Skip to main content

Degrees of freedom (df)

Degrees of freedom (df) is a statistical concept representing the number of independent values that are "free to vary" in a data set when estimating a population parameter from a sample. In simpler terms, it's about how many pieces of information in a dataset can be chosen independently, given that some constraints or calculations are already in place (Sutton,  2020).

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

An example from psychology


Imagine a psychologist is conducting a study to see if a new therapeutic intervention improves self-esteem. They recruit a sample of 10 participants and measure their self-esteem before the intervention and after the intervention. 

To analyze the data, the researcher might use a statistical test like a dependent samples t-test (also called a paired samples t-test), which compares the means of two related groups (in this case, the same participants before and after the intervention). 

In a dependent samples t-test, the degrees of freedom are calculated as the number of pairs of observations (or the number of participants in this case) minus 1. So, for a study with 10 participants, the degrees of freedom would be: 

 df = n - 1 = 10 - 1 = 9

This means that out of the 10 data points (representing the change in self-esteem for each participant), 9 of them are free to vary independently to estimate the mean difference in self-esteem. The last data point, however, is determined by the previous 9 and the calculated mean difference. 


Why are degrees of freedom important?


Determining Critical Values: Degrees of freedom are crucial for finding the correct critical values for statistical tests, which are used to determine if a result is statistically significant.


Shape of Distributions: Degrees of freedom influence the shape of probability distributions like the t-distribution and chi-square distribution, affecting the likelihood of obtaining certain test statistics.


Validity and Reliability: Appropriately calculating degrees of freedom helps ensure the validity and reliability of research findings by providing a more accurate assessment of the precision of parameter estimates. 


Reference for using scales in research:

Buy Creating Surveys on

GOOGLE BOOKS

 

AMAZON

 


 

 

 





Reference for clinicians and students on understanding assessment

Buy Applied Statistics for Counselors

 GOOGLE BOOKS

 

AMAZON


NOTICE:

The information about scales and measures is provided for clinicians and researchers based on professional publications. The links to authors, materials, and references can change. You may be able to locate details by contacting the main author of the original article or another author on the article list.


Post Author

Geoffrey W. Sutton, Professor Emeritus of Psychology at Evangel University, holds a master’s degree in counseling and a PhD in psychology from the University of Missouri-Columbia. His postdoctoral work encompassed education and supervision in forensic and neuropsychology. As a licensed psychologist, he conducted clinical and neuropsychological evaluations and provided psychotherapy for patients in various settings, including schools, hospitals, and private offices. During his tenure as a professor, Dr. Sutton taught courses on psychotherapy, assessment, and research. He has authored over one hundred publications, including books, book chapters, and articles in peer-reviewed psychology journals. His website is https://suttong.com You can find Dr. Sutton's books on   AMAZON    and  GOOGLE. Many publications are free to download at ResearchGate   and Academia  

 







Labels:

Comments

Post a Comment

Popular posts from this blog

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. It is a likert-type rating scale with high internal consistency values and has been used with youth and adults. 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 e...
Post a Comment
Read more

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 ...
Post a Comment
Read more

Academic Self-Efficacy Scale ASE

  Overview The  Academic Self-Efficacy Scale is an application of Self-Efficacy Theory   to examine the relationship between self-efficacy and academic performance using 8-items rated on a 7-point scale. The work of Chemers et al. (2001) has been widely cited. Format The 8-items are rated on a 7-point Likert-type scale ranging from 1 = Very Untrue to 7 = Very True. Sample Items 2. I know how to take notes. 6. I usually do very well in school and at academic tasks.   Reliability, Validity, and Other Research notes In the article describing the development and use of the ASE, the authors observed: “As predicted, academic self-efficacy was significantly and directly related to academic expectations and academic performance.” (Chemers et al., 2001, p. 61)   Sutton et al. (2011) reported Cronbach's alpha of .83 in their study of academic self-esteem and personal strengths. ASE was highly positively correlated with ACT scores (.24) and GPA (.39)....
Post a Comment
Read more