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.
(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.
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