PSYC 241 Lecture Notes - Lecture 4: Variance, Squared Deviations From The Mean, Statistical Inference

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7 Feb 2017
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Lesson 4: Variability
Variability
A measure of how spread out the scores are in distribution
Accompanies central tendency as basic descriptive statistic
Central Tendency and Variability
Central tendency = central point of distribution
Variability = how scores are scattered around central point
Central tendency and variability are the two primary values used to describe a
distribution of scores
Variability
Variability
A descriptive measure
An important component of most inferential statistics
As a descriptive statistic
Measures degree of which scores are spread out or clustered together
For inferential statistics,
Provides a measure of how accurately any individual score or sample represents
entire population
When population variability is small, all of scores are clustered close together
Any individual score or sample will provide a good representation of the entire
set
When variability is large and scores are widely spread, one or two extreme scores can
give distorted picture of general population
The Range
Total distance covered by distribution
From highest score to lowest score
Upper and lower real limits
The Standard Deviation
Standard distance between a score and the mean
Preferable to range, because range is based on most extreme scores
The calculation of standard deviation can be summarized as a four-step process:
1. Compute the deviation (distance from the mean) for each score
Column of deviation scores
Deviation (distance) from the mean for each raw score
Tell us:
Distance from mean for a particular score
Whether score is above or below the mean
2. Square each deviation
Sum of squares Conceptual Formula
SS =∑X - μ2
Sum of squares is the summed total of the squared deviation scores
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