Variability Flashcards
It provides a quantitative measure of the differences between scores in a distribution and describes the degree to which the scores are spread out or clustered together.
Variability
3 Measures of Variability
- Variance
- Range
- Standard Deviation
The first step toward defining ad measuring variability which is the distance covered by the scores in a distribution.
Range
The distance from the mean.
Deviation
2 parts of Deviation score
- Sign
- Number
It tells the direction from the means–that is, whether the score is located above or below the mean.
Sign
It gives the actual distance from the mean.
Number
It equals of the squared deviations and it is the average distance from the mean.
Variance
It is the square root of the variance and provides a measure of the standard, or average distance from the mean.
Standard Deviation
It is the sum of the squared deviation scores.
Sum of Squares (SS)
2 formulas of SS
- Definitional Formula
- Computational Formula
The first of SS’ formula where the symbols literally define the process of adding up the squared deviations.
Definitional Formula
An alternative formula that has been developed for computing SS where it performs calculations with the scores and therefore minimizes the complications of decimals and fractions.
Computational Formula
It is represented by the symbol σ2 and equals the mean squared distance from the mean and is obtained by dividing the sum of squares by N.
Population Variance
It is represented by the symbol σ2 and equals the square root of the population variance.
Population Standard Deviation
It is represented by the symbol s2 and equals the mean squared distance from the mean and is obtained by dividing the sum of squares by n-1.
Sample Variance
It is represented by the symbol s and equal the square root of the sample variance.
Sample Standard Deviation
It is often called sample variance.
Estimated Population Variance
It is often called as sample standard deviation.
Estimated Population Standard Deviation
It determines the number of scores in the sample that are independent and free to vary.
Degrees of Freedom (df)
The classification of sample statistic if the average value of the statistic if equal to the population parameter.
Unbiased
A classification of sample statistic if the average value of the statistic either underestimates or overestimates the corresponding population parameter.
Biased
This term is used to indicate that the sample variance represents unexplained and uncontrolled differences between scores.
Error Variance
3 situations to use Range
- Sample sizes are similar
- Small data sets
- Skewed Distributions
Formula of Deviation score
X - M
Formula of Definitional Formula
SS= Σ(X - M)2
Formula of Computational Formula
SS= ΣX2 - (ΣX)2/N
Formula of Population Variance
o2 = SS/N
Formula of Population Standard Deviation
o = √SS/N
Formula of Sample Variance
s2 = SS/n - 1
Formula of Sample Standard Deviation
s = √s2