Psychological Testing and Assessment Chapter 3

measurement

the act of assigning numbers or symbols to characteristics of things according to rules

scale

set of numbers/symbols whose properties model empirical properties of the objects to which the numbers are assigned

continuous scale

scale measuring a continuous variable, wide range of values, always involves error (height, weight)

discrete scale

scale measuring a discrete variable, categorical (male/female, yes/no)

error

the collective influence of all factors on a test score or measurement beyond those specifically measured by the test or measurement

nominal scales

simplest form, classification or categorization based on one or more distinguishing characteristics, where each thing must be placed into mutually exclusive and exhaustive categories (DSM diagnoses, apples, oranges)

ordinal scales

like nominal scales, but in addition to classification there is also rank ordering on some characteristic (class rank, olympic medalists)

interval scales

in addition to previous qualities, equal intervals between numbers, exactly equal units (IQ scores, most other psychological measures)

ratio scales

in addition to previous qualities, it has a true zero point (height, reaction time)

distribution

a set of test scores arrayed for recording or study

raw score

straightforward, unmodified accounting of performance that is usually numerical

frequency distribution (simple)

all scores are listed alongside the number of times each score occurred

grouped frequency distribution

test-score intervals, class intervals, replace the actual test scores

graph

diagram or chart composed of lines, points, bars, or other symbols that describe and illustrate data

histogram

graph with vertical lines drawn at the true limits of each test score, forming a series of contiguous rectangles

measures of central tendency

statistic that indicates the average or midmost score between the extreme scores in a distribution

arithmetic mean

the sum of the observations divided by the number of observations, most appropriate measure for interval or ratio data when distributions are approx. normal

median

middle score in a distribution, or in the middle of the middle two scores in a distribution

mode

most frequently occurring score in a distribution

bimodal distribution

two scores that occur with the highest frequency, at two ends

variability

indication of how scores in a distribution are scattered or dispersed

measures of variability

statistics that describe the amount of variation in a distribution

range

difference between the highest and lowest scores, outliers can mess with it

quartiles

dividing points between the four quarters in the distributions (Q1, 25, Q2, 50. Q3, 75)

interquartile range

difference between Q3 and Q1

semi-interquartile range

interquartile range divided by 2

average deviation

like standard deviation but not squared

standard deviation

squaring the deviation from the mean

skewness

nature and extent to which symmetry is absent

positive skew

relatively few of the scores fall at the high end of the distribution

negative skew

relatively few of the scores fall at the low end of the distribution

kurtosis

refers to the steepness of a distribution

platykutic/leptokurtic/mesokurtic

relatively flat/relatively peaked/somewhere in the middle

normal curve

bell-shaped, smooth, mathematically defined curve that is highest at its center, approaches x-axis asymptotically

standard score

raw score that has been converted from one scale to another scale, latter scale has some arbitrarily set mean and standard deviation

z score

conversion of a raw score into a number indicating how many standard deviation units the raw score is below or above the mean of the distribution

T score

fifty plus or minus ten scale

stanine

standard score with mean of 5 and standard deviation of 2, divided into 9 units

nonlinear transformation

used when data under consideration are not normally distributed yet comparisons with normal distributions need to be made

normalizing a distribution

sketching the skews curve into the shape of a normal curve

normalized standard score scale

corresponding scale of standard scores from normalizing a distribution