PSYC*1010 Chapter 4: Variability Flashcards
What is variability?
The distribution of scores in a set
What does variability measure?
How well an individual score (or group of score) represents the entire distribution
Which type of statistical measurement is variability crucial for?
Inferential statistics
What does low variability mean in terms of inferential statistics?
Low variability means that existing patterns can be seen clearly
What does high variability mean in terms of inferential statistics?
High variability tends to obscure patterns that might exist
What are three common measures of variability?
- Range
- Variance
- Standard deviation
What is range?
The distance covered by the scores in a distribution
Why does range not give an accurate description of variability for an entire distribution?
Because all scores are not being considered
Range is considered a _______ and ___________ measure of variability.
Crude, Unreliable
How is the range of discrete variables calculated?
Range = largest score - smallest score
How is the range of continuous variables calculated?
Range = upper real limit of the largest score - lower real limit of the smallest
How can the range of whole numbers be defined and calculated?
- When scores are whole numbers, the range can also be defined as the number of measurement categories
- Range of whole numbers = largest score - smallest score + 1
What is a deviation score?
The difference between a score in a set and the mean of all scores in that set
What is the notation for sum of squares?
SS
How is the sum of squares calculated for a population or sample
- Calculate mean of set
- Find deviation for each score
- Square the deviation of each score
- Calculate the sum of all squared deviations
What is the difference between the sum of squares for a population and the sum of squares for a sample?
- The only difference is in the notation
- The formula for a sample used M to represent mean
- The notation for a population used μ to represent mean
What is variance?
The average squared distance from the mean
Which measure of variance is not an intuitive nor easy to understand descriptive measure?
Variance
What is the notation σ^2 used to represent?
Population variance
What is the notation s^2 used to represent?
Sample variance
How is population variance calculated?
Population variance is obtained by dividing the sum of squares by the population number (N)
How is sample variance calculated?
Sample variance is obtained by dividing the sum of squares by (n-1)
Why is there an adjustment made to the divisor when calculating sample variance?
To make the sample variance a more accurate and unbiased estimation of population variance
What is sample variance often classified as and why?
Sample variance is often classified as error variance to indicate that it represents unexplained and uncontrolled differences between scores
Does it become easier or more difficult to see systematic differences or patterns that may exist as error variance increases?
As error variance increases, it becomes more difficult to see any systematic differences or patterns that may exist
What is standard deviation?
A measure of the standard/ average distance from the mean data are
What does standard deviation describe about the distribution of scores?
Whether scores are clustered around the mean or scattered
Roughly what percentage of scores in a distribution are within one standard deviation of the mean?
70%
Roughly what percentage of scores in a distribution are within two standard deviations of the mean?
90%
What is the notation σ used to represent?
Population standard deviation
How is population standard deviation calculated?
Population standard deviation is obtained by taking the square root of the population variance
What is the notation s used to represent?
Sample standard deviation
How is sample standard deviation calculated?
Sample standard deviation is obtained by taking the square root of the sample variance
How will the standard deviation change if a constant is added or subtracted to each score?
The standard deviation will not change
How will the standard deviation change if each score is multiplied by a constant?
The standard deviation will be multiplied by the same constant
What is the basic assumption of inferential statistics?
That the sample is representative of the population
How does the variability of a sample compare to the variability of a population?
The sample tends to be less variable than their population
T or F: The discrepancy between the variability of a sample and their population causes bias in the direction of overestimating the population value.
- False
- Less variability in samples causes bias in the direction of underestimating the population value
Why can bias in sample variability be corrected?
Because the bias tends to be consistent and predictable
What are degrees of freedom?
The number of values that are free to vary
When are degrees of freedom used?
When calculating sample mean, sample variance, and sample standard deviation
How are degrees of freedom calculated?
df = n-1
When is a sample statistic biased?
If the average value of the statistic either overestimates or underestimates the corresponding population parameter
When is a sample statistic unbiased?
If the average value of the statistic is equal to the population parameter
How is the position of the mean identified in a frequency distribution graph?
In a frequency distribution graph, the position of the mean is identified by drawing a vertical line labelled with μ or M
How is standard deviation represented in a frequency distribution graph?
In a frequency distribution graph, standard deviation is represented by a line or an arrow drawn from the mean outward for a distance equal to the SD and labelled with σ or s
