Basic Statistics
Psychology of Testing and Measurements
Chapter 2, Lecture

Scales of Measurement
Levels of Measurement = the mathematical precision with which the values of a variable can be expressed; 4 levels with progressively more precision.
    Nominal
    Ordinal
    Interval
    Ratio

Purposes of Statistics
Once variables are quantified using various scales of measurements, statistics can be used for the following purposes:

Descriptive

Inferential

Types of Descriptive Statistics
Frequency distribution – a display of scores on a measurement according to how frequently each score was obtained.

Percentile ranks – a rank of an individual percentage in relation to all others (# cases below individual score / # total cases X 100); % of cases below the percentile

Measures of Central Tendency
What is central tendency? Central tendency is the degree to which scores are similar

Mean

Median

Mode

Measures of Variation
What is variation? Variation is the degree to which scores differ.
    Range: The lowest score subtracted from the largest score
    Standard Deviation: the average deviation around the mean. (s squared = variance)

Normal Distribution
The normal curve is a hypothetical probability distribution that is frequently used in social science research.
The normal distribution is a “good” model of many natural phenomenon.
As sample size increases, the distribution of sample means approximates normal curve.

Characteristics of the Normal Curve
Symmetric-each side is an exact representation of the other
Total area under curve = 100%
Mean = 0

Standard Scores
In behavioral research many different scales of measurements are used to measure the outcome of a study.

In order to interpret a person’s score it is often helpful to convert raw scores into a standard score that show’s this person’s relative status in a distribution of scores.

We need to determine the distance of a score from its mean and then convert that distance into a number of standard deviations that the score falls above or below the mean. This is known as a Z score

Norms
Norms – performances by defined groups on particular tests (degree of tremors experienced by alcohol abusers after abstaining 2 weeks)
Age-related norms – scoring norms for particular age groups (8 year old cognitive ability)
Tracking – tendency to stay at about the same level relative to one’s peers; measured over time (height, weight, growth)
Criterion-referenced tests – describes performance on specific criteria; used to diagnose problems or strengths. (norm-referenced – compares with an average or norm.