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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.
  • 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