Chapter 4: How do Test Users Interpret Test Scores?

level of measurement

The relationship among the numbers we have assigned to the information - nominal, ordinal, equal interval, or ratio

nominal scale

The most basic level of measurement, in which numbers are assigned to groups or categories of information

categorical data

Data grouped according to a common property

ordinal scales

The second level of measurement, in which numbers are assigned to order or rank individuals or objects from greatest to least (or vice versa) on the attribute being measured

interval scales

Level of measurement in which numbers are assigned with the assumption that each number represents a point that is an equal distance from the points adjacent to it

ratio scales

The level of measurement in which numbers are assigned to points with the assumption that each point is an equal distance from the numbers adjacent to it and there is a point that represents an absolute absence of the property being measured, called zero

raw score

The basic score calculated when an individual completes a psychological test

norm group

A previously test group of individuals whose scores are used for comparison purposes

frequency distribution

An orderly arrangement of a group of numbers (or test scores) showing the number of times each score occurred in a distribution

class intervals

A way of grouping adjacent scores to display them in a table or graph

histogram

A bar graph used to represent frequency data in statistics

normal probability distribution

A theoretical distribution that exists in our imagination as a perfect and symmetrical distribution

normal curve

A symmetrical distribution of scores that, when graphed, is bell shaped

descriptive statistics

Numbers calculated from a distribution that describe or summarize the properties of the distribution of test scores, such as mean, median, mode, and standard deviation

measure of central tendency

A value that helps us understand the middle of a distribution or set of scores

mean

The arithmetic average of a group of test scores in a distribution

median

The middle score in a distribution

mode

The most frequently occurring score in a distribution

outliers

Scores that are exceptionally higher or lower than other scores in a distribution

measures of variability

Numbers that represent the spread of the scores in the distribution, such an range, variance, and standard deviation

range

A measure of variability calculated by subtracting the lowest number in a distribution from the highest number in the distribution

variance

A measure of variability that indicates whether individual scores in a distribution tend to be similar to or substantially different from the mean of the distribution

standard deviation

A measure of variability that represents the degree to which scores vary from the mean

measures of relationship

Statistics that describe the relationship between two sets of scores, such as the correlation coefficient

correlation coefficient

A statistic that provides an index of the strength and relationship between two sets of scores; a statistic that describes the relationship between two distributions of scores

Pearson product-moment correlation coefficient

Represented by r, a correlation coefficient that measures the linear association between two variables, or sets of test scores, that have been measured on interval or ratio scales

standard scores

A widely understood transformation of raw test scores in testing, such as z scores and T scores, that allow the test user to more easily evaluate a person's performance in comparison with other persons who took the same test or a similar test

linear transformations

A method for changing raw scores for interpretation purposes that does not change the characteristics of the raw data in any way, such as z scores and T scores

area transformations

A method for changing scores for interpretation purposes that changes the unit of measurement and the unit of reference, such as percentile ranks

percentage

A linear transformation of raw scores obtained by dividing the number of correctly answered items by the total number of items

standard deviation unit

A number that represents how many standard deviations an individual score is located away from the mean

z score

Standard scores, which have a mean of zero and a standard deviation of 1, that are used to compare test scores from two tests that have different characteristics

T scores

Standard scores, which have a mean of 50 and a standard deviation of 10, that are used to compare test scores from two tests that have different characteristics

stanines

Standard score scales with nine points that allow us to describe a distribution in words instead of numbers (from 1 = very poor to 9 = very superior)

norms

A group of scores that indicate the average performance of a group and the distribution of scores above and below this average

norm-based interpretation

The process of comparing an individual's score with the scores of another group of people who took the same test

age norms

Norms that allow test users to compare an individual's test score with scores of people in the same age group

grade norms

Norms that allow test users to compare a student's test score with scores of other students in the same grade

percentile rank

An area transformation that indicates the percentage of people who scored at or below a particular raw score