pols 7000x statistics in political science class 2 brooklyn college – cuny shang e. ha...

POLS 7000XSTATISTICS IN POLITICAL SCIENCE

CLASS 2

BROOKLYN COLLEGE – CUNYSHANG E. HA

Leon-Guerrero and Frankfort-Nachmias, Essentials of Statistics for a Diverse Society, Chapter 2

Leon-Guerrero/Frankfort-Nachmias: Essentials of Social Statistics for a Diverse Society© 2012 SAGE Publications

Chapter 2: The Organization and Graphic Presentation of Data

Frequency Distributions Proportions and Percentages Percentage Distributions Statistics in Practice: Labor Force Participation

Among Latinos The Construction of Frequency Distributions Cumulative Distributions Rates Reading the Research Literature: Statistical

Tables Graphic Presentation of Data A Cautionary Note: Distortions in Graphs Statistics in Practice: Diversity at a Glance


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


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.)


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.

StateMinimumAge State

MinimumAge

Arkansas 14 Texas 17

Virginia 15 California 18

Alabama 16 Colorado 18

Delaware 16 Connecticut 18

Indiana 16 Illinois 18

Kentucky 16 Louisiana 18

Mississippi 16 Maryland 18

Missouri 16 Nebraska 18

Nevada 16 New Jersey 18

Oklahoma 16 New Mexico 18

Wyoming 16 Ohio 18

Georgia 17 Oregon 18

New Hampshire 17 Tennessee 18

North Carolina 17


Creating a Frequency Distribution

Minimum Age

Frequency

14 1

15 1

16 9

17 4

18 12

Total (N) 27


N

fP

)100((%) P

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


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%


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


Frequency Distributions for Nominal Variables

Gender Tallies Frequency Percentage

Male IIIIIIIIIIIIIII 15 37.5

Female IIIIIIIIIIIIIIIIIIIIIIIII

25 62.5

Total (N) 40 100.0

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.

Happiness Tallies Freq. (f) Percentage

Very Happy IIIIIIIII 9 22.5

Pretty Happy IIIIIIIIIIIIIIIIIIIIIIIII

25 62.5

Not too Happy

IIIIII 6 15.0

Total (N) 40 100.0


Employment Status Example


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


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 Age

Freq. (f) Percentage

Cumulative Frequency

14 1 3.7 1

15 1 3.7 1

16 9 33.3 2

17 4 14.8 11

18 12 44.4 27

Total (N) 27 100.1*

*Doesn’t total to 100% due to rounding.


Cumulative Percentage Distribution

Minimum Age

Freq. (f) Percentage

Cumulative Percentage

1 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) 27 100.1*

*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 1990Total population in 1990

Marriage rate, 1990 = 2,448,000 marriages250,000,000 Americans

Marriage rate, 1990 = .0098


Reading Statistical TablesBasic 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?


Graphic Presentation

The Pie Chart The Bar Graph The Histogram The Line Graph Times Series Charts Distortions in Graphs

It is important to choose the appropriate graphs to make statistical information coherent.


The Pie Chart: The Race and Ethnicity of the Elderly

Pie chart: a graph showing the differences in frequencies or percentages among categories of a nominal or an ordinal variable. The categories are displayed as segments of a circle whose pieces add up to 100 % of the total frequencies.


Too many categories can be messy!


We can reduce some of the categories


The Bar Graph: The Living Arrangements and Labor Force Participation of the Elderly

Bar graph: a graph showing the differences in frequencies or percentages among categories of a nominal or an ordinal variable. The categories are displayed as rectangles of equal width with their height proportional to the frequency or percentage of the category.


The Bar Graph: The Living Arrangements and Labor Force Participation of the Elderly


Can Display More Info by Splitting Sex


The Histogram

Histogram: a graph showing the differences in frequencies or percentages among categories of an interval-ratio variable. The categories are displayed as contiguous bars, with width proportional to the width of the category and height proportional to the frequency or percentage of that category.


The Histogram


The Line Graph

Line Graph: A graph showing the differences in frequencies or percentages among categories of an interval-ratio variable. Points representing the frequencies of each category are placed above the midpoint of the category and are joined by a straight line.


The Line Graph


Time Series Charts

Time series chart: a graph displaying changes in a variables at different points in time. It shows time (measured in units such as years or months) on the horizontal axis and the frequencies (percentages or rates) of another variable on the vertical axis.


Time Series Charts


Distortions in Graphs

Graphs not only quickly inform us; they can quickly deceive us. Because we are often more interested in general impressions than in detailed analyses of the numbers, we are more vulnerable to being swayed by distorted graphs.

What are graphical distortions?

How can we recognize them?


Shrinking and Stretching the Axes: Visual Confusion


Statistics in Practice

The following graphs are particularly suitable for making comparisons among groups:

- Bar chart- Line graph- Time series chart


Why use charts and graphs?– What do you lose?

– ability to examine numeric detail offered by a table– potentially the ability to see additional

relationships within the data– potentially time: often we get caught up in

selecting colors and formatting charts when a simply formatted table is sufficient

– What do you gain?– ability to direct readers’attention to one aspect

of the evidence– ability to reach readers who might otherwise be

intimidated by the same data in a tabular format– ability to focus on bigger picture rather than

perhaps minor technical details

pols 7000x statistics in political science class 2 brooklyn college – cuny shang e. ha...

Documents

essentials of statistics

diverse society

graphs statistics

sage publications proportions

sage publications chapter

bureau of justice statistics

sage publications example

total n27 slide