act of assigning numbers or symbols to characteristics of things (people, events, whatever) according to rules

set of numbers (or other symbols) whose properties model empirical properties of the objects to which the numbers are assigned.

has a sample space that can be counted.

the values can be any real number in the scale’s sample space.

best to round continuous scales

simplest form of measurement ● involve classification or categorization, where all things measured must be placed into mutually exclusive and exhaustive categories.

have categories with a clear and uncontroversial order ● measurements in which people are ranked (0-100)

emphasized that what he tried to do with his test to classify (and rank) people.

meaningful distances between numbers, each unit on the scale is exactly equal to any other unit on the scale. ● possible to add and subtract scores, which allows for calculating means and standard deviations

has a true zero point, which indicates the absence of the thing being measured

absence of a quantity

the values that a variable can take on.

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

most frequently used level of measurement in psychology

an instrument used to measure strength of hand grip

a set of test scores arrayed for recording or study.

a straightforward, unmodified accounting of performance that is usually numerical.

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

indicate that individual scores have been used and the data have not been grouped.

test-score intervals, also called class intervals, replace the actual test scores.

upper limits of the distribution

lower limits of the distribution

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

graph with vertical lines drawn at the true limits of each test score (or class interval), forming a series of contiguous rectangles. - X-axis (abscissa) - test scores to be placed (single scores or the midpoints of the class intervals) ● Y-axis (ordinate) - numbers indicative of the frequency of occurrence

x-axis

y-axis

A graphic illustration of data wherein numbers indicative of frequency are set on the vertical axis, categories are set on the horizontal axis, and the rectangle bars that describe the data are typically noncontiguous

expressed by a continuous line connecting the points where test scores or class intervals (X-axis) meet frequencies (Y-axis).

one graphic representation of data of particular interest to measurement professionals

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

most commonly used measure of central tendency

takes into account the actual numerical value of every score.

middle score in a distribution

- most frequently occurring score in a distribution of scores ● not a very commonly used measure of central tendency.

there are two scores that occur with the highest frequency (of two).

meaning of X

"the sum of"

an indication of how scores in a distribution are scattered or dispersed

statistics that describe the amount of variation in a distribution

“add all the test scores.”

sum

equal to the difference between the highest and the lowest scores.

the dividing points between the four quarters in the distribution are the, refers to a specific point

refers to an interval

quarter-points in a distribution of scores.

is a measure of variability equal to the difference between Q3 and Q1.

equal to the interquartile range divided by 2.

another tool that could be used to describe the amount of variability in a distribution

ameasureofvariabilityequalto the square root of the average squared deviations about the mean. ● equal to the square root of the variance

equal to the arithmetic mean of the squares of the differences between the scores in a distribution and their mean.

the nature and extent to which symmetry is absent. ● indication of how the measurements in a distribution are distributed.

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

negative skew

steepness of a distribution in its center

, characterized by a high peak and “fatter” tails compared to a normal distribution.

values indicate a distribution with a rounded peak and thinner tails.

relatively flat

relatively peaked

somewhere in the middle

being the first to refer to the curve as the normal curve

bell-shaped, smooth, mathematically defined curve that is highest at its center. ● the mean, the median, and the mode all have the same exact value.

meaning that it approaches, but never touches, the axis

area on the normal curve between 2 and 3 standard deviations above the mean.

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

other name for normal curve

results from the 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.

z-score

composed of a scale that ranges from 5 standard deviations below the mean to 5 standard deviations above the mean.

t score

a term that was a contraction of the words standard and nine. ● a standard score with a mean of 5 and a standard deviation of approximately 2, divided into nine units

standard score obtained that retains a direct numerical relationship to the original raw score.

may be required when the data under consideration are not normally distributed yet comparisons with normal distributions need to be made.

, normalizing a distribution involves “stretching” the skewed curve into the shape of a normal curve and creating a corresponding scale of standard scores

a number that provides us with an index of the strength of the relationship between two things. ● expresses a linear relationship between two (and only two) variables, usually continuous in nature.

expression of the degree and direction of correspondence between two things.

, two variables simultaneously increase or simultaneously decrease, then those two variables are said to be

, when one variable increases while the other variable decreases.

if a correlation is zero, then absolutely no relationship exists between the two variables

statistical tool of choice when the relationship between the variables is linear and when the two variables being correlated are continuous

a deviation about a mean of a distribution

individual deviations about the mean of a distribution

moments squared

the moments cubed, and so forth

value indicating how much variance is shared by two variables (X and Y) being calculated

frequently used when the sample size is small (fewer than 30 pairs of measurements) and especially when both sets of measurements are in ordinal (or rank-order) form.

simple graphing of the coordinate points for values of the X-variable (placed along the graph’s horizontal axis) and the Y-variable (placed along the graph’s vertical axis). ● they provide a quick indication of the direction and magnitude of the relationship, if any, between the two variables.

, an “eyeball gauge” of how curved a graph is

extremely atypical point located at a relatively long distance—an outlying distance—from the rest of the coordinate points in a scatterplot

family of techniques used to statistically combine information across studies to produce single estimates (effect size) of the data under study.

statistic used to express the strength of the relationship or the magnitude of the differences in data

, defined as professional practice that is based on clinical and research findings ● Methods, protocols, techniques, and procedures, used by professionals, that have a basis in clinical and research findings