PSYC*1010 Chapter 4: Variability

Question 1

What is variability?

Answer 1

The distribution of scores in a set

Question 2

What does variability measure?

Answer 2

How well an individual score (or group of score) represents the entire distribution

Question 3

Which type of statistical measurement is variability crucial for?

Answer 3

Inferential statistics

Question 4

What does low variability mean in terms of inferential statistics?

Answer 4

Low variability means that existing patterns can be seen clearly

Question 5

What does high variability mean in terms of inferential statistics?

Answer 5

High variability tends to obscure patterns that might exist

Question 6

What are three common measures of variability?

Answer 6

• Range
• Variance
• Standard deviation

Question 7

What is range?

Answer 7

The distance covered by the scores in a distribution

Question 8

Why does range not give an accurate description of variability for an entire distribution?

Answer 8

Because all scores are not being considered

Question 9

Range is considered a _______ and ___________ measure of variability.

Answer 9

Crude, Unreliable

Question 10

How is the range of discrete variables calculated?

Answer 10

Range = largest score - smallest score

Question 11

How is the range of continuous variables calculated?

Answer 11

Range = upper real limit of the largest score - lower real limit of the smallest

Question 12

How can the range of whole numbers be defined and calculated?

Answer 12

• 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

Question 13

What is a deviation score?

Answer 13

The difference between a score in a set and the mean of all scores in that set

Question 14

What is the notation for sum of squares?

Answer 14

SS

Question 15

How is the sum of squares calculated for a population or sample

Answer 15

• Calculate mean of set
• Find deviation for each score
• Square the deviation of each score
• Calculate the sum of all squared deviations

Question 16

What is the difference between the sum of squares for a population and the sum of squares for a sample?

Answer 16

• 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

Question 17

What is variance?

Answer 17

The average squared distance from the mean

Question 18

Which measure of variance is not an intuitive nor easy to understand descriptive measure?

Answer 18

Variance

Question 19

What is the notation σ^2 used to represent?

Answer 19

Population variance

Question 20

What is the notation s^2 used to represent?

Answer 20

Sample variance

Question 21

How is population variance calculated?

Answer 21

Population variance is obtained by dividing the sum of squares by the population number (N)

Question 22

How is sample variance calculated?

Answer 22

Sample variance is obtained by dividing the sum of squares by (n-1)

Question 23

Why is there an adjustment made to the divisor when calculating sample variance?

Answer 23

To make the sample variance a more accurate and unbiased estimation of population variance

Question 24

What is sample variance often classified as and why?

Answer 24

Sample variance is often classified as error variance to indicate that it represents unexplained and uncontrolled differences between scores

Question 25

Does it become easier or more difficult to see systematic differences or patterns that may exist as error variance increases?

Answer 25

As error variance increases, it becomes more difficult to see any systematic differences or patterns that may exist

Question 26

What is standard deviation?

Answer 26

A measure of the standard/ average distance from the mean data are

Question 27

What does standard deviation describe about the distribution of scores?

Answer 27

Whether scores are clustered around the mean or scattered

Question 28

Roughly what percentage of scores in a distribution are within one standard deviation of the mean?

Answer 28

70%

Question 29

Roughly what percentage of scores in a distribution are within two standard deviations of the mean?

Answer 29

90%

Question 30

What is the notation σ used to represent?

Answer 30

Population standard deviation

Question 31

How is population standard deviation calculated?

Answer 31

Population standard deviation is obtained by taking the square root of the population variance

Question 32

What is the notation s used to represent?

Answer 32

Sample standard deviation

Question 33

How is sample standard deviation calculated?

Answer 33

Sample standard deviation is obtained by taking the square root of the sample variance

Question 34

How will the standard deviation change if a constant is added or subtracted to each score?

Answer 34

The standard deviation will not change

Question 35

How will the standard deviation change if each score is multiplied by a constant?

Answer 35

The standard deviation will be multiplied by the same constant

Question 36

What is the basic assumption of inferential statistics?

Answer 36

That the sample is representative of the population

Question 37

How does the variability of a sample compare to the variability of a population?

Answer 37

The sample tends to be less variable than their population

Question 38

T or F: The discrepancy between the variability of a sample and their population causes bias in the direction of overestimating the population value.

Answer 38

- False - Less variability in samples causes bias in the direction of underestimating the population value

Question 39

Why can bias in sample variability be corrected?

Answer 39

Because the bias tends to be consistent and predictable

Question 40

What are degrees of freedom?

Answer 40

The number of values that are free to vary

Question 41

When are degrees of freedom used?

Answer 41

When calculating sample mean, sample variance, and sample standard deviation

Question 42

How are degrees of freedom calculated?

Answer 42

df = n-1

Question 43

When is a sample statistic biased?

Answer 43

If the average value of the statistic either overestimates or underestimates the corresponding population parameter

Question 44

When is a sample statistic unbiased?

Answer 44

If the average value of the statistic is equal to the population parameter

Question 45

How is the position of the mean identified in a frequency distribution graph?

Answer 45

In a frequency distribution graph, the position of the mean is identified by drawing a vertical line labelled with μ or M

Question 46

How is standard deviation represented in a frequency distribution graph?

Answer 46

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