chapter2 v.ppt
TRANSCRIPT
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Chapter 2: Organization of
Information:
Frequency Distributions Frequency Distributions Proportions and Percentages Percentage Distributions
Comparisons The Construction of Frequency Distributions
Frequency Distributions for Nominal Variables Frequency Distributions for Ordinal Variables Frequency Distributions for Interval-Ratio Variables
Cumulative Distributions Rates Reading the Research Literature
Basic Principles Tables with a Different Format
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Frequency Distributions
A table reporting the number of observationsfalling into each category of the variable.
Identity Frequency (f)
Native American 947,500
Native American of multiple ancestry 269,700
Native American of Indian descent 5,537,600Total (N) 6,754,800
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Death Penalty Statutes
In 1993, 36 states and Washington, D.C. had
statutes permitting capital punishment. Of these
36 states, 27 set a minimum age for execution.
Assume you are a member of a legal reformgroup that is trying to get the states that do not
have a minimum age for execution to change
their laws. You want to prepare a report
describing the minimum age for execution in the
27 states have an established minimum age for
execution. (The data are on the following slides.)
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Death Penalty Statutes
Source: Kathleen Maguire and Ann L. Pastore, eds., Sourcebook of Criminal JusticeStatistics. 1994. U.S. Department of Justice, Bureau of Justice Statistics. Washington,D.C.: U.S. Government Printing Office, 1995, pp. 115-116.
StateMinimum
Age StateMinimum
Age
Arkansas 14 Texas 17
Virginia 15 California 18
Alabama 16 Colorado 18
Delaware 16 Connecticut 18
Indiana 16 Illinois 18
Kentucky 16 Louisiana 18Mississippi 16 Maryland 18
Missouri 16 Nebraska 18
Nevada 16 New Jersey 18
Oklahoma 16 New Mexico 18
Wyoming 16 Ohio 18
Georgia 17 Oregon 18New Hampshire 17 Tennessee 18
North Carolina 17
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Frequency
1
1
9
4
12
Total N 27
Creating a Frequency Distribution
Minimum Age Tally
14 |
15 |
16 |||||||||
17 ||||
18 ||||||||||||
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Creating a Frequency Distribution
Minimum Age Frequency
14 1
15 1
16 9
17 4
18 12
Total N 27
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N
fP
Proportion (P):a relative frequencyobtained by dividing the frequency in
each category by the total number of
cases.
Percentage (%):a relative frequencyobtained by dividing the frequency in
each category by the total number of
cases and multiplying by 100.
N:total number of cases
Proportions and percentages are
relative frequencies
)100((%) P
Proportions and Percentages
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Minimum Age Frequency Proportion Percentage
14 1 1/27=.037 3.7
15 1 .037 3.716 9 .333 33.3
17 4 .148 14.8
18 12 .444 44.4Total N 27 1.0 100.0
Proportions and Percentages
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PercentageDistributions
A table showing the percentage of observationsfalling into each category of the variable.
Minimum
Age Frequency Percentage4 1 3.7
15 1 3.7
16 9 33.3
17 4 14.8
18 12 44.4
Total N 27 100.0
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Frequency Distributions for
Nominal VariablesGender Tallies Freq. (f) Percentage
Male ||||||||||||||| 15 37.5
Female ||||||||||||||||||||||||| 25 62.5
Total (N) 40 100.0
Note: The categories for nominal variables (male,female) need not be listed in any particularorder.
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Frequency Distributions for
Ordinal VariablesHappiness Tallies Freq. (f) Percentage
Very Happy ||||||||| 9 22.5
Pretty Happy ||||||||||||||||||||||||| 25 62.5Not too happy |||||| 6 15.0
Total (N) 40 100.0
Note: Because the categories or values of ordinal variables are rank-ordered, they must be listed in a way that reflects their rankfrom the lowest to the highest or from the highest to thelowest.
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Employment Status Example
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Employment Status Example
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Frequency Distributions for
Interval-Ratio Variables
Number of Children Freq. (f) Percentage
0 5 12.5
1 10 25.0
2 10 25.0
3 5 12.5
4 5 12.5
5 1 2.56 2 5.0
7 or more 2 5.0Total (N) 40 100.0
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Cumulative Distributions
Sometimes we are interested in locating therelative position of a given score in a distribution.
Cumulativefrequency distribution:adistribution showing the frequency at or beloweach category (class interval or score) of thevariable.
Cumulativepercentage distribution:adistribution showing the percentage at or beloweach category (class interval or score) of thevariable.
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Cumulative Frequency
Distribution
Minimum Cumulative
Age Freq. (f) Percentage Frequency
14 1 3.7 1
15 1 3.7 2
16 9 33.3 11
17 4 14.8 15
18 12 44.4 27Total (N) 27 100.0
* Doesnt total to 100% due to rounding
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Minimum Cumulative
Age Frequency Percentage Percentage
14 1 3.7 3.7
15 1 3.7 7.416 9 33.3 40.7
17 4 14.8 55.5
18 12 44.4 99.9*Total N 27 100.0
* Does not total to 100% due to rounding
Cumulative Percentage Distribution
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RatesA number obtained by dividing the number of
actualoccurrences in a given time period by thenumber ofpossible occurrences.
Whats the problem with the ratecomputation below?
Marriage rate, 1990 = Number of marriages in 1990
Total population in 1990
Marriage rate, 1990 = 2,448,000 marriages250,000,000 Americans
Marriage rate, 1990 = .0098
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Reading Statistical Tables
Basic principles for understanding what theresearcher is trying to tell you:
What is the source of the table? How many variables are presented? What
are their names?
What is represented by the numberspresented in the first column? In the secondcolumn?