Descriptive statistics

Descriptive statistics allow us to describe a set of scores or multiple sets of scores. There are typically four categories of descriptive statistics; central tendency, dispersion, distribution, and relation.

1. Central Tendency: There are three general measures of central tendency.

(1). Mean. The mean is the most frequently used to describe the center of a distribution of scores.

(2). Median. The median is the point that delineates two halves of a series of scores.

 (3). Mode. The mode is the most frequently occurring score in a series.

2.  Dispersion: There are five general measures of dispersion.

 (1). Variance. Variance is the sum of the squared deviations from the mean divided by the degrees of freedom. In lay terms, variance is the average deviation of the scores around the mean.

 (2). Standard Deviation. Standard deviation is the square-root of the variance. It is a standardized measure of dispersion (most frequently used) which allows us to compare distributions of different variables. Notice that sums of squares is crucial to both.

 (3). Z-scores (also called Standard Scores). Z-scores represent a transformation applied to each score which allows us to compare scores from different distributions.

 (4). Range. The range is simply the highest score minus the lowest score and gives an idea of the spread of scores or distance.

 (5). Minimum & Maximum. Simply the minimum and maximum scores. All measures of dispersion provide an idea of distance or spread.

3.  Distribution: There are two measures of distribution, both offer a description of the shape of a distribution of scores.

(1) Skewness refers to the amount of non-symmetry a distribution of scores contains. Negative skew is when the tail points to the smaller values and most scores are located at the higher values. Positive skew is when the tail points to the larger values and most scores are located at the smaller values. Zero skew indicates symmetry.

(2) Kurtosis is used to measure the amount of tail magnitude, commonly referred to as peakedness orflatness of a distribution. Kurtosis is also referred to as a measure of normality. It is based on the size of a distribution's tails. A distribution with a large, positive kurtosis has thin tails and the distribution looks peaked. This is known as leptokurtic. A distribution with a large, negative kurtosis has large tails or thick tails and the distribution looks flat. This is known as platykurtic (like a plateau).

4. Relation: There are two measures of relation; both refer to the amount of shared variance two variables have.  Measures of relation are unique in that they are descriptive, but can also be used inferentially when assessing magnitude. 

(1)Covariance is an unstandardized measure of relation. 

(2)Correlation is a standardized measure of relation; meaning it can be used to compare the relationships between multiple variables.