Chapter 2:Strategies for Understanding the Meanings of Data Key Words Frequency Tables Pie Chart, Bar Chart, Line Chart Stem and Leaf Histogram, Polygon, Shapes Cross Tabulation Scatter Diagram Parameter, Statistic Mean (Average), Median, Mode, Percentiles Range, Variance, Standard Deviation, Coefficient of Variation Box and-whisker Plots 1
Learning Outcomes: After studying this chapter, you will: 1. Understand how data can be appropriately organized and displayed. 2. Understand how to reduce data sets into a few useful, descriptive measures. 3. Be able to calculate and interpret measures of central tendency, such as the mean, median, and mode. 4. Be able to calculate and interpret measures of dispersion, such as the range, variance, and standard deviation. Dr. Ahmed Jaradat, AGU 2
Descriptive Statistics: Organizing and Summarizing Data Qualitative (Categorical) and quantitative variables are: Graphed Charted Tabled and Statistically summarized in very different ways Grade Sex Group Total Female 6 31 18 29 33 Male 9 14 20 11 10 A 5 19 18 18 25 B 10 26 20 22 18 3
Data Summarization and Presentation Qualitative Data: 1. Tables 1. Frequency Table 2. Relative Frequency Table 3. Percent Frequency Table 4. Cross Tabulation 2. Graphs 1. Bar chart a. Simple Bar Chart b.clustered Bar Chart c.stacked Bar Chart 2. Pie Chart Quantitative Data: 1. Tables 1. Frequency Table 2. Relative Frequency Table 3. Percent Frequency Table 4. Cumulative Frequency Table 5. Cumulative Relative Freq. Table 6. Stem and Leaf Display 7. Cross Tabulation 2. Graphs 1. Line Graph 2. Histogram 3. Frequency Polygon 4. Cumulative Frequency Polygon 5. Scatter Diagram 6. Box and Whisker Plot Dr. Ahmed Jaradat, AGU 4
Summarization and Presentation of Qualitative Data: Frequency Tables Frequency distribution of Smoking Status of 5244 persons Smoking Status Frequency Ever Smoked Cigarettes 3222 Stop Smoked Cigarettes 748 Currently Smoked Cigarettes 1274 Total 5244 Relative Frequency 0.614 0.143 0.243 1.000 Percent Frequency 61.4 14.3 24.3 100.0 5
Summarization and Presentation of Qualitative Data: Simple Bar Chart Dr. Ahmed Jaradat, AGU 6
Number of persons Number of Persons Summarization and Presentation of Qualitative Data: Clustered (Grouped) Bar Chart 3000 2500 2000 1500 1000 500 0 Ever Smoked Cigarettes Stop Smoked Cigarettes Smoking Status Currently Smoked Cigarettes 1200 1000 Male Femal 800 600 400 200 Ever Smoked Cigarettes Stop Smoked Cigarettes Currently Smoked Cigarettes 0 < 18 18-25 25-30 30-40 >40 Age 7
Number of Persons Summarization and Presentation of Qualitative Data: 1800 1600 1400 1200 1000 Stacked Bar Chart 800 600 400 Currently Smoked Cigarettes Stop Smoked Cigarettes Ever Smoked Cigarettes Pie Chart 200 0 < 18 18-25 25-30 30-40 >40 Age 8
Summarization and Presentation of Quantitative Data: Frequency Tables Summarizing Final Grades 2013/2014 Using Tables Grade Limits Number ofrelative Students Frequency Percent Frequency Cumulative Frequency Cumulative Percent Freq. 40-49 9 50-59 6 60-69 45 70-79 38 80-89 40 90-100 43 181 0.05 0.03 0.25 0.21 0.22 0.24 1.00 4.97 3.31 24.86 20.99 22.10 23.76 100.00 9 15 60 98 138 181 4.97 8.29 33.15 54.14 76.24 100.00 Dr. Ahmed Jaradat, AGU 9
Summarization and Presentation of STA231:, Academic Year 2013/2014 Sex Group Grade Total Average < 60 60-69 70-79 80-89 90-100 Female 6 31 18 29 33 117 78.69 Male 9 14 20 11 10 64 72.77 A 5 19 18 18 25 85 78.61 B 10 26 20 22 18 96 74.81 Total 15 8.29% 45 24.86% 38 20.99% 40 22.10% 43 23.76% 181 100% 76.6 Dr. Ahmed Jaradat, AGU 10
Stem and Leaf Display: Final Grades/ 2013-2014 Stem 4 5 6 7 8 9 10 Leaf 115577799 111233 000000000000111223455556666666777777778899999 00001111112222333444444455556666677889 0000001122222222233333344556666678888999 0001111222222333444555566666788999 000000000 9 6 45 38 40 34 9 11
Line Chart: Temperatures in Manama, in C o, over a 12-hour period 12
Number of clinicians Line graph 7 6 5 4 3 2 1 0 2010 2011 2012 2013 2014 Clinic 1 Clinic 2 Clinic 3 Number of Clinicians Working in Each Clinic During Years 2010-2014 Dr. Ahmed Jaradat, AGU 13
Choosing the Right Graph Use a bar graph if you are not looking for trends (or patterns) over time; and the items (or categories) are not parts of a whole Use a pie chart if you need to compare different parts of a whole, there is no time involved and there are not too many items (or categories). Use a line graph if you need to see how a quantity has changed over time. Line graphs enable us to find trends (or patterns) over time. 14
How to Choose between Tables, Figures, and Text to Present Data Use Table Use Figure Use Text To show many and precise numerical values and other specific data in a small space To compare and contrast data values or characteristics among related items or items with several shared characteristics or variables To show the presence or absence of specific characteristics To show trends, patterns, and relationships across and between data sets when general pattern is more important than the exact data values (What to use: graphs, data plots) To summarize research results (What to use: graphs, data plots, maps, and pie charts) To present a visual explanation of a sequence of events, procedures, geographic features, or physical characteristics (What to use: schematic diagrams, images, photographs, and maps) When you don t have extensive or complicated data to present When putting you data into a table would mean creating a table with 2 or fewer columns When the data that you are planning to present is peripheral to the study or irrelevant to the main study findings Dr. Ahmed Jaradat, AGU 15
Histogram: Final Grades/2013-2014 16
Frequency Polygon Dr. Ahmed Jaradat, AGU 17
Frequency Polygon Relative Frequencies of Serum Cholesterol levels for 2294 U.S. Males, 1976-1980 Dr. Ahmed Jaradat, AGU 18
Shapes of Histogram Symmetry: A histogram is said to be symmetric, if when we draw a vertical line down the center of the histogram, the two sides are identical in shape and size: Variable Variable 19
Shapes of Histograms Skewness : A skewed histogram is one with a long tail extending to either the right or the left: Negatively Skewed Positively Skewed 20
Shapes of Histograms Bell Shape: A special type of symmetric Unimodal histogram is one that is bell shaped: Many statistical techniques require that the population be bell shaped. Drawing the histogram helps verify the shape of the population in question Bell Shaped 21
Cross-Tabulations and Scatter Diagrams Thus far we have focused on methods that are used to summarize the data for one variable at a time. Often one is interested in tabular and graphical methods that will help understand the relationship between two variables. Cross-tabulation and a scatter diagram are two methods for summarizing the data for two (or more) variables simultaneously. Cross-tabulation: is a tabular method for summarizing the data for two variables simultaneously. Cross-tabulation can be used when: Both variables are qualitative Both variables are quantitative One variable is quantitative and one is qualitative The left and top margin labels define the classes for the two variables. 22
Cross-Tabulations: Both Variables are Qualitative Distribution of 60 patients at the chest department of Al-Salmaniya hospital in May 2008 according to smoking & lung cancer Smoking Lung Cancer Positive Negative Total No. % No. % No. % Smoker 15 65.2 8 34.8 23 100 Non Smoker 5 13.5 32 86.5 37 100 Total 20 33.3 40 66.7 60 100 23
Cross-Tabulations: One Variable is Quantitative and One is Qualitative Age (Years) Sex Male Female Total 20-30 3 (12%) 2 (10%) 5 30-40 9 (36%) 6 (30%) 15 40-50 7 (8%) 5 (25%) 12 50-60 4 (16%) 3 (15%) 7 60-0 2 (8%) 4 (20%) 6 Total 25 (100%) 20 (100%) 45 24
Both Variables are Quantitative Height/cm Weight/kg <150 150-160 >160 Total < 50 50-69 70-89 90-109 110 Total 25
Scatter Diagram A scatter diagram is a graphical presentation of the relationship between two quantitative variables. One variable is shown on the horizontal axis and the other variable is shown on the vertical axis. The general pattern of the plotted points suggests the overall relationship between the variables. 26
Scatter Diagram Positive Correlation Negative Correlation No Correlation Dr. Ahmed Jaradat, AGU 27