Skip to main content

### 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.

Applications

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

References

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   www.suttong.com

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

### Personal Self-Concept Questionnaire (PSQ)

The Personal Self-Concept Questionnaire  ( PSQ )   Overview The Personal Self-Concept Questionnaire (PSQ) measures self-concept based on ratings of 18 items, which are grouped into four categories: Self-fulfilment, autonomy, honesty, and emotional self-concept. Subscales : The PSQ has four subscales 1. Self-fulfilment (6 items) 2. Autonomy (4 items) 3. Honesty (3 items) 4. Emotional self-concept (5 items)  ðŸ‘‰ [ Read more about Self-Concept and Self-Identity] The PSQ is a Likert-type scale with five response options ranging from totally disagree to totally agree. Reliability and Validity In the first study, coefficient alpha = .85 and in study two, alpha = .83. Data analysis supported a four-dimensional model (see the four categories above). Positive correlations with other self-concept measures were statistically significant. Other notes The authors estimated it took about 10 minutes to complete the PSQ. Their first study included people ages 12 to 36 ( n = 506). In the second s

### Student Self-Efficacy

Assessment name:  STUDENT SELF-EFFICACY SCALE * Note. This post has been updated to provide an available measure of student self-efficacy. ———- Scale overview:  The  student self-efficacy scale i s a 10-item measure of self-efficacy. It was developed using data from university nursing students in the United States. Authors: Melodie Rowbotham and Gerdamarie Schmitz Response Type:  A four-choice rating scale as follows: 1 = not at all true 2 = hardly true 3 = moderately true 4 = exactly true   Self-efficacy is the perception that a person can act in a way to achieve a desired goal.  Scale items There are 10 items. Examples: I am confident in my ability to learn, even if I am having a bad day. If I try hard enough, I can obtain the academic goals I desire.   Psychometric properties The authors reported that their sample scores ranged from 25 to 40 with a scale mean of 34.23 ( SD  = 3.80. Internal consistency was high at alpha = .84. The authors reported the results of a principal compon

### Mathematics Self-Efficacy and Anxiety Questionnaire (MSEAQ)

Scale name: Mathematics Self-Efficacy and Anxiety Questionnaire (MSEAQ) Scale overview: The Mathematics Self-Efficacy and Anxiety Questionnaire (MSEAQ) is a 29-item self-report measure of both mathematics self-efficacy and mathematics anxiety. Author: Diana Kathleen May Response Type: Items are rated on a 5-point Likert-type scale following a “no response” option: 1 = Never 2 = Seldom 3 = Sometimes 4 = Often 5 = usually Sample items 1. I feel confident enough to ask questions  in my mathematics class. 6. I worry that I will not be able to get a  good grade in my mathematics course.   Subscales and basic statistics for the MSEAQ       Self-Efficacy M = 44.11, SD = 10.78, alpha = .93       Anxiety M = 46.47, SD = 12.61, alpha = .93       Total Scale M = 90.58, SD = 22.78, alpha = .96 Reliability: See the Cronbach’s alpha levels reported above. Validity: There were significant positive correlations with similar measures. The results of a Fa