Showing posts with label correlation. Show all posts
Showing posts with label correlation. Show all posts

Wednesday, July 20, 2022

Effect Sizes (ES) in statistics

In statistics, an effect size (ES) indicates the strength of the relationship between two variables.

In psychological experiments, researchers are interested in the strength of the effect of the Independent Variable on the Dependent Variable.

In psychotherapy studies, researchers may be interested in the effects of treatment on a measure of the dependent variable. A research questions may be framed: How effective is a set of 6 CBT sessions on the reduction of depression?

Psychologists have often described effect sizes as small, medium, or large.

Cohen's d

Cohen's d is a measure of effect size between two groups. The mean of one group is subtracted from a second group and divided by the pooled standard deviation of the two groups.

ES = (M1 - M2) / SD

Effect Size  Label

0.2     Small

0.5     Medium

0.8     Large

Pearson Correlation Coefficient (r)

0.1 to 0.3  Small

0.3 to 0.5  Medium

0.5 to 1.0   Large

Converting Cohen's d to the correlation coefficient

r =  d/ d2 + 4

Note. Negative values also indicate strength of a relationship.

Cite this post

Sutton, G. (2022, July 20). Effect sizes (ES) in statistics. Assessment, Statistics, and Research. Retrieved from


Cohen, J. (1992). A power primer. Psychological Bulletin, 112(1), 155–159.

Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: Lawrence Erlbaum Associates.

Sutton, G. W. (2020). Applied statistics: Concepts for counselors, second edition. Springfield, MO: Sunflower.

 Link to an Index of Statistical Concepts in Psychology, Counseling, and Education

 Reference for using scales in research:

Creating Surveys on AMAZON or GOOGLE


Reference for clinicians on understanding assessment

Applied Statistics Concepts for Counselors on AMAZON or GOOGLE


Resource Link:  A-Z Statistical Terms

Resource Link:  A – Z Test Index

Related Terms

Standard Deviation


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Saturday, February 19, 2022



The Spearman-Brown formula estimates test score reliability of a full-length test when using a split-half method of reliability.

The split-half method divides a test in two and calculate a correlation between the scores of the two halves. Longer tests are yield higher reliability values so the Spearman-Brown formula estimates the reliability value for the full test.

Other names for the Spearman-Brown formula are Spearman-Brown Prophecy Formula, Spearman-Brown Correction.

Learn more about test statistics in

Applied Statistics Concepts for Counselors on   AMAZON or   GOOGLE

Please check out my website

   and see my books on   AMAZON       or  GOOGLE STORE

Also, consider connecting with me on    FACEBOOK   Geoff W. Sutton    

   TWITTER  @Geoff.W.Sutton    

You can read many published articles at no charge:

  Academia   Geoff W Sutton     ResearchGate   Geoffrey W Sutton 

Monday, March 29, 2021

Correlation coefficient the Pearson r in statistics


The term correlation can refer to a statistic and a type of research. 

Understanding correlations is an important building block of many complex ideas in statistics and research methods. My focus in this post is on the common correlation statistic, also called the Pearson r.

The Pearson r is a statistical value that tells the strength and direction of the relationship between two normally distributed variables measured on an interval or ratio scale.

Researchers examine the two sets of values and calculate a summary statistic called a correlation coefficient. The longer name for a common correlation statistic is the Pearson Product Moment Correlation Coefficient but sometimes it is referred to as the Pearson r. The symbol for correlation is a lower case and italicized r.  In behavioural research, we normally round values to two decimal points. A moderately strong positive correlation example is r = .78.

      Sometimes, the relationship between the two variables is negative. For example, the relationship between depression and self-esteem is often negative. As depression increases, self-esteem decreases. An example of a negative correlation would be written as r = -.45. The minus sign tells us that as one variable increases, the other variable decreases. The relationship is commonly described in journal articles as an inverse relationship.

An example from published research is the relationship between perceived stress and humility couples experience as they transition to parenthood. As a part of their work, Jennifer Ripley and her research team (2016) found that the correlation between a measure of perceived stress and a measure of humility ranged from -.33 to -.45, which indicates that high stress is associated with low humility.

The relationship between two variables not only varies in a positive or negative direction but it also varies in terms of strength. Large r values indicate a stronger relationship. When r = .75 or -.75, the relationship is of equal strength but in different directions. Relationships with a low number such as r = .15 or r = -.11 indicate weak relationships.

      When r values are at or near zero, we say there is no relationship between the variables. For example, we may find no relationship between scores on questionnaires about humility and depression.

Correlation is not causation

The fact that two variables have a strong relationship does not mean one variable causes the other.

Read more about correlations in Chapter 13 of 

Applied Statistics Concepts for Counselors on AMAZON or GOOGLE

Graphing the Correlations

This is an example of fictitious data illustrating a positive correlation between anxiety and depression. Anxiety and depression are different states but both may be present.

The following is an example of  fictitious data illustrating a negative correlation between self-esteem and depression. A high self-esteem score of 8 reflects low depression. Low self-esteem near 2 reflects a high level of depression at 7.


Correlations are commonly calculated in many research projects where the relationship between variables is important.

Correlations are also important to understanding the reliability of test scores and test validity.

Key concepts

Correlation coefficient

Pearson Product Moment Correlation

Inverse relationship

Positive correlation

Negative correlation

Link to A-Z list of Statistical Terms


Ripley, J. S., Garthe, R. C., Perkins, A., Worthington, E. J., Davis, D. E., Hook, J. N., & ... Eaves, D. (2016). Perceived partner humility predicts subjective stress during transition to parenthood. Couple and Family Psychology: Research and Practice5(3), 157-167. doi:10.1037/cfp0000063

Sutton, G. W. (2020). Applied statistics: Concepts for counselors, second edition. Springfield, MO: Sunflower. AMAZON  Paperback ISBN-10: 168821772X, ISBN-13: 978-168217720    website: counselorstatistics

Please check out my website

   and see my books on   AMAZON       or  GOOGLE STORE

Also, consider connecting with me on    FACEBOOK   Geoff W. Sutton    

   TWITTER  @Geoff.W.Sutton    

You can read many published articles at no charge:

  Academia   Geoff W Sutton     ResearchGate   Geoffrey W Sutton 

Thursday, January 14, 2021

Cramer’s V


Cramer’s V. A correlation coefficient that may be used with nominal data. It is often included with chi-square test reports.

Creating Surveys on AMAZON    or   GOOGLE  Worldwide

Links to Connections

Checkout My Website


See my Books





FOLLOW me on

   FACEBOOK   Geoff W. Sutton  


   TWITTER  @Geoff.W.Sutton




Read published articles:


  Academia   Geoff W Sutton   


  ResearchGate   Geoffrey W Sutton 

Sunday, October 1, 2017

Take a brief Counseling Test Quiz 101

Can you answer these questions that every counselor ought to know?

Choose the BEST available answer.

I'll post the answers below.

1. If the correlation between a test of intelligence and a test of achievement is usually between .88 and .92, how well can you use the intelligence test results to predict achievement test results?

A. Very well
B. Moderately well
C. Not well at all
D. None of the above

2. A personality test score was high on a scale of Extraversion. The validity of the Extraversion scale was reported as .52 to .57 compared to similar tests. How much confidence should the person have that their score is "valid?"

A. A high degree
B. A moderate degree
C. A low degree
D. None of the above

3. School counselors administered a questionnaire to 1,000 students. They calculated results for answers about four school improvements rated on a scale of 1 to 5. Most of the scores were in the range of 18 to 20. The counselors reported a mean rating of 4.6 for each of the 4 items. Based on these data, what should they have reported?

A. The mean is fine-- an average is all that is needed.
B. They should report the Mean and Standard Deviation.
C. They should report the reliability with the mean.
D. They should report the median and range.

4. An agency director asks a counselor to determine if there was evidence of improvement in well-being for clients in one of three treatment groups. Assuming a normal distribution of the data, which of the following statistical procedures could provide the best answer?

A. An independent samples t test
B. A one-way analysis of variance
C. A two-way analysis of variance
D. A chi-square test


1. A. Other things being equal, the correlation between the two tests is strong thus, most of the time the intelligence test score will be a good predictor of the achievement test score. See Chapter 12 in Applied Statistics: Concepts for Counselors.

2. C. We do not know much about the validation of the Extraversion scale ; however, we know the validity values in the .50s are low so the best answer, given the limited data, is C. Validity coefficients range from 0.0 to 1.0. Important note: Validity is a product of the interpretation of data based on scores. Although it is common to refer to a test's validity, tests really do not have validity. Instead, there is a history of validity statistics and interpretations associated with validity. See chapter 20 in Applied Statistics: Concepts for Counselors.

3. D. The data appeared skewed given that 4 items on a 5-point scale would yield a maximum of 20. So, based on the limited data, the median would be the most typical value. When reporting the mean, counselors ought to report the standard deviation, but in this case, the median appears to be the best value. See Chapters 7-10 of Applied Statistics: Concepts for Counselors.

4. A one-way analysis of variance can be used to analyze data from two or more groups. If the overall value is statistically significant, t tests or other post hoc tests can be used to compare pairs of means. See Chapters 15-17 of Applied Statistics: Concepts for Counselors.

APPLIED STATISTICS: CONCEPTS FOR COUNSELORS is available as an eBook or paperback from AMAZON.

Book website

"If you need to review basic statistics and don’t know where to begin, this book is perfect! It makes difficult concepts easy to understand. I would recommend it for my undergraduate students who haven’t had Statistics in a while and need a refresher, or for graduate students facing their first graduate level research class!"
...Heather L. Kelly, Psy.D., Professor of Psychology, Evangel University
Springfield, Missouri, USA

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