Skip to main content

variance and standard deviation

Variance is a measure of the dispersion of values in a distribution of values.

 In psychology and behavioral science statistics, the variance is typically a reference to the extent to which numerical values vary around the arithmetic mean of a data set. Theoretically, the values vary around a population mean but in most cases, researchers work with samples.

In statistics, write sigma squared for the population variance σ2

Write final form sigma squared for the sample variance ς2

In reports, write VAR for variance.

How it works

If we have a set of different numerical values such as scores on a test we can calculate a mean, which is the average of all the scores divided by the number of scores.

The difference of one score from the mean is a deviation score. X is a score and the Greek letter mu μ is the symbol for the population mean.

In a sample, which is what we normally have in psychology, we subtract a score X from the sample mean M. Thus, X - M = the deviation score. 

If a person earns a 7 on a test where the mean is 10 then their score is 3 points below the mean. The deviation score is -3 (minus three).

To find an average deviation for all the scores on the test, we must subtract each score from the mean. We end up with a set of positive and negative values.

We want to find an average but if we add the positive and negative values we will end up with zero. To solve the problem, 

square each deviation score

add them together to get the sum of the squares (SS)

 then divide by the number of scores (n) to get the variance.

The variance = the SS divided by n

Standard Deviation (SD)

The standard deviation is the average unit by which scores are distant from the mean.

Find the standard deviation by taking the square route of the variance.

In reports, write SD for standard deviation.

Examples in tests

A common mean for IQ tests is 100 and a common standard deviation is 15 points.

In personality tests, a common standard score is a T-score. The mean is T = 50 and SD = 10.

Key concepts in this post

deviation score

mean

sum of squares

standard deviation

variance

Buy Applied Statistics for Counselors

 

GOOGLE BOOKS

 

AMAZON

 








Buy Creating Surveys on

GOOGLE BOOKS

 

AMAZON















Related post






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 


Comments

Popular posts from this blog

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

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)  👉 [ 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

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). An Arabic version of t