On a graph, a positive correlation will have a positive slope.

Related Terms

Examples of positive correlation in the following topics:

  • Correlation and Causation

    • A correlation can be positive/direct or negative/inverse.
    • A positive correlation means that as one variable increases (e.g., ice cream consumption) the other variable also increases (e.g., crime).
    • Ice cream consumption is positively correlated with incidents of crime.
    • This diagram illustrates the difference between correlation and causation, as ice cream consumption is correlated with crime, but both are dependent on temperature.
    • Thus, the correlation between ice cream consumption and crime is spurious.

  • Correlational Research

    • The strength, or degree, of a correlation ranges from -1 to +1 and therefore will be positive, negative, or zero.
    • Direction refers to whether the correlation is positive or negative.
    • In contrast, two correlations of .05 and .98 have the same direction (positive) but are very different in their strength.
    • A positive correlation, such as .8, would mean that both variables increase together.
    • Another popular example is that there is a strong positive correlation between ice cream sales and murder rates in the summer.

  • The Correlation Coefficient r

    • If r = 1, there is perfect positive correlation.
    • If r = − 1, there is perfect negative correlation.
    • A positive value of r means that when x increases, y tends to increase and when x decreases, y tends to decrease (positive correlation).
    • We say "correlation does not imply causation."
    • (a) A scatter plot showing data with a positive correlation. 0 < r < 1 (b) A scatter plot showing data with a negative correlation. − 1 < r < 0 (c) A scatter plot showing data with zero correlation. r=0

  • An Intuitive Approach to Relationships

    • Correlation refers to any of a broad class of statistical relationships involving dependence.
    • These are all examples of a statistical factor known as correlation.
    • Correlation refers to any of a broad class of statistical relationships involving dependence.
    • Familiar examples of dependent phenomena include the correlation between the physical statures of parents and their offspring and the correlation between the demand for a product and its price.
    • This graph shows a positive correlation between world population and total carbon emissions.

  • Coefficient of Correlation

    • The most common coefficient of correlation is known as the Pearson product-moment correlation coefficient, or Pearson's $r$.
    • Pearson's correlation coefficient when applied to a sample is commonly represented by the letter $r$ and may be referred to as the sample correlation coefficient or the sample Pearson correlation coefficient.
    • A positive value of $r$ means that when $x$ increases, $y$ tends to increase and when $x$ decreases, $y$ tends to decrease (positive correlation).
    • If $r=1$, there is perfect positive correlation.
    • Put the summary statistics into the correlation coefficient formula and solve for $r$, the correlation coefficient.

  • Aging and Health

    • For instance, maintaining a positive attitude has been shown to be correlated with better health among the elderly.
    • Older individuals with more positive attitudes and emotions engage in less risky behavior and have lower levels of stress, both of which are correlated with better health.

  • Properties of Pearson's r

    • State the relationship between the correlation of Y with X and the correlation of X with Y
    • A correlation of -1 means a perfect negative linear relationship, a correlation of 0 means no linear relationship, and a correlation of 1 means a perfect positive linear relationship.
    • Pearson's correlation is symmetric in the sense that the correlation of X with Y is the same as the correlation of Y with X.
    • For example, the correlation of Weight with Height is the same as the correlation of Height with Weight.
    • For instance, the correlation of Weight and Height does not depend on whether Height is measured in inches, feet, or even miles.

  • Describing linear relationships with correlation

    • We denote the correlation by R.
    • If the relationship is strong and positive, the correlation will be near +1.
    • Sample scatterplots and their correlations.
    • The first row shows variables with a positive relationship, represented by the trend up and to the right.
    • Sample scatterplots and their correlations.

  • Exercises

    • Make up a data set with 10 numbers that has a positive correlation.
    • Is this a positive or negative association?
    • Is this a positive or negative association?
    • Just from looking at these scores, do you think these variables are positively or negatively correlated?
    • (AM) Would you expect the correlation between the Anger-Out and Control-Out scores to be positive or negative?

  • Values of the Pearson Correlation

    • Give the symbols for Pearson's correlation in the sample and in the population
    • The Pearson product-moment correlation coefficient is a measure of the strength of the linear relationship between two variables.
    • It is referred to as Pearson's correlation or simply as the correlation coefficient.
    • The symbol for Pearson's correlation is "$\rho$" when it is measured in the population and "r" when it is measured in a sample.
    • An r of -1 indicates a perfect negative linear relationship between variables, an r of 0 indicates no linear relationship between variables, and an r of 1 indicates a perfect positive linear relationship between variables.