changingminds.org

How we change what others think, feel, believe and do

| Menu | Quick | Books | Share | Search | Settings |

Sum of the Squares, SS

 

Explanations > Social ResearchStatistical principles > Sum of the Squares, SS

Description | Example | Discussion | See also

 

Description

In measuring how spread out a set of measures are, the sum of the squares, often indicated as SS, gives a measure that is simple to calculate and use.

It is calculated as the square of the sum of differences between each measure and the average.

SS = SUM(Xi - AVERAGE(X))

The average of a set of x's may be written as x-bar (or x with a horizontal line above it).

Example

In a set of measure, SS is calculated as below. Column B, below is the gap between x in Column A and the average of Column A. This is squared in Column C to get rid of the minus signs (otherwise summing these would be close to zero).

 

Column A Column B Column C
     
x x - x-bar (x-x-bar)^2
5 0.25 0.0625
6 1.25 1.5625
2 -2.75 7.5625
8 3.25 10.5625
3 -1.75 3.0625
5 0.25 0.0625
2 -2.75 7.5625
7 2.25 5.0625
     
number of measures, n: 8
sum of measures: 38
average, x-bar: 4.75
     
Sum of squares, SS: 35.5

 

Discussion

Subtracting each number from the average (or mean) gives an indicate of individual spread. Adding these up, however, could well result in something close to zero. If the differences are squared, this gets rid of the minus signs, allowing the sum to add up to something sensible.

Whilst SS may be adequate for comparing the spread of two similar lists of numbers, it increases with the size of a list, and hence makes comparison of unequal length lists invalid.

See also

Variance, Variation

Site Menu

| Home | Top | Quick Links | Settings |

Main sections: | Disciplines | Techniques | Principles | Explanations | Theories |

Other sections: | Blog! | Quotes | Guest articles | Analysis | Books | Help |

More pages: | Contact | Caveat | About | Students | Webmasters | Awards | Guestbook | Feedback | Sitemap | Changes |

Settings: | Computer layout | Mobile layout | Small font | Medium font | Large font | Translate |

 

 

Please help and share:

 

Quick links

Disciplines

* Argument
* Brand management
* Change Management
* Coaching
* Communication
* Counseling
* Game Design
* Human Resources
* Job-finding
* Leadership
* Marketing
* Politics
* Propaganda
* Rhetoric
* Negotiation
* Psychoanalysis
* Sales
* Sociology
* Storytelling
* Teaching
* Warfare
* Workplace design

Techniques

* Assertiveness
* Body language
* Change techniques
* Closing techniques
* Conversation
* Confidence tricks
* Conversion
* Creative techniques
* General techniques
* Happiness
* Hypnotism
* Interrogation
* Language
* Listening
* Negotiation tactics
* Objection handling
* Propaganda
* Problem-solving
* Public speaking
* Questioning
* Using repetition
* Resisting persuasion
* Self-development
* Sequential requests
* Storytelling
* Stress Management
* Tipping
* Using humor
* Willpower

Principles

+ Principles

Explanations

* Behaviors
* Beliefs
* Brain stuff
* Conditioning
* Coping Mechanisms
* Critical Theory
* Culture
* Decisions
* Emotions
* Evolution
* Gender
* Games
* Groups
* Habit
* Identity
* Learning
* Meaning
* Memory
* Motivation
* Models
* Needs
* Personality
* Power
* Preferences
* Research
* Relationships
* SIFT Model
* Social Research
* Stress
* Trust
* Values

Theories

* Alphabetic list
* Theory types

And

About
Guest Articles
Blog!
Books
Changes
Contact
Guestbook
Quotes
Students
Webmasters

 

| Home | Top | Menu | Quick Links |

© Changing Works 2002-2016
Massive Content — Maximum Speed