PPA 415 – Research Methods in Public Administration

Lecture 2 - Counting and Charting Responses

Percentages and Proportions

Percentages and proportions supply a frame of reference for reporting research results by standardizing the raw data: percentages by base 100 and proportions by base 1.00.

100*N

f (%) Percentage

(p) Proportion

N

f

Percentages and Proportions

Example from IAEM-NEMA Survey, 2006.Problems with the government response to Hurricane Katrina arose largely because

of inadequate leadership and management of the crisis by FEMA.

7 6.3 7.1 7.1

24 21.6 24.2 31.3

26 23.4 26.3 57.6

27 24.3 27.3 84.8

15 13.5 15.2 100.0

99 89.2 100.0

12 10.8

111 100.0

Strongly disagree

Disagree

Neutral

Agree

Strongly agree

Total

Valid

SystemMissing

Total

Frequency Percent Valid PercentCumulative

Percent

Percentages and Proportions

Guidelines. When working with a small number of cases,

report the actual frequencies. Always report the number of observations

along with proportions and percentages. Proportions and percentages can be used for

any level of measurement.

Percentage Change

2 at time or value frequency, score, second

1 at time or value frequency, score,first

100

2

1

1

12

f

fwhere

f

ffchangePercentage

Percentage Change Example

Percentage Change Example

%12.7%82.36

%82.36%20.341972-1970 change %

%16.20%12.46

%12.46%82.361970-1968 change %

%71.24%26.61

%26.61%12.461968-1966 change %

%91.5%84.57

%84.57%26.611966-1964 change %

%27.15%18.50

%18.50%84.571964-1958 change %

Ratios and Rates

We determine ratios by dividing the frequency of one category by another.Problems with the government response to Hurricane Katrina arose largely because

of inadequate leadership and management of the crisis by FEMA.

7 6.3 7.1 7.1

24 21.6 24.2 31.3

26 23.4 26.3 57.6

27 24.3 27.3 84.8

15 13.5 15.2 100.0

99 89.2 100.0

12 10.8

111 100.0

Strongly disagree

Disagree

Neutral

Agree

Strongly agree

Total

Valid

SystemMissing

Total

Frequency Percent Valid PercentCumulative

Percent

Ratios and Rates

The ratio of people who agree that the FEMA response was inadequate to those who disagree is (27+15)/(24+7) =42/31 = 1.35 to 1. That is, for every 10 people who disagree, there are 13.5 who agree.

Rates are defined as the number of actual occurrences of some phenomenon divided by the number of actual occurrences per some unit of population.

Ratios and Rates

Example: In the IAEM-NEMA Survey (Local), I asked how many emergency managers would rank wildfires as the mostly likely source of catastrophic disaster in their jurisdiction.

The survey result indicated that eight out of 111 respondents believed this to be true. Expressed as a rate per 1,000 emergency managers, this would be (8/111)*1000, or 72.1 emergency managers per 1000 believe fires to be the most likely cause of catastrophic disasters in their jurisdiction.

Frequency Distributions

Tables that summarize the distribution of a variable by reporting the number of cases contained in each category of the variables.

Helpful and commonly used ways of organizing and working with data.

Almost always the first step in any statistical analysis.

The problem is that the raw data rarely reveals any consistent pattern. Data must be grouped to identify patterns.

Frequency Distributions

The categories of the frequency distribution must be exhaustive and mutually exclusive. (Each case must be counted in one and only one category).

Frequency distributions must have a descriptive title, clearly labeled categories, percentages, cumulative percentages, and a report of the total number of cases.

Frequency Distributions - Nominal

Type of Organization

42 41.2 41.2 41.2

49 48.0 48.0 89.2

11 10.8 10.8 100.0

102 100.0 100.0

Public organization

Private organization

Nonprofit organization

Total

ValidFrequency Percent Valid Percent

CumulativePercent

Frequency Distributions - Ordinal

Articulate - Communicates effectively with others.

7 6.9 6.9 6.9

10 9.8 9.8 16.7

57 55.9 55.9 72.5

28 27.5 27.5 100.0

102 100.0 100.0

Disagree

Neutral

Agree

Strongly agree

Total

ValidFrequency Percent Valid Percent

CumulativePercent

Frequency Distributions – Grouped Interval

Years of Emergency Management Experience

25 22.5 24.0 24.0

27 24.3 26.0 50.0

13 11.7 12.5 62.5

16 14.4 15.4 77.9

9 8.1 8.7 86.5

6 5.4 5.8 92.3

4 3.6 3.8 96.2

4 3.6 3.8 100.0

104 93.7 100.0

7 6.3

111 100.0

0-5

5-10

10-15

15-20

20-25

25-30

30-35

Over 35

Total

Valid

SystemMissing

Total

Frequency Percent Valid PercentCumulative

Percent

Frequency Distributions

Procedures for Constructing Frequency Distributions for Interval-Ratio Variables. Decide how many class intervals you wish to use.

(10-15 intervals). Find the size of the class interval. Divide the range of

the scores by the number of intervals and rounding to a convenient whole number.

State the lowest interval so that its lower limit is equal to or below the lowest score. State the highest interval so that its highest limit is equal to or higher than the highest score.

Frequency Distributions

Procedures for Constructing Frequency Distributions for Interval-Ratio Variables. State the limits of the class intervals at the same level

of precision as you have used to measure the data. Do not overlap intervals.

Apparent limits (0-2). Real limits (-0.5-2.5).

Count the number of cases in each class interval and report these subtotals in a column labeled “frequency”. Report the total number of cases (N) at the bottom of this column.

Frequency Distributions

Procedures for Constructing Frequency Distributions for Interval-Ratio Variables. Inspect the frequency distribution carefully.

Adjust intervals. Remember to give your table a clear, concise

title, and number the table if your report contains more than one. All categories and columns must also be clearly labeled.

Frequency Distributions - Examples

Frequencies - Example

Number of retirement home visits

6 6.7 6.7 6.7

2 2.2 2.2 8.9

1 1.1 1.1 10.0

1 1.1 1.1 11.1

2 2.2 2.2 13.3

1 1.1 1.1 14.4

1 1.1 1.1 15.6

1 1.1 1.1 16.7

1 1.1 1.1 17.8

7 7.8 7.8 25.6

1 1.1 1.1 26.7

5 5.6 5.6 32.2

2 2.2 2.2 34.4

3 3.3 3.3 37.8

1 1.1 1.1 38.9

4 4.4 4.4 43.3

2 2.2 2.2 45.6

3 3.3 3.3 48.9

3 3.3 3.3 52.2

6 6.7 6.7 58.9

1 1.1 1.1 60.0

4 4.4 4.4 64.4

3 3.3 3.3 67.8

4 4.4 4.4 72.2

1 1.1 1.1 73.3

1 1.1 1.1 74.4

1 1.1 1.1 75.6

1 1.1 1.1 76.7

1 1.1 1.1 77.8

1 1.1 1.1 78.9

1 1.1 1.1 80.0

2 2.2 2.2 82.2

2 2.2 2.2 84.4

1 1.1 1.1 85.6

1 1.1 1.1 86.7

7 7.8 7.8 94.4

1 1.1 1.1 95.6

4 4.4 4.4 100.0

90 100.0 100.0

0

1

2

3

6

7

8

9

10

12

15

16

17

18

19

20

21

22

23

24

25

26

27

28

30

32

33

35

36

40

42

46

47

48

49

50

51

52

Total

ValidFrequency Percent Valid Percent

CumulativePercent

Frequencies - Example

Recoded visit

10 11.1 11.1 11.1

5 5.6 5.6 16.7

8 8.9 8.9 25.6

12 13.3 13.3 38.9

18 20.0 20.0 58.9

12 13.3 13.3 72.2

3 3.3 3.3 75.6

2 2.2 2.2 77.8

2 2.2 2.2 80.0

6 6.7 6.7 86.7

12 13.3 13.3 100.0

90 100.0 100.0

0 to 4 (-.5 to 4.5)

5 to 9 (4.5 to 9.5)

10 to 14 (9.5 to 14.5)

15 to 19 (14.5 to 19.5)

20 to 24 (19.5 to 24.5)

25 to 29 (24.5 to 29.5)

30 to 34 (29.5 to 34.5)

35 to 39 (34.5 to 39.5)

40 to 44 (39.5 to 44.5)

45 to 49 (44.5 to 49.5)

50 to 54 (49.5 to 54.5)

Total

ValidFrequency Percent Valid Percent

CumulativePercent

Charts and Graphs

Researcher use charts and graphs to present their data in ways that are visually more dramatic than frequency distributions.

Pie charts and bar charts are appropriate for discrete data at any level of measurement.

Histograms and line charts or frequency polygons are used for interval and ratio variables.

Pie Chart - Nominal

Pie Chart - Ordinal

Bar Chart - Nominal

Bar Chart - Ordinal

Histogram

Line Chart