@ 2012 wadsworth, cengage learning chapter 5 description of behavior through numerical...

@ 2012 Wadsworth, Cengage Learning

Chapter 5Chapter 5

Description of Description of Behavior Through Behavior Through

Numerical Numerical RepresentationRepresentation



Topics

1. Measurement2. Scales of Measurement3. Measurement and Statistics4. Pictorial Description of Frequency

Information5. Descriptive Statistics


Topics (cont’d.)

6. Pictorial Presentations of Numerical Data7. Transforming Data8. Standard Scores9. Measure of Association


Measurement


Measurement

• “What can we measure?” • “What do the measurements mean?”• Four properties:

– Identity– Magnitude– Equal intervals– Absolute zero


Scales of Measurement


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


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



• 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



• 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


Measurement and Statistics


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


Pictorial Description of Frequency Information


Pictorial Description of Frequency Information

Table 5.2


Pictorial Description of Frequency Information (cont’d.)

Figure 5.1 Bar graph of dream data


Pictorial Description of Frequency Information (cont’d.)

Figure 5.2 Frequency polygon of dream data


Figure 5.3 Four types of frequency distributions: (a) normal, (b) bimodal, (c) positively skewed, and (d) negatively skewed


Descriptive Statistics


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


Figure 5.4 Mean, median, and mode of (a) a normal distribution and (b) a skewed distribution


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)


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


Measures of Variability (cont’d.)

• Formula for variance:

• Square root of the variance: standard deviation (SD)


Pictorial Presentations of Numerical Data


Pictorial Presentation of Numerical Data

Figure 5.6 Effects of room temperature on response rates in rats


Pictorial Presentation of Numerical Data (cont’d.)

Figure 5.7 Effects of different forms of therapy


Transforming Data


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


Standard Scores


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


Measure of Association


Figure 5.10 Scatter diagrams showing variousrelationships that differ in degree and direction


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


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


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

@ 2012 wadsworth, cengage learning chapter 5 description of behavior through numerical...

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