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

Frequency Distributions A table reporting the number of observations falling into each category of the variable. IdentityFrequency (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

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.)

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

Frequency Total N27 Creating a Frequency Distribution Minimum AgeTally 14| 15| 16||||||||| 17|||| 18||||||||||||

Creating a Frequency Distribution Minimum Age Frequency Total N27

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 Proportions and Percentages

Minimum Age Frequency Proportion Percentage 14 11/27= Total N Proportions and Percentages

Percentage Distributions A table showing the percentage of observations falling into each category of the variable. Minimum Age Frequency Percentage Total N

Frequency Distributions for Nominal Variables GenderTalliesFreq. (f)Percentage Male ||||||||||||||| Female ||||||||||||||||||||||||| Total (N) Note:The categories for nominal variables (male, female) need not be listed in any particular order.

Frequency Distributions for Ordinal Variables HappinessTalliesFreq. (f)Percentage Very Happy |||||||||922.5 Pretty Happy ||||||||||||||||||||||||| Not too happy ||||||615.0 Total (N) 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.

Employment Status Example

Frequency Distributions for Interval-Ratio Variables Number of ChildrenFreq. (f)Percentage or more2 5.0 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.

Cumulative Frequency Distribution Minimum Cumulative Age Freq. (f)PercentageFrequency Total (N) * Doesn’t total to 100% due to rounding

Minimum Cumulative Age Frequency Percentage Percentage * Total N * Does not total to 100% due to rounding Cumulative Percentage Distribution

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? 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

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?