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Statistics Resources

This guide contains all of the ASC's statistics resources. If you do not see a topic, suggest it through the suggestion box on the Statistics home page.

All About Correlations

The correlation analysis is used to measure the direction and relationship between two variables. It's important to note that correlation does not equal causation. That means that while a relationship may be observed, it's impossible to say that one variable caused or affected the other variable. The relationship observed may be due to other variables not accounted for in the model.

Research Question & Hypotheses Examples

RQ: What is the relationship between height and age?

  • H0: There is no relationship between height and age.
  • Ha: There is a relationship between height and age.

RQ: Is there a significant linear relationship between hours of exercise and weight?

  • H0: There is not a significant linear relationship between hours of exercise and weight.
  • Ha: There is a significant linear relationship between hours of exercise and weight.

Direction

The direction of the relationship can be assessed by looking at the sign of the correlation coefficient.

  • positive - a positive relationship indicates that the variables move in the same direction. As the value of one variable increases, the value of the other variable also increases.
    • Example: As age increases, height also increases.
  • negative - a negative relationship indicates that the variables move in opposite directions. As the value of one variable increases, the value of the other variable decreases.
    • Example: As hours of exercise increase, weight decreases.

Strength

The strength of the relationship can be assessed by evaluating the numerical value of the correlation coefficient. Correlation values can range from -1 to +1.

  • -1 = perfect negative correlation
  • -.7 = strong negative correlation
  • -.5 = moderate negative correlation
  • -.3 = weak negative correlation
  • 0 = no correlation
  • .3 = weak positive correlation
  • .5 = moderate positive correlation
  • .7 = strong positive correlation
  • 1 = perfect positive correlation

Graphs depicting the slope of a line

Effect Size

The measure of effect size used for correlation analyses is called the coefficient of determination or R-Squared. This value can be found by simply squaring the value of the correlation coefficient (r). For example, if r = .3, then the effect size is .09. This is interpreted as saying that 9% (.09 x 100 = 9%) of the variability in one variable is explained by the other variable.

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