Measurement: the process of assigning numerals or numbers to observations
We enhance our ability to measure attributes by defining the basic size of the unit of measurement for a test -- the use of real numbers
Real numbers are also continuous because they represent any quantity along a number line
Properties of Measurement in Relation to Numbers
The score from a psychological test is based on the properties of numbers and how we treat 0
The level of measurement of a particular score can be determined by the presence or absence of 4 properties
Nominal
number of classes (classification), mode
Qualitative: sex or hair color, distinguishing labels or categories
Ordinal
median, percentiles, order statistics
Quantitative: class rank, hardness of minerals, order finish in a competitive running race
Interval
equality of intervals of scores along the score continuum
Quantitative: temperature (Celsius), standardized test scores
Ratio
equality of ratio
Quantitative: temperature (Kelvin)
Scaling
the mathematical techniques used for determining what numbers should be used to represent different amounts of a property or attribute being measured
Statistical Foundations for Psychometrics
Descriptive Statistical Techniques
used to organize and describe data
order and group scores into distributions and describe the scores
calculate a single number that summarizes a set of scores
represent scores graphically
applied to samples and populations
Inferential Statistical Techniques
used to help make educated guesses about populations based on the samples
Variables, Frequency Distributions, and Scores
measurements acquired on a variable/s are part of the data collection process -- refers to a property whereby members of a group differ from one another (i.e., measurements change from one person to another)
Constant
refers to property whereby members of a group do not differ from one another (e.g., all persons in a study or taking an examination are female; thus, biological sex is constant)
variables can be qualitative or quantitative; quantitative variables can be discrete or continuous
Discrete
values can only be whole numbers
Continuous
can assume any value
Frequency Distribution
a tabulation of the number of occurrences of each score value
Shape, Central Tendency, and Variability of Score Distributions
The shape of a distribution is defined as symmetric, positively skewed, and negatively skewed; can also be unimodal or bimodal
Central Tendency
the score value at the center (position at the center of the x-axis) that marks the center of the distribution of scores -- mean, median, and mode
Since a measure of central tendency is a single number, it is a concise way to provide an initial view of the set of scores.
Measures of central tendency can quickly and easily be compared.
Many inferential statistical techniques use a measure of central tendency to test hypotheses of various types.
Measures of variability for a set of scores or measurements provide a value of how spread or dispersed the individual scores are in a distribution -- variance and standard deviation
Variance
the degree to which measurements or scores differ from the mean of the population or sample
Standard Deviation
the square root of the variance
Percentiles
used to provide an index of the relative standing for a person with a particular score relative to the other scores (persons) in a distribution
Z-Score
A way to rescale or standardize the value of 0 so that it means the same thing in every distribution. We can then directly compare scores from different tests with different distributions.
T-Score
a mean of 50 and a standard deviation of 10
Stanine Cycle
All raw scores are converted to a single-digit system of scores ranging from 1 to 9. The mean of stanine scores is always 5 and the standard deviation is 2.