Chapter 2: Organization of Information: Frequency Distributions

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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 observations
  falling 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 5,537,600
• Total (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 reform group
  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 Justice Statistics.
1994. U.S. Department of Justice, Bureau of
Justice Statistics. Washington, D.C. U.S.
Government Printing Office, 1995, pp. 115-116.
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Creating a Frequency Distribution
Frequency 1 1 9
4 12 Total N 27

• 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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Proportions and Percentages

• Proportion (P) a relative frequency obtained by
  dividing the frequency in each category by the
  total number of cases.
• Percentage () a relative frequency obtained 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

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Proportions and Percentages

• Minimum Age Frequency Proportion
  Percentage
• 14 1 1/27.037 3.7
• 15 1 .037 3.7
• 16 9 .333 33.3
• 17 4 .148 14.8
• 18 12 .444 44.4
• Total N 27 1.0 100.0

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Percentage Distributions

• A table showing the percentage of observations
  falling into each category of the variable.
• Minimum
• Age Frequency Percentage
• 4 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 Variables

• Gender 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 particular
  order.

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Frequency Distributions for Ordinal Variables

• Happiness Tallies Freq. (f) Percentage
• Very Happy 9 22.5
• Pretty Happy
  25 62.5
• Not 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 rank from the
  lowest to the highest or from the highest to the
  lowest.

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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 2.5
• 6 2 5.0
• 7 or more 2 5.0 Total
  (N) 40 100.0

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Cumulative Distributions

• Sometimes we are interested in locating the
  relative position of a given score in a
  distribution.
• Cumulative frequency distribution a distribution
  showing the frequency at or below each category
  (class interval or score) of the variable.
• Cumulative percentage distribution a
  distribution showing the percentage at or below
  each category (class interval or score) of the
  variable.

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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 27
• Total (N) 27 100.0
• Doesnt total to 100 due to rounding

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Cumulative Percentage Distribution

• Minimum Cumulative
• Age Frequency Percentage
  Percentage
• 14 1 3.7 3.7
• 15 1 3.7 7.4
• 16 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

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Rates

• A number obtained by dividing the number of
  actual occurrences in a given time period by the
  number of possible occurrences.
• Whats the problem with the rate
  computation below?
• Marriage rate, 1990 Number of marriages in
  1990
• Total population in 1990
• Marriage rate, 1990 2,448,000 marriages
• 250,000,000 Americans
• Marriage rate, 1990 .0098

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Reading Statistical Tables

• Basic principles for understanding what the
  researcher 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 numbers presented in
  the first column? In the second column?