# 0.3 Calculating correlations: parametric and non parametric  (Page 4/4)

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 Verbal IQ (Wechsler Verbal Intelligence 3) Performance IQ (Wechsler Performance Intelligence 3) Verbal IQ (Wechsler Verbal Intelligence 3) Pearson Correlation 1 .664 ** Sig. (2-tailed) .000 N 1182 1180 Performance IQ (Wechsler Performance Intelligence 3) Pearson Correlation .664 ** 1 Sig. (2-tailed) .000 N 1180 1180 **. Correlation is significant at the 0.01 level (2-tailed).
[In this matrix, it appears that four unique correlations are present, one per cell. In fact, only one unique correlation, or r , is present in this four cell matrix.]

## Step six:

• Check For Effect Size
• 1. Go to the correlation box
• 2. Find Pearson’s Correlation Row or Spearman rho’s and follow it to the variable column.
• 3. Your effect size will be located in the cell where the above intersect.
• 4. The effect size is calculated as:

## Cohen's criteria for correlations (1998)

• .1 = small (range from .1 to .29)
• .3 = moderate (range from .3 to .49)
• .5 = large (range from .5 to 1.0)
Correlations cannot be greater than 1.00, therefore a 0 should not be placed in front of the decimal.

## Step seven:

• Check the Level of Variance the Variables Have in Common
• 1. Square the Pearson Correlation Value or Spearman rho value to find the variance
• 2. In this example, the Verbal IQ and the Performance IQ share 44.09% of the variance in common (see correlation value of .664).
 Verbal IQ (Wechsler Verbal Intelligence 3) Performance IQ (Wechsler Performance Intelligence 3) Verbal IQ (Wechsler Verbal Intelligence 3) Pearson Correlation 1 .664 ** Sig. (2-tailed) .000 N 1182 1180 Performance IQ (Wechsler Performance Intelligence 3) Pearson Correlation .664 ** 1 Sig. (2-tailed) .000 N 1180 1180 ** Correlation is significant at the 0.01 level (2-tailed).

## Step eight:

• Write the Numerical Sentence
• 1. r ( n ) sp = sp correlation coefficient, sp p sp < sp .001 (or Bonferroni-adjusted alpha significance error rate).
• 2. Using this example: r (1180) = .66, p <.001
[sp means to insert a space.] Remember that all mathematical symbols are placed in italics.

## Step nine:

• Narrative and Interpretation
• 1. r value
• 2. sample size or n
• 3. p value
• 4. r 2 value
• 5. r (1180) = .66, p <.001, 44.09% of variance accounted for.
• 6. Note that the r value itself is the effect size.

So, how do you "write up" your Research Questions and your Results? Schuler W. Huck (2000) in his seminal book entitled, Reading Statistics and Research, points to the importance of your audience understanding and making sense of your research in written form. Huck further states:

This book is designed to help people decipher what researchers are trying to communicate in the written or oral summaries of their investigations. Here, the goal is simply to distill meaning from the words, symbols, tables, and figures included in the research report. To be competent in this arena, one must not only be able to decipher what's presented but also to "fill in the holes"; this is the case because researchers typically assume that those receiving the research report are familiar with unmentioned details of the research process and statistical treatment of data.

Researchers and Professors John Slate and Ana Rojas-LeBouef understand this critical issue, so often neglected or not addressed by other authors and researchers. They point to the importance of doctoral students "writing up their statistics" in a way that others can understand your reporting and as importantly, interpret the meaning of your significant findings and implications for the preparation and practice of educational leadership. Slate and LeBouef provide you with a model for "writing up your Parametric and Non-Parametric Correlations statistics."

## References

• Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.) . Hillsdale, NJ: Lawrence Erbaum
• Onwuegbuzie, A. J.,&Daniel, L. G. (2002). Uses and misuses of the correlation coefficient. Research in the Schools, 9 (1) , 73-90.
• StatSoft, Inc. (2011). Electronic statistics textbook. Tulsa, OK: StatSoft. WEB: (External Link)

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