Chapter 2: The 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 © 2011 SAGE PublicationsFrankfort-Nachmias and Leon-Guerrero, Statistics for a Diverse Society, 6e

Frequency Distributions  A table reporting the number of observations falling into each category of the variable. IdentityFrequency (f) Native American947,500 Native American of multiple ancestry269,700 Native American of Indian descent5,537,600 Total (N)6,754,800 © 2011 SAGE PublicationsFrankfort-Nachmias and Leon-Guerrero, Statistics for a Diverse Society, 6e

Example: 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 slide.) © 2011 SAGE PublicationsFrankfort-Nachmias and Leon-Guerrero, Statistics for a Diverse Society, 6e

Death Penalty Statutes Source: Kathleen Maguire and Ann L. Pastore, eds., Sourcebook of Criminal Justice Statistics U.S. Department of Justice, Bureau of Justice Statistics. Washington, D.C.: U.S. Government Printing Office, 1995, pp © 2011 SAGE PublicationsFrankfort-Nachmias and Leon-Guerrero, Statistics for a Diverse Society, 6e

Creating a Frequency Distribution Minimum AgeFrequency Total (N)27 © 2011 SAGE PublicationsFrankfort-Nachmias and Leon-Guerrero, Statistics for a Diverse Society, 6e

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 © 2011 SAGE PublicationsFrankfort-Nachmias and Leon-Guerrero, Statistics for a Diverse Society, 6e

Proportions and Percentages Minimum AgeFrequencyProportionPercentage 1411/27= % % % % % Total (N) % © 2011 SAGE PublicationsFrankfort-Nachmias and Leon-Guerrero, Statistics for a Diverse Society, 6e

Percentage Distributions  A table showing the percentage of observations falling into each category of the variable. © 2011 SAGE PublicationsFrankfort-Nachmias and Leon-Guerrero, Statistics for a Diverse Society, 6e Minimum AgeFrequencyPercentage Total N

Frequency Distributions for Nominal Variables © 2011 SAGE PublicationsFrankfort-Nachmias and Leon-Guerrero, Statistics for a Diverse Society, 6e GenderTalliesFreq. (f)Percentage MaleIIIIIIIIIIIIIII FemaleIIIIIIIIIIIIIIIIIIIIIIIII Total (N) Note: The categories for nominal variables (e.g., gender: male, female) need not be listed in any particular order.

Frequency Distributions for Ordinal Variables  Note: Because the categories or values of ordinal variables are rank-ordered, they must be listed in a way that reflects their rank-ordering from the lowest to the highest or from the highest to the lowest. Categories should be displayed in order. © 2011 SAGE PublicationsFrankfort-Nachmias and Leon-Guerrero, Statistics for a Diverse Society, 6e HappinessTalliesFreq. (f)Percentage Very HappyIIIIIIIII922.5 Pretty HappyIIIIIIIIIIIIIIIIIIIIIIIII Not too HappyIIIIII615.0 Total (N)

Employment Status Example © 2011 SAGE PublicationsFrankfort-Nachmias and Leon-Guerrero, Statistics for a Diverse Society, 6e

Employment Status Example © 2011 SAGE PublicationsFrankfort-Nachmias and Leon-Guerrero, Statistics for a Diverse Society, 6e

Frequency Distributions for Interval-Ratio Variables © 2011 SAGE PublicationsFrankfort-Nachmias and Leon-Guerrero, Statistics for a Diverse Society, 6e Number of Children Freq. (f)Percentage (%) or more25.0 Total (N)

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. © 2011 SAGE PublicationsFrankfort-Nachmias and Leon-Guerrero, Statistics for a Diverse Society, 6e

Cumulative Frequency Distribution © 2011 SAGE PublicationsFrankfort-Nachmias and Leon-Guerrero, Statistics for a Diverse Society, 6e Minimum Age Freq. (f)Cumulative Frequency Total (N)27 *Doesn’t total to 100% due to rounding.

Cumulative Percentage Distribution © 2011 SAGE PublicationsFrankfort-Nachmias and Leon-Guerrero, Statistics for a Diverse Society, 6e Minimum AgeFreq. (f)PercentageCumulative Percentage (C%) * Total (N) * *Does not total 100% due to rounding

Rates A number obtained by dividing the number of actual occurrences in a given time period by the number of possible occurrences. What’s the problem with the “rate” computation below? Why is it not an accurate statistic? 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 © 2011 SAGE PublicationsFrankfort-Nachmias and Leon-Guerrero, Statistics for a Diverse Society, 6e

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? © 2011 SAGE PublicationsFrankfort-Nachmias and Leon-Guerrero, Statistics for a Diverse Society, 6e