1/16/2017 Welcome to DMC- 617: Statistics and Informatics for Disaster Managers by M D . K HALID H ASAN MS(SWE), MPS, MDM C hapter 3 Data Summarization and Presentation Learning Objectives: Outline: By the end of this chapter, you will be able to: Data Summarization 1. Explain the purpose of descriptive statistics in _Percentages and Proportion making data comprehensible. _Rates, Ratios and Percent Changes 2. Compute and interpret percentages, _Frequency Distributions proportions, ratios, rates, and percentage Data Presentation change. _Pie Charts 3. Construct and analyze frequency distributions _Bar Charts for variables at each of the three levels of _Histogram measurement. _Line Charts 4. Construct and analyze bar and pie charts, _Stem-and-Leaf Displays histograms, and line graphs. _Dot Plots _Scatter Plots _Box Plots Md. Khalid Hasan Institute of Disaster Management and Vulnerability Studies khalidhasan@du.ac.bd University of Dhaka 1
1/16/2017 Percentages and Proportions ? ? ? Percentages and proportions supply a frame of reference for reporting research results in the sense that they standardize the raw data: percentages to the base 100 and proportions to the base 1.00. The mathematical definition of percentages is: Where, f = frequency, or the number of cases in any category N= the number of cases in all categories Md. Khalid Hasan Institute of Disaster Management and Vulnerability Studies khalidhasan@du.ac.bd University of Dhaka Percentages and Proportions ? ? ? Social scientists use proportions as well as percentages. Proportions vary from 0.00 to 1.00: They standardize results to a base of 1.00 instead of the base of 100 for percentages. The mathematical definition of proportions is: Where, f = frequency, or the number of cases in any category N= the number of cases in all categories Md. Khalid Hasan Institute of Disaster Management and Vulnerability Studies khalidhasan@du.ac.bd University of Dhaka 2
1/16/2017 Applying Statistics: Communicating with Statistics Md. Khalid Hasan Institute of Disaster Management and Vulnerability Studies khalidhasan@du.ac.bd University of Dhaka How can we choose between Percentages and Proportions ? ? ? _ Percentages are easier for most people (including statisticians) to comprehend and generally would be preferred, especially when the goal is to express results clearly and quickly. _ Proportions are used less frequently—generally when we are dealing with probabilities. The preference for percentages is based solely on ease of communication; these statistics are equally valid ways of expressing results and you should be proficient in both. _ When the number of cases is small (say, fewer than 20), it is usually preferable to report the actual frequencies rather than percentages or proportions. With a small number of cases, percentages are unstable and can change drastically with relatively minor changes in the size of the data set. Md. Khalid Hasan Institute of Disaster Management and Vulnerability Studies khalidhasan@du.ac.bd University of Dhaka 3
1/16/2017 How can we choose between Percentages and Proportions ? ? ? _ Always report the number of observations along with proportions and percentages. This permits the reader to judge the adequacy of the sample size and, conversely, helps to prevent the researcher from lying with statistics. _ Percentages and proportions can be computed for variables at any level of measurement. Md. Khalid Hasan Institute of Disaster Management and Vulnerability Studies khalidhasan@du.ac.bd University of Dhaka Ratios, Rates, and Percentage Change ? ? ? Ratios are especially useful for comparing the relative size of different categories of a variable and are determined by dividing the frequency of one category by the frequency of another. The formula for a ratio is: Where, f 1 = the number of cases in the first category f 2 = the number of cases in the second category Md. Khalid Hasan Institute of Disaster Management and Vulnerability Studies khalidhasan@du.ac.bd University of Dhaka 4
1/16/2017 Ratios, Rates, and Percentage Change ? ? ? Rates provide still another way of summarizing the distribution of a single variable. Rates are defined as the number of actual occurrences of some phenomenon divided by the number of possible occurrences per some unit of time. Rates are usually multiplied by some power of 10 to eliminate decimal points. For example, Md. Khalid Hasan Institute of Disaster Management and Vulnerability Studies khalidhasan@du.ac.bd University of Dhaka Ratios, Rates, and Percentage Change ? ? ? Measuring social change, in all its variety, is an important task for all social sciences. One very useful statistic for this purpose is the percentage change , which tells us how much a variable has increased or decreased over a certain span of time. To compute this statistic, we need the scores of a variable at two different points in time. The scores could be in the form of frequencies, rates, or percentages. The percentage change will tell us how much the score has changed at the later time relative to the earlier time. Where, f 1 = First score, frequency, or value f 2 = Second score, frequency, or value Md. Khalid Hasan Institute of Disaster Management and Vulnerability Studies khalidhasan@du.ac.bd University of Dhaka 5
1/16/2017 TABLE: Projected Population Growth for Six Nations, 1990–2020 Md. Khalid Hasan Institute of Disaster Management and Vulnerability Studies khalidhasan@du.ac.bd University of Dhaka Frequency distributions Frequency distributions are tables that report the number of cases in each category of a variable. They are very helpful and commonly used ways of organizing and working with data. In fact, the construction of frequency distributions is almost always the first step in any statistical analysis. TABLE: Data from Counseling Center Survey Md. Khalid Hasan Institute of Disaster Management and Vulnerability Studies khalidhasan@du.ac.bd University of Dhaka 6
1/16/2017 Frequency Distributions for Variables Measured at the Nominal Level TABLE: Sex of Respondents, Counseling TABLE: Marital Status of Respondents, Center Survey Counseling Center Survey Md. Khalid Hasan Institute of Disaster Management and Vulnerability Studies khalidhasan@du.ac.bd University of Dhaka Frequency Distributions for Variables Measured at the Interval-Ratio Level TABLE: Satisfaction with Services, TABLE: Age of Respondents, Counseling Counseling Center Survey Center Survey (interval width = one year of age) Md. Khalid Hasan Institute of Disaster Management and Vulnerability Studies khalidhasan@du.ac.bd University of Dhaka 7
1/16/2017 Cumulative Frequency and Cumulative Percentage TABLE: Age of Respondents, Counseling Center Survey TABLE: Age of Respondents, Counseling Center Survey Md. Khalid Hasan Institute of Disaster Management and Vulnerability Studies khalidhasan@du.ac.bd University of Dhaka Graphic Presentations of Data Md. Khalid hasan Institute of Disaster Management and Vulnerability Studies Khalidhasan@du.ac.bd University of Dhaka 8
1/16/2017 Pie Charts A circle divided into portions that represent the relative frequencies or percentages of a FIGURE: Marital Status of Respondents, population or a sample belonging to Counseling Center Survey (N= 20) different categories is called a pie chart . TABLE: Marital Status of Respondents, Counseling Center Survey Md. Khalid Hasan Institute of Disaster Management and Vulnerability Studies khalidhasan@du.ac.bd University of Dhaka Bar Charts When the data are qualitative or categorical, bar graphs can be used to represent the data. FIGURE: Marital Status of Respondents, A bar graph represents the data by using Counseling Center Survey (N= 20) vertical or horizontal bars whose heights or lengths represent the frequencies of the data. TABLE: Marital Status of Respondents, Counseling Center Survey Md. Khalid Hasan Institute of Disaster Management and Vulnerability Studies khalidhasan@du.ac.bd University of Dhaka 9
1/16/2017 Bar Charts When the data are qualitative or categorical, bar graphs can be used to represent the data. FIGURE: Marital Status of Respondents, A bar graph represents the data by using Counseling Center Survey (N= 20) vertical or horizontal bars whose heights or lengths represent the frequencies of the data. TABLE: Marital Status of Respondents, Counseling Center Survey Md. Khalid Hasan Institute of Disaster Management and Vulnerability Studies khalidhasan@du.ac.bd University of Dhaka Histograms Histograms look a lot like bar charts and, in fact, are constructed in much the same way. However, the bars in a histogram touch each other in a continuous series from the lowest to the highest scores. These graphs are most appropriate for interval-ratio level variables that have many scores covering a wide range. FIGURE: Distribution of Income by Household, United States, 2009 Md. Khalid Hasan Institute of Disaster Management and Vulnerability Studies khalidhasan@du.ac.bd University of Dhaka 10
Recommend
More recommend
