• Study Resource
• Explore

Survey

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Document related concepts

History of statistics wikipedia, lookup

Psychometrics wikipedia, lookup

Transcript
```Chapter 5
Description of
Behavior Through
Numerical
Representation
Topics
1.
2.
3.
4.
Measurement
Scales of Measurement
Measurement and Statistics
Pictorial Description of Frequency
Information
5. Descriptive Statistics
Topics (cont’d.)
6.
7.
8.
9.
Pictorial Presentations of Numerical Data
Transforming Data
Standard Scores
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
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
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
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
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 score
or
– 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 various
relationships 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