Descriptive Statistics

descriptive statistics

a type of statistic that quantitatively describes or summarizes features from a collection of information

measures of central tendency

• mean: the arithmetic average; the most sensitive to outliers

• median: middle value when observations are ordered from least to greatest, or greatest to least

• mode: most frequent observation

measures of variability/dispersion

• range: highest score minus lowest score

• standard deviation: “average” scatter away from the mean (also square root of variance)

• variance: how much each score varies from the mean; the square of the standard deviation

percentile

the percentage of scores that fall at or below a particular score

z-score

the number of standard deviations your score is away from the mean

normal distribution

about 68% of scores fall within 1 SD of the mean; about 96% of scores fall within 2 SDs of mean

if you convert every score in a distribution to a z-score, then

the mean of the distribution of z-scores will be 0 and the SD will be 1.

T-scores

T-score distribution has a mean of 50 and SD of 10; often used in test score distribution

correlation coefficient

a measure of some type of linear correlation, ergo, the extent to which two variables are related; ranges from -1.00 to 1.00

factor analysis

a technique that attempts to account for interrelationships found among various variables by seeing how they “hang together”; a cluster of variables highly correlated with one another are assumed to be measuring the same factor