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.

Percentages and Proportions Example from IAEM-NEMA Survey, 2006.

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

Percentage Change Example

Ratios and Rates We determine ratios by dividing the frequency of one category by another.

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

Frequency Distributions - Ordinal

Frequency Distributions – Grouped Interval

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 ( ). 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

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