 
Descriptive Statistics
 Descriptive statistics are used to summarize
data
 To obtain and define a measure, some type of
numerical value must be associated with the measure
 One method of classifying numbers in
measurement is by using numerical scales
Scales of Measure Hierarchy
 Nominal  classification scale with NO
order, magnitude, or size
 Ordinal  a scale that provides information
of the rank order of the scores, but no magnitude or differences can be
determined
 Interval  a scale that provides both order
and magnitude, but has no true zero point
 Ratio  a scale that possesses all of the
characteristics of the interval scale and has a true zero point
Measures of Central Tendency
 Measures of central tendency describe the
distribution of scores around a midpoint
 Most statistical methods for data analysis
assume that the distribution of scores is normal
 A normal distribution is graphically
represented by a normal (bell shaped) curve
 The three descriptive statistics used to
determine central tendency are the mean, median and mode
The Mean
 The Mean  the most commonly used measure of
central tendency, refers to the arithmetic average of a group of scores
 It is the most sensitive measure of central
tendency
 It is the most appropriate measure of
central tendency when using ratio data
 It considers all information about the the
data
 It is influenced by extreme scores,
especially in small sample
The Median
 The median is the score that represents the
exact middle in a distribution
 It is not affected by extreme scores, so it
is a more representative of the central tendency when extreme scores are
present
 It is a measure of position within the
distribution
 It is NOT used for additional statistical
calculations
The Mode
 The mode is the score within a distribution
that occurs most frequently
 It is the least used measure of central
tendency
 It is not used for additional statistical
calculations
 It is the most unstable measure of central
tendency
Distribution Shapes
 The graphical shape of a distribution can
tell a person about the distribution of scores and about the sample being
measured
 The distribution shape can be defined by
symmetry or by height and width
 The term for the symmetry of a distribution
is skewedness, while the height and width is described by kurtosis
Skewed Distributions
 A distribution can be positively skewed,
normal, or negatively skewed.
 Skewedness is described by the where scores
cluster within a distribution
Kurtosis
 Distributions can also be described by
height and width
 Leptokortic means that the data are very
similar (homogeneous),
 Platykurtic means the data are very
different (heterogeneous)
 Bimodal data cluster at both ends of the
distribution
Variability
 A curves kurtosis is the general
introduction into the discussion of variability
 The degree or spread of scores is defined as
the variability
 Three types of variability
 Range
 SemiInterquartile range
 Variance
Variance
 The variance is the squared deviation of
each score from the mean, or for lack of a better example, the standard
deviation squared (s^{2})
 The measured or observed variance is the sum
of the true variance and the error variance.
Standard Scores
 To put variance into perspective, we can
determine standard scores within a distribution
 Standard scores are scores that are
standardized around a mean.
 The two standard scores we will discuss are
the zscore and Tscore
The zScore
 The zscore for an individual gives us an
estimate of how many standard deviations an individual’s score fall from
the mean
 The zscore is simply the difference between
an individual’s score and the mean divided by the standard deviation
The Tscore
 The Tscore standardizes scores around a
mean of 50
 The Tscore is simply = 50 + 10*(zscore).
 Either standardized score (z or T) is a way
of determining where an individual’s score falls from the mean.
 In a normal distribution, you can determine
the percentile for each scores
Statistics
 The correlation coefficient  determines the
relation between scores and variables
 Linear regression  predicts future outcomes
based on the correlation between independent and dependent variables.
Inferential Statistics
 A method of hypothesis testing
 The null hypothesis and research hypothesis
 Types of error; Type 1 (alpha) and type II
(beta)
 Types of variable; independent vs dependent
Possible Test Items From These
Notes:
 Be able to define and differentiate between
the types of statistics, scales, measures of central tendency, and
distributions.
 Be able to define variance, the types of
variance, and how variance is used in a normal distribution.
 Know the different standardized scores
available, how they are connected to a normal distribution, and what
interpretations can be made with standardized scores.
 Be able to define and differentiate between
standard deviation, variance, and correlation.
 Know the difference between independent and
dependent variables, types of errors, and types of hypotheses.
 Be able to describe probability and its
importance in evaluation, the usage of the different statistical tests and
with which types of scales of measure are used with each.
