SP 225 Lecture 5 Percentages, Proportions, Rates of Change and Frequency Distributions

Proportion  The number of cases in one category of a variable divided by the number of cases in all categories of a variable

Rates  Definition: A proportion written with a base other than 1

Percentage  Definition: a rate written with a base of 100

Percentage Change  Definition: A statistic that tells how much a variable has changed over time.

Frequency Distribution Definition: A table that summarizes the distribution of a variable by reporting the number of cases contained in each of its categories

Frequency Distribution Climate of the World’s Countries Frequency Desert7 Arid Desert5 Arid6 Tropical32 Mediterranean10 Maritime4 Temperate34 Arctic4 Total102

Frequency Distribution with Percentages Climate of the World’s Countries FrequencyPercentage Desert76.9% Arid Desert54.9% Arid65.8% Tropical3231.4% Mediterranean109.8% Maritime43.9% Temperate3433.3% Arctic43.9% Total102100%

Frequency Distribution with Cumulative Frequency Climate of the World’s Countries FrequencyPercentageCumulative Frequency Desert76.9%7 Arid Desert54.9%12 Arid65.8%18 Tropical3231.4%50 Mediterranean109.8%60 Maritime43.9%64 Temperate3433.3%98 Arctic43.9%102 Total102100%

Frequency Distribution with Cumulative Percentages Climate of the World’s Countries FrequencyPercentageCumulative Frequency Cumulative Percentage Desert76.9%7 Arid Desert54.9%1211.8% Arid65.8%1817.6% Tropical3231.4%5049.0% Mediterranean109.8%6058.8% Maritime43.9%6462.7% Temperate3433.3%9896.0% Arctic43.9%102100% Total102100%

Frequency Tables SPSS

Making Decisions Based on Ordinal Data  Cannot truly calculate an average score  Cannot directly compare categories

Frequency Tables for Interval/Ratio Data  Group categories  Groups represent ranges of values

Constructing a Frequency Table 1. Decide upon a number of groups 2. Find the range of data by subtracting the minimum value from the maximum value 3. Divide the range by the number of groups to get the minimum group size 4. Define the lower limit of the lower interval and begin building the groupings 5. Count the number of cases in each group

Example Frequency Table

Constructing a Frequency Table in SPSS  Use recode command to group data  Groups must be created manually before frequency table is constructed

Reading For Next Class  No Additional Reading