Descriptive Statistics & Data Displays (MUST BE DONE WITHIN 12 HOURS)

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Chapter 3     Viva La Différence:

Understanding Variability

What You Will Learn in Chapter 3  Understanding the value of variability as a

descriptive tool

 Computing the range

 Computing the standard deviation

 Computing the variance

 Understanding what the standard deviation and variance have in common and how they are different

Why Understanding Variability Is Important

 Variability reflects how scores differ from one another.

 Also called spread or dispersion

Measures of Variability

 Three measures of variability are commonly used to reflect the degree of variability, including range, standard deviation, and variance.

 Typically report the average and the variability together to describe a distribution

Computing the Range  Range is the most general estimate of

variability

 There are two types of range, although the most commonly used is the exclusive range.

Exclusive Range  General formula for range

 Also known as the exclusive range

 Range = h − l

 Where h is the highest score, and l is the lowest score

Inclusive Range  Inclusive Range = h − l + 1

 This type of range is less commonly seen.

 Where h is the highest score, and l is the lowest score

Computing Standard Deviation  Most frequently used measure of variability

 SD = s = represents the average amount of variability in a set of scores

Important Symbols  s = standard deviation

 Σ = sigma, which tells you to find the sum of what follows it

 X = each individual score

 = X-bar = mean of all of the scores in the sample

 n = sample size

Why n – 1?  Standard deviation is an estimate of the

POPULATION standard deviation.

 To make it an unbiased estimate, you must subtract 1 from n.

 This artificially inflates the SD (it makes it bigger) because it makes the denominator smaller.

Things to Remember . . .  Standard deviation is computed as the average

distance from the mean.

 The larger the standard deviation, the more spread out the values are.

 Like the mean, the standard deviation is sensitive to extreme scores.

 If s = 0, then there is no variability among scores, and the scores are essentially identical in value.

Computing Variance  Variance = standard deviation squared

 If you take the standard deviation and never complete the last step (taking the square root), you have the variation.

Standard Deviation or Variance

 While the formulas are quite similar, the two are also quite different.

 Standard deviation is stated in original units.

 Variance is stated in units that are squared.

Using the Computer to Compute

Understanding and Interpreting

Real-World Stats  Stapelberg and colleagues looked at variability

in heart rate as it related to coronary heart disease.

 They found decreased heart rate variability in both depressive disorders and coronary heart disease.

 Researchers think that both diseases disrupt control feedback loops that help the heart function efficiently.

Chapter 3     �Viva La Différence: Understanding Variability
What You Will Learn in Chapter 3
Why Understanding Variability Is Important
Measures of Variability
Computing the Range
Exclusive Range
Inclusive Range
Computing Standard Deviation
Important Symbols
Why n – 1?
Things to Remember . . .
Computing Variance
Standard Deviation or Variance
Using the Computer to Compute
Understanding and Interpreting
Real-World Stats