Chapter 5

Question 1

variability

Answer 1

• amount of spread in a distribution of scores

- range, semi-interquartile range, standard deviation, variance

Question 2

range

Answer 2

• obtained by subtracting lowest score from highest score
• can be used with ordinal, interval, and ratio data
• limitations: only takes 2 scores into account; value greatly affected by sample size

Question 3

semi-interquartile range

Answer 3

• Q
• one half of the distance between the 1st and 3rd quartile points in a distribution
• quartile points: Q1 (P25), Q2 (P50), Q3 (P75)
• Q = Q3-Q1 divided by 2

Question 4

variance

Answer 4

• average squared deviation (aka: mean square)
• add up the squares of each deviation score (sum of squares) and divide by N
• can only be used with interval and ratio data
• squared deviations used because simple deviations add to 0
• because variance uses squared scores, it doesn’t describe the amount of variability in same units of measurement as original scale (just an interim step to calculate other stats)

Question 5

sum of squares

Answer 5

• SS
• sum of all squared deviation scores
• used to calculate variance

Question 6

standard deviation

Answer 6

• square root of variance
• more sensitive to outliers than semi-quartile range
• can only be used with interval and ratio data
• describes variability in same units of measurement as original scale

Question 7

sampling error

Answer 7

• the statistic - the parameter
• in other words, the sample - population
• SS based on sample mean will differ from SS based on population mean
• To adjust/correct for a mean that is too small, degrees of freedom (n-1) must be used

Question 8

expected values

Answer 8

• If a statistic is unbiased, its expected value is equal to the parameter it estimates.
• uncorrected stats are biased
• square root of unbiased stat is biased

Question 9

score transformations

Answer 9

• if we add or subtract a constant to each score in distrib, it does not affect variability
• ex. adding 10 to all scores
• however, if we multiply or divide by a constant, variability is also multiplied or divided by that same constant (EXCEPT for variance -> multiplied/divided by square of constant)

Question 10

standard scores

Answer 10

• comparing one’s score on 2 variables is difficult when variables have different means and SD’s
• standard scores have values for the mean and SD that are fixed, known, and never vary -> “allows us to compare apples and oranges”
• z-score scale is a standard score scale

Question 11

z-score

Answer 11

• most basic and useful standard score
• observations expressed in SD units from mean
• z-score distribution has mean of 0 and SD of 1
• z-scores can be transformed into any other standard scale that doesn’t involve negative numbers or decimals

Question 12

t-score

Answer 12

• standard score
• mean of 50, SD of 10
• usually rounded to the nearest whole number

Question 13

IQ score

Answer 13

• standard score

- mean of 100, SD of 15

Question 14

why not use percentile scales?

Answer 14

• percentile scale is ordinal -> unequal units

- distort magnitude of differences -> near mean = narrow, away from mean = wide

Question 15

normal distribution

Answer 15

34% -> 14% -> 2% on either side