BHS 307 Statistics for the Behavioral Sciences

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BHS 307 Statistics for the Behavioral Sciences

• Chapter 15 t-Test for Correlation Coefficient

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Population Correlation Coefficient

• Two correlated variables are similar to a matched
  sample because in both cases, observations are
  paired.
• A population correlation coefficient (r) would
  represent the mean of rs for all possible pairs
  of samples.
• Hypotheses
• H0 r 0
• H1 r / 0

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t-Test for Rho (r)

• Similar to a ttest for a single group.
• Tests whether the value of r is significantly
  different than what might occur by chance.
• Do the two variables vary together by accident or
  due to an underlying relationship?

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Calculating t for Correlated Variables

• Except that r is used in place of X, the formula
  for calculating the t statistic is the same.
• The standard error of prediction is used in the
  denominator to calculate the standard deviation.
• Compare against the critical value for t with df
  n 2 (n pairs).

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Importance of Sample Size

• Lower values of r become significant with greater
  sample sizes
• As n increases, the critical value of t
  decreases, so it is easier to obtain a
  significant result.
• Cohens rule of thumb (Ch 6, p 135)
• .10 weak relationship
• .30 moderate relationship
• .50 strong relationship