Chapter 5
Description of
Behavior Through
Numerical
Representation
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Topics
1.
2.
3.
4.
Measurement
Scales of Measurement
Measurement and Statistics
Pictorial Description of Frequency
Information
5. Descriptive Statistics
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Topics (cont’d.)
6.
7.
8.
9.
Pictorial Presentations of Numerical Data
Transforming Data
Standard Scores
Measure of Association
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Measurement
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Measurement
• “What can we measure?”
• “What do the measurements mean?”
• Four properties:
– Identity
– Magnitude
– Equal intervals
– Absolute zero
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Scales of Measurement
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Scales of Measurement
• Nominal measurement
– Occurs when people are placed into different
categories
– Example: classify research participants as men or
women
– Differences between categories are of kind
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Scales of Measurement (cont’d.)
• Ordinal measurement
– A single continuum underlies a particular
classification system
– Example: pop-music charts
– Represents some degree of quantitative difference
– Transforms information expressed in one form to
that expressed in another
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Scales of Measurement (cont’d.)
• Interval measurement
– Requires that:
• Scale values are related by a single underlying
quantitative dimension
• There are equal intervals between consecutive scale
values
– Example: household thermometer
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Scales of Measurement (cont’d.)
• Ratio measurement
– Requires that:
• Scores are related by a single quantitative dimension
• Scores are separated by equal intervals
• There is an absolute zero
– Example: weight, length
• Scales of measurement are related to:
– How a particular concept is being measured
– The questions being asked
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Measurement and Statistics
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Measurement and Statistics
• No statistical reason exists for limiting a
particular scale of measurement to a
particular statistical procedure
• Your statistics do not know and do not care
where your numbers come from
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Pictorial Description of
Frequency Information
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Pictorial Description of
Frequency Information
Table 5.2
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Pictorial Description of
Frequency Information (cont’d.)
Figure 5.1 Bar graph of dream data
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Pictorial Description of
Frequency Information (cont’d.)
Figure 5.2 Frequency polygon of dream data
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Figure 5.3 Four types of frequency distributions: (a) normal,
(b) bimodal, (c) positively skewed, and (d) negatively skewed
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Descriptive Statistics
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Measures of Central Tendency
• Mean
– Arithmetic average of a set of scores
• Median
– List scores in order of magnitude; the median is
the middle score
or
– In the case of an even number of scores, the score
halfway between the two middle scores
• Mode
– Most frequently occurring score
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Figure 5.4 Mean, median, and mode of (a) a normal
distribution and (b) a skewed distribution
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Measures of Variability
• Attempts to indicate how spread out the
scores are
• Range: reflects the difference between the
largest and smallest scores in a set of data
• Variance: average of the squared deviations
from the mean
• To determine variance:
– First calculate the sum of squares (SS)
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Measures of Variability (cont’d.)
• Deviation method: sum of squares is equal to
the sum of the squared deviation scores
• Second way to calculate the sum of squares:
computational formula
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Measures of Variability (cont’d.)
• Formula for variance:
• Square root of the variance: standard
deviation (SD)
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Pictorial Presentations of
Numerical Data
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Pictorial Presentation of
Numerical Data
Figure 5.6 Effects of room temperature on response rates in rats
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Pictorial Presentation of
Numerical Data (cont’d.)
Figure 5.7 Effects of different forms of therapy
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Transforming Data
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Transforming Data
• Transformations are important
– Used to compare data collected using one scale
with those collected using another
• A statement is meaningful if:
– The truth or falsity of the statement remains
unchanged when one scale is replaced by another
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Standard Scores
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Standard Scores
• Formula for z score:
• Two important characteristics of the z score:
– If we were to transform a set of data to z scores,
the mean of these scores would equal 0
– The standard deviation of this set of z scores
would equal 1
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Measure of Association
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Figure 5.10 Scatter diagrams showing various
relationships that differ in degree and direction
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Measure of Association (cont’d.)
• Formula for the Pearson product moment
correlation coefficient (r):
• Correlations:
– Have to do with associations between two
measures
– Tell nothing about the causal relationship between
the two variables
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Measure of Association (cont’d.)
• When you square the correlation coefficient
(r2) and multiply this number by 100
– You have the amount of the variance in one
measure due to the other measure
• Regression:
– Mathematical way to use data
– Estimates how well we can predict that a change
in one variable will lead to a change in another
variable
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Summary
• Three important measures of central tendency
are the mean, median, and mode
• Some scores may be transformed from one
scale to another
• Variability, or dispersion, is related to how
spread out a set of scores is
• A correlation aids us in understanding how
two sets of scores are related
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