it is the best course for epidemiology and biostatics, Summaries of Mathematical Methods

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Organizing and | Displaying Data Objectives At the end of this lecture students will be familiar with: Raw data, frequency table, bar chart, pie chart, Histogram, Polygon 2 Example of raw data Table 1: Excel and SPSS 5 Name Age Sex Weight(Kg) Variable Variable Ahmad 45 M 78 Rehana 25 F 61 Kamila 56 F 55 Masod 34 M 67 Karim 45 M 82 Noria 25 F 55 Data quality  Tow type of inaccuracies  Imprecision: is the random inability to get the same result upon repetition  Bias: is a systematic deviation from the truth 6 1305 ss. ote . 120- *.s ooe _ ] * * ° 3 110- * bg a = es, ee 7 oe @ : ooree . #8 3 1004 =—-—- —- See i Cé#Fs Tee Level S ooo E oe = . a w= LJ o ho- | “4 T T T T T T T T T T a B c Ty Precise Precise Imprecise Imprecise & & Pd & unbiased biased unbiased biased 7 10 Organizing & Graphing Qualitative Data  Frequency Distributions  Relative Frequency and Percentage Distributions  Graphical Presentation of Qualitative Data  Bar Graphs  Pie Charts 11 Frequency Distributions Definition A frequency distribution for qualitative data, lists all categories and the number of elements that belong to each of the categories. 12 Example Stress on Job Tally Frequency (f) Very Somewhat None |||| |||| |||| |||| |||| |||| | 10 14 6 Sum = 30 Table 1: Frequency Distribution of Stress on Job 15 Relative Frequency & Percentage Distributions cont. Calculating Percentage Percentage = (Relative frequency) * 100 16 Example Determine the relative frequency and percentage for the data in table 1. 17 Solution Stress on Job Relative Frequency Percentage Very Somewhat None 10/30 = .333 14/30 = .467 6/30 = .200 .333(100) = 33.3 .467(100) = 46.7 .200(100) = 20.0 Sum = 1.00 Sum = 100 Table 2: Relative Frequency and Percentage Distributions of Stress on Job 20 Graphical Presentation of Qualitative Data Definition A graph made of bars whose heights represent the frequencies of respective categories is called a bar graph. 21 Bar graph for the frequency distribution of table 1 0 2 4 6 8 10 12 14 16 Very Somewhat None Strees on Job F re q u e n c y 22 Graphical Presentation of Qualitative Data cont. Definition A circle divided into portions that represent the relative frequencies or percentages of a population or a sample belonging to different categories is called a pie chart. Count the black dots! :o) + 25 26 Organizing and Graphing Quantitative Data  Frequency Distributions tables  Relative and Percentage Distributions  Graphical Presentation of Quantitative Data  Histograms  Polygons 27 Frequency Distributions Definition A frequency distribution for quantitative data, lists all the classes and the number of values that belong to each class. 30 Representing the simple frequency table using the bar chart Number of decayed teeth 5.004.003.002.001.00.00 F re q u e n c y 6 5 4 3 2 1 0 22 5 4 2 1 We can represent the above simple frequency table using the bar chart. 31 Frequency Distribution for Continuous Random Variables For large samples, we can’t use the simple frequency table to represent the data. We need to divide the data into groups or intervals or classes. So, we need to determine:  The number of interval  The range  The width of the interval 1- The number of intervals (k). Too few intervals are not good because information will be lost. Too many intervals are not helpful to summarize the data. A commonly followed rule is that 6 ≤ k ≤ 15, or the following formula may be used, k = 1 + 3.322 (log n) 32 Example: Assume that the number of observations equal 100, then k = 1+3.322(log 100) = 1 + 3.3222 (2) = 7.6  8. Assume that the smallest value = 5 and the largest one of the data = 61, then R = 61 – 5 = 56 and w = 56 / 8 = 7. 35 36 Example:  We wish to know how many class interval to have in the frequency distribution of a data on ages of 189 subjects who Participated in a study on smoking cessation  Solution :Since the number of observations equal 189, then  k = 1+3.322(log 189) = 1 + 3.3222 (2.276)  9,  R = 82 – 30 = 52 and  w = 52 / 9 = 5.778  It is better to let w = 10 37 FrequencyClass interval 1130 – 39 4640 – 49 7050 – 59 4560 – 69 1670 – 79 180 – 89 189Total Sum of frequency =sample size=n 40 Graphical Presentation of Quantitative Data. Definition A histogram is a graph in which classes are marked on the horizontal axis and the frequencies, relative frequencies, or percentages are marked on the vertical axis. The frequencies, relative frequencies, or percentages are represented by the heights of the bars. In a histogram, the bars are drawn adjacent to each other. Frequency histogram 0 10 20 30 40 50 60 70 80 34.5 44.5 54.5 64.5 74.5 84.5 41 42 Shapes of histograms 1. Symmetric 2. Skewed 3. Uniform or rectangular 4 A histogram with uniform distribution. 45 46 Graphical Presentation of Quantitative Data Cont. Definition A graph formed by joining the midpoints of the tops of successive bars in a histogram with straight lines is called a polygon. It is particularly useful when comparing two or more frequencies. 47 Frequency polygon 0 10 20 30 40 50 60 70 80 34.5 44.5 54.5 64.5 74.5 84.5 4 Line Graph 450 400 350 300 250 200 150 100 50 Number of cases of X disease in Someland between 1983 - 1992 51 Cumulative Frequency Distributions Definition A cumulative frequency distribution gives the total number of values that fall below the upper boundary of each class. 52 Cumulative Frequency Distributions cont. Calculating Cumulative Relative Frequency and Cumulative Percentage 100 frequency) relative e(Cumulativ percentage Cumulative set data in the nsobservatio Total class a offrequency Cumulative frequency relative Cumulative   55 Solution Vehicles Owned Number of Households (f) 0 1 2 3 4 5 2 18 11 4 3 2 Σf = 40 Frequency Distribution of Vehicles Owned 56 Bar graph for example vehicles owned 0 2 4 6 8 10 12 14 16 18 20 No Car 1 Car 2 Cars 3 Cars 4 Cars 5 Cars Vehicles owned F re q u e n c y 57 Ogive for the cumulative frequency distribution 123.5 145.5 167.5 189.5 211.5 233.5 30 25 20 15 10 5C u m u la ti v e f re q u e n c y 255 & e £ & = . = 60 Favorite Type of Movie  41 Federal Assistance Programs 35 34 ig_ 12 24 r 12 132 @ Dept of Health and Human Services Bi Dept of Agriculture m Dept of the Interior Dept of Education Dept of Justice @ Dept of Housing and Urban Development M Environmental Protection Agency Dept of Commerce @ Dept of Homeland Security mw Dept of Transportation i Dept of Defense @ Deptof Labor Mi Dept of Veterans Affairs @ Dept of Energy m Dept of State 62