@ 2012 wadsworth, cengage learning chapter 5 description of behavior through numerical...
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@ 2012 Wadsworth, Cengage Learning
Chapter 5Chapter 5
Description of Description of Behavior Through Behavior Through
Numerical Numerical RepresentationRepresentation
@ 2012 Wadsworth, Cengage Learning
@ 2012 Wadsworth, Cengage Learning
Topics
1. Measurement2. Scales of Measurement3. Measurement and Statistics4. Pictorial Description of Frequency
Information5. Descriptive Statistics
@ 2012 Wadsworth, Cengage Learning
Topics (cont’d.)
6. Pictorial Presentations of Numerical Data7. Transforming Data8. Standard Scores9. Measure of Association
@ 2012 Wadsworth, Cengage Learning
Measurement
@ 2012 Wadsworth, Cengage Learning
Measurement
• “What can we measure?” • “What do the measurements mean?”• Four properties:
– Identity– Magnitude– Equal intervals– Absolute zero
@ 2012 Wadsworth, Cengage Learning
Scales of Measurement
@ 2012 Wadsworth, Cengage Learning
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
@ 2012 Wadsworth, Cengage Learning
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
@ 2012 Wadsworth, Cengage Learning
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
@ 2012 Wadsworth, Cengage Learning
Measurement and Statistics
@ 2012 Wadsworth, Cengage Learning
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
@ 2012 Wadsworth, Cengage Learning
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 scoreor
– In the case of an even number of scores, the score halfway between the two middle scores
• Mode– Most frequently occurring score
@ 2012 Wadsworth, Cengage Learning
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)
@ 2012 Wadsworth, Cengage Learning
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
@ 2012 Wadsworth, Cengage Learning
Measures of Variability (cont’d.)
• Formula for variance:
• Square root of the variance: standard deviation (SD)
@ 2012 Wadsworth, Cengage Learning
Pictorial Presentations of Numerical Data
@ 2012 Wadsworth, Cengage Learning
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
@ 2012 Wadsworth, Cengage Learning
Transforming Data
@ 2012 Wadsworth, Cengage Learning
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
@ 2012 Wadsworth, Cengage Learning
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
@ 2012 Wadsworth, Cengage Learning
Figure 5.10 Scatter diagrams showing variousrelationships 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
@ 2012 Wadsworth, Cengage Learning
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