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Correlation. Bivariate statistics. What is Correlation?. When a researcher want to measure the association between variables Identifying the relationships and summarizing them Involves interval-level variables. Correlation . Designed to answer the following questions:

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Bivariate statistics

What is correlation
What is Correlation?

  • When a researcher want to measure the association between variables

  • Identifying the relationships and summarizing them

  • Involves interval-level variables


  • Designed to answer the following questions:

    • Is there a relationships between variables?

      • Bivariate

      • Multivariate: How do multiple independent variables predict a dependent variable?

    • How strong is the relationship?

    • What is the direction of the relationship?

      • Positive or negative

Correlations should
Correlations should

  • Make sense

  • Be based on theory

Which of these correlate
Which of these correlate?

  • Hours per week studying and GPA

  • Quality of relationships with faculty and satisfaction with college

  • Hours partying per week and GPA

How about these
How about these?

  • Hours in the library and number of presents one receives at Christmas

  • Number of Facebook friends and number of presents one receives at Christmas


  • To begin to understand a relationship between 2 variables is to examine a scattergram

  • Scattergramsare graphic displays that permit the researcher to quickly perceive several important features in a relationship.

    • Page 150 text


  • 2 axes; right angles to each other

  • Independent variable (x) along the horizontal axis (the abscissa)

  • Dependent variable (Y) along the vertical axis (the ordinate)

  • Both axes represent unit measures of each variable

  • Then, for each case, locate the point along the X axis that corresponds to the score of that case on the Y axis


  • Example

    • Families with 2 wage earners and how they handle housework

      • The number of children in the family is related to the amount of time the husband contributes to housekeeping chores


  • Overall pattern of the dots (or observation points) succinctly summarizes the nature of the relationship between 2 variables.

  • The straight line through the cluster of the dots is called the regression line.

  • Tells us some impressions about the existence, strength and direction of the relationship


  • Relationship exists:

    • Y changes as X changes

    • If not associated, Y would not change

  • Strength:

    • Observing the spread of the dots around regression line

  • Direction:

    • Observing the angle of the line with respect to the X axis


  • Positive relationship: High scores on X also tend to have high scores on Y

  • Negative relationship: Opposite high scores on Y associated with low scores on X


  • Analyze statistically the association or correlation between variables

  • Statistic: correlation coefficient

    • Pearson’s r

  • R will always be between -1.00 and +1.00

  • If the correlation is negative; we have a negative relationship

  • If it’s positive, the relationship is positive

  • Formula

  • Pearson s r measures
    Pearson’s r measures:

    • strength of the relationship

      0 to +/- .30 = weak

      +/- .31 to +/- 60 = moderate

      >.60 or <-.60 = strong

    • direction of the relationship

      • Positive r means variables increase and decrease together.

      • Negative r means when one variable increases, the other decreases.

    There is a significant relationship when
    There is a significant relationship when:



    • Correlation is not causation because

      • Direction of cause is unclear

      • An outside variable may cause the relationship


    • The two variables have a linear relationship

    • Scores on one variable are normally distributed for each value of the other variable and vice versa

    • Outliers can have a big effect on the correlation

      • Text page 149

    How to carry out a bivariate correlation
    How to carry out a bivariate correlation

    • State the research question (What is the association between…?

    • Test of statistical significance

    • Strength of association

    • Effect size

    Problem a wellness
    Problem A: Wellness

    • Research question:

    • What are the associations between weight, age, exercise and cholesterol?


    The first table provides descriptive statistics: mean standard deviation and N


    This table is our primary focus. This is a correlation matrix. This where we determine which variables are correlated including the Pearson correlation coefficient, and the significance level. SPSS flags or asterisks the correlation coefficients that are statistically significant.


    • To investigate if there were statistically significant associations between weight, sex, age, exercise and cholesterol, correlations were computed. Bivariate analysis shows that 2 of the 10 pairings of variables were significantly correlated. The strongest negative correlation was between exercise and cholesterol r (16)=-.66, p<.05. This means that students who had exercised more were likely to have low cholesterol.

    Interpretation continued
    Interpretation (continued)

    • Weight was also negatively correlated with gender (sex) r(16)=-.80, p<.001. This means that gender of the student was very likely associated with weight.


    • How can we say the results in plain language?

    Text information
    Text information

    • Page 149: Concepts used in bivariate correlation

    • Page 155: Steps for bivariate correlation

      • (For our purposes: Do not check Spearman’s)

    • Page 159: How to read SPSS output of correlation matrix

    • Page 160: How to write interpretation