ASES A Statistics Refresher

Continuous scales

theoretically possible to divide any of the values of the scale. Typically having a wide range of possible values (e.g. height or a depression scale).

Discrete scales

categorical values (e.g. male or female)

Error

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

Nominal Scales

involve classification or categorization based on one or more distinguishing characteristics; all things measured must be placed into mutually exclusive and exhaustive categories (e.g. apples and oranges, DSM-IV diagnoses, etc.).

Ordinal Scales

Involve classifications, like nominal scales but also allow rank ordering (e.g. Olympic medalists).

Interval Scales

contain equal intervals between numbers. Each unit on the scale is exactly equal to any other unit on the scale (e.g. IQ scores and most other psychological measures).

Ratio Scales

Interval scales with a true zero point (e.g. height or reaction time).

Psychological Measurement

Most ________ are truly ordinal but are treated as interval measures for statistical purposes.

Distributions

a set of test scores arrayed for recording or study.

Raw Score

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

Frequency Distribution

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

histogram

a graph with vertical lines drawn at the true limits of each test score (or class interval), forming a series of contiguous rectangles

Bar graph

numbers indicative of frequency appear on the Y -axis, and reference to some categorization (e.g., yes/ no/ maybe, male/female) appears on the X -axis.

frequency polygon

test scores or class intervals (as indicated on the X -axis) meet frequencies (as indicated on the Y -axis).

Central tendency

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

Mean

Sum of the observations (or test scores), in this case divided by the number of observations.

Median

The middle score in a distribution. Particularly useful when there are outliers, or extreme scores in a distribution.

Mode

The most frequently occurring score in a distribution. When two scores occur with the highest frequency a distribution is said to be bimodal.

Variability

an indication of the degree to which scores are scattered or dispersed in a distribution.

Range

difference between the highest and the lowest scores.

Interquartile range

difference between the third and first quartiles of a distribution.

Semi-interquartile range

the interquartile range divided by 2

Average deviation

the average deviation of scores in a distribution from the mean.

Variance

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

Standard deviation

the square root of the average squared deviations about the mean. It is the square root of the variance. Typical distance of scores from the mean.

Skewness

the nature and extent to which symmetry is absent in a distribution.

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

the steepness of a distribution in its center.

Platykurtic

relatively flat.

Leptokurtic

relatively peaked.

Mesokurtic

somewhere in the middle.

normal curve

a bell-shaped, smooth, mathematically defined curve that is highest at its center. Perfectly symmetrical.

standard score

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.

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 scores

can be called a fifty plus or minus ten scale; that is, a scale with a mean set at 50 and a standard deviation set at 10

Stanine

a standard score with a mean of 5 and a standard deviation of approximately 2. Divided into nine units.

Normalizing a distribution

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

coefficient of correlation

a number that provides us with an index of the strength of the relationship between two things.

Positive correlations

indicate that as one variable increases or decreases, the other variable follows suit.

Negative correlations

indicate that as one variable increases the other decreases.

Pearson r

A method of computing correlation when both variables are linearly related and continuous.

Spearman Rho

A method for computing correlation, used primarily when sample sizes are small or the variables are ordinal in nature.

Scatterplot

Involves simply plotting one variable on the X (horizontal) axis and the other on the Y (vertical) axis

Meta-analysis

allows researchers to look at the relationship between variables across many separate studies.

a family of techniques to statistically combine information across studies to produce single estimates of the data under study.