## Thursday, January 20, 2022

### 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

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### Factor Analysis Principal Components Analysis

Factor analysis (FA) is a statistical method of reducing a large set of data to a smaller set by identifying patterns in the data that have common characteristics. Factor analysis is sometimes called data reduction or dimension reduction.

The original numerical values in the data set are observed variables (also called manifest variables) such as the items in a large survey or test. Factor analysis may find patterns characterized by a shared statistical relationship representing a factor, which is also called a dimension. A researcher examines the content of the items linked to this factor and chooses a factor label such as verbal skills for related items on an intelligence test.

The factors may be treated as variables in additional research. These are secondary variables. Because they are created from the observed variables, they are considered latent variables. For example, if 5 items on a personality test are associated with one factor labeled "agreeableness" then agreeableness is a latent variable.

The set of identified factors is referred to as the structure of the data set. If the data are from a test then researchers refer to the structure of the test.

Factors are identified based on the variance they account for in the data. The amount of variance explained by a factor is represented by an eigenvalue. Researchers look for eigenvalues of 1.0 or more to consider a factor to be a valuable contribution to explaining the underlying structure of a data set.

Not all factors are equal. That is, when more than one factor have been identified, they will contribute differently to explaining the variance in the data set.

Different kinds of Factor Analysis

Exploratory Factor Analysis (EFA). When researchers do not know the structure of a data set, they use EFA to discover the set of factors.

Confirmatory Factor Analysis (CFA).  When researchers wish to test a hypothesis about a data set, they perform CFA. For example, if they believe their forgiveness questionnaire contains one factor called forgiveness, they can examine the structure to see if one factor best accounts for the data set. If one factor is the best solution then they have found support for their hypothesis.

Principal Components Analysis (PCA) is a common form of confirmatory factor analysis.

Factor Analysis is important to understanding tests in Counseling and Psychotherapy. See

Applied Statistics Concepts for Counselors on   AMAZON or   GOOGLE

Factor Analysis is often used to reduce the data collected from survey research.

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

You can read many published articles at no charge:

Academia   Geoff W Sutton     ResearchGate   Geoffrey W Sutton

## Monday, January 17, 2022

### Perceived Conflict between Evolution and Religion Scale (PCoRE)

Scale name: Perceived Conflict between Evolution and Religion (PCoRE)

Scale overview:

Authors: M. Elizabeth Barnes, K. Supriya, Yi Zheng, Julie A. Roberts, and Sara E. Brownell

Response Type: Participants rate each item on a 5-point Likert-type scale from strongly disagree to strongly agree.

Subscales with a sample item: There are four subscales as follows:

1. Perceived conflict between evolution and belief in God

My belief in God makes it harder to believe that all of life on Earth evolved from ancient microscopic life.

2. Perceived conflict between evolution and religious teachings

The teachings of my religion contradict that all of life on Earth evolved from ancient microscopic life.

3. Perceived conflict with evolution among religious community

My religious community does not believe that all of life on Earth evolved from ancient microscopic life.

4. Perceived conflict between evolution and religious beliefs

My personal religious beliefs make it harder to believe that humans evolved from ancient ape ancestors.

Reliability: The article includes reliability calculations.

Validity: The article contains information about process, content, concurrent, and construct validity.

Availability: The full scale is available is available in a pdf supplement https://www.lifescied.org/doi/suppl/10.1187/cbe.21-02-0024

Permissions – See this link for general permissions. https://www.lifescied.org/permissions

Author contact:  liz.barnes@mtsu.edu

Article Reference

Barnes, M. E., Supriya, K., Zheng, Y., Roberts, J.A., & Brownell, S.E. (2021). A New Measure of Students’ Perceived Conflict between Evolution and Religion (PCoRE) Is a Stronger Predictor of Evolution Acceptance than Understanding or Religiosity. CBE—Life Sciences Education, 20, 3. https://doi.org/10.1187/cbe.21-02-0024

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 Test Index

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## Friday, January 14, 2022

### z-scores or standard scores

A z-score tells you the distance of the score from the arithmetic mean of a set of scores that are normally distributed.

The z-score represents standard deviation units thus, a z-score of 1 means it is one standard deviation above the mean of the set of scores. A z-score of minus one (-1) means the score is one standard deviation below the mean of the set of scores.

The z-scores are often plotted along the x-axis of  a normal distribution, which is sometimes called the bell curve.

Use lower case italics when reporting z-scores in APA style. The upper case Z is a different score.

You can calculate a z-score by subtracting a raw score from the mean and dividing by the standard deviation of the set of scores.

Example: A raw score on a test = 60. If the mean = 50 and the standard deviation = 10 then (60-50) = 10 and 10 divided by 10 = 1.0. The z score is 1.0, it is one standard deviation above the mean.

Most z- scores fall between -3.0 and +3.0 but it is possible to have scores beyond - 3or + 3.

Related posts

Mean

Normal curve or distribution

Resources

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### Parent-Child Relationship Scale CPRS Review

Scale name: Parent-Child Relationship Scale CPRS Scale overview: The Parent-Child Relationship Scale (CPRS) is a 15-item parent self-re... 