Analysis of data

Types of Tables, Bar Graphs, Diagrams

1. ANALYSIS OF DATA POOJA GODIYAL

2. Introduction Important phase of research process Involves computation of certain measures along with searching for patterns of relationship that exists among groups 9/8/2021 POOJA GODIYAL

3. Introduction Data collection is followed by the analysis and interpretation of data, where collected data are analysed and interpreted in accordance with study objectives Analysis and interpretation of data includes compilation editing coding classification presentation of data 9/8/2021 POOJA GODIYAL

4. Definition Analysis is the process of organizing and synthesizing the data so as to answer the research questions and test hypothesis Purpose To describe the data in meaningful terms To analyze the data so that patterns of relationship can be detected 9/8/2021 POOJA GODIYAL

5. Steps of Quantitative Data Analysis Data preparation: Involves following steps Compilation: Includes gathering all the collected data and arranging it in orderly manner Editing: Involves checking the gathered data for accuracy, utility and completeness Coding: Numerous replies can be reduced to a small number of classes through coding Code is an abbreviation, a symbol, a number or an alphabet which is assigned by the researcher to every schedule item 9/8/2021 POOJA GODIYAL

6. Steps of Quantitative Data Analysis Classification: divide and arrange the entire data into the different categories, groups or classes on the basis of common characteristics Tabulation: Involves orderly arrangement of data in columns and rows 2. Describing the data: Descriptive statistics are used to describe the basic features of data and to provide simple summaries about the sample Percentage, means of central tendency and means of dispersion are the examples of descriptive statistics 9/8/2021 POOJA GODIYAL

7. Steps of Quantitative Data Analysis 3. Drawing the inferences of data: Inferential statistics helps in drawing inferences from the data For example, finding the difference, relationship and association between two more variables by the help of parametric and non parametric statistical tests 4. Interpretation of data: Refers to critical examination of the analyzed study results to draw inferences and conclusions 9/8/2021 POOJA GODIYAL

8. SCALES OF MEASUREMENTS Measurement is the assignment of numbers to objects according to specific rules, to characterize quantities of attribute There are four level of measurements: Nominal measurement Ordinal measurement Interval measurement Ratio measurement 9/8/2021 POOJA GODIYAL

9. PROPERTIES OF MEASUREMENT SCALE Identity: Each value on the measurement scale has a unique meaning Magnitude: Value on the measurement scale have an ordered relationship to one another. That is some values are larger and some are smaller Equal intervals: Scale units along the scale are equal to one another. This means, for example, that the difference between 1 and 2 would be equal to the difference between 19 and 20 A minimum value of zero: the scale has a true zero point, below which no values exist 9/8/2021 POOJA GODIYAL

10. NOMINAL LEVEL MEASUREMENT Lowest of the four levels of measurement Only satisfies the identity property of measurement Consists of categories that are not more or less than each other but are different from one another in some way They have no quantitative values For example: Gender: Male, Female Habitat: Urban, Rural, Slums 9/8/2021 POOJA GODIYAL

11. ORDINAL LEVEL MEASUREMENT Has the property of both identity and magnitude Each value on the ordinal scale has a unique meaning, and it has an ordered relationship to every other value on the scale Rank objects based on their relative standing on a specific attribute For example: Health status: Poor, Fair,Good Income status: Low income, Middle income, Upper income Central tendency: Median 9/8/2021 POOJA GODIYAL

12. INTERVAL LEVEL MEASUREMENT Has the property of identity, magnitude and equal intervals There is more or less, equal numerical distance between intervals For example: Fahrenheit scale to measure temperature This scale is made up of equal temperature units, so that the difference between 40 and 50 degrees Fahrenheit is equal to the difference between 50 and 60 degrees Fahrenheit With an interval scale, you know not only whether different values are bigger or smaller, you also know how much bigger or smaller they are 9/8/2021 POOJA GODIYAL

13. INTERVAL LEVEL MEASUREMENT For example, suppose it is 60 degrees Fahrenheit on Monday and 70 degrees on Tuesday. You know not only that it was hotter on Tuesday, you also know that it was 10 degrees hotter Central tendency: 9/8/2021 POOJA GODIYAL

14. RATIO LEVEL MEASUREMENT It is the highest level of measurement Satisfies all four properties of measurement For example: Each value on the weight scale has a unique meaning, weights can be rank ordered, units along the weight scale are equal to one another, and the scale has a minimum value of zero Weight scale have a minimum value of zero because objects at rest can be weightless, but they cannot have negative weight Central tendency: 9/8/2021 POOJA GODIYAL

15. Solve the problem Which of the following measurement properties is satisfied by the centigrade scale? 1. Magnitude 2. Equal intervals 3. A minimum value of zero 1 only 2 only 3 only 1 and 2 only 2 and 3 only 9/8/2021 POOJA GODIYAL

16. DESCRIPTIVE STATISTICS Used to organize and summarize the data to draw meaningful interpretations Classification Measures to condense data Frequency and percentage distribution Tabulation Graphic presentations 9/8/2021 POOJA GODIYAL

17. DESCRIPTIVE STATISTICS Measures of central tendency Measures of dispersion Measures of relationship (correlation coefficient) 9/8/2021 POOJA GODIYAL

18. MEASURES TO CONDENSE DATA An appropriate presentation of data involves organization of data in such a manner that meaningful conclusions and inferences can drawn to answer the research question 9/8/2021 POOJA GODIYAL

19. TABLES First step before data can be used for further statistical analysis and interpretation Tabulation means the systematic presentation of the information contained in the data in rows and columns General principles of tabulation Table should be precise, understandable and self explanatory Every table should have title Title must describe the content clearly and precisely 9/8/2021 POOJA GODIYAL

20. TABLES Items should be arranged alphabetically or according to size, importance and causal relationship to facilitate comparison The unit of measurement must be clearly stated Totals can be placed at the bottom of the column Two or three small tables are to be preferred to one large one 9/8/2021 POOJA GODIYAL

21. Parts of a table A good statistical table must contain: Table number: It should be placed at the top of the table Title: Should be brief, concise and self explanatory Subheads: Should be given below the title in a prominent type usually enclosed in brackets for further description of the content of the table 9/8/2021 POOJA GODIYAL

22. Parts of a table Caption and stubs: Captions are headings for vertical columns and stubs are the headings for horizontal rows Body of table: Arrangement of the data according to description given in the form of captions and stubs compose the body of the table Footnotes: When some characteristics cannot be adequately explained in the body of the table, footnotes are used to explain those items Source note: used when secondary data is used, to mention the source from which these data are retrieved 9/8/2021 POOJA GODIYAL

23. Types of the table Frequency Distribution Table: Presents the frequency and distribution of the information collected Table 10.1 Socio demographic profile of patients S . No. Socio demographic variables N=60 f (%) 1 Age (in years) 20 – 40 18 (30.0) 41 – 60 42 (70.0) 2 Gender Male 39 (65.0) Female 21 (35.0) 3 Marital status Married 52 (86.7) Unmarried 08 (13.3) 9/8/2021 POOJA GODIYAL

24. Types of the table Contingency Table: Tables that report on the frequency distribution of nominal variables simultaneously and that include the totals are known as contingency tables Also known as cross tables Presents frequency distribution of two or more variables to establish the relationship or association between them Tables could be 2 x 2, 2 x 3 and 3 x 3, depending on the number of variables These tables are generally used in Chi square test 9/8/2021 POOJA GODIYAL

25. Types of the table Table 10.2 Type of ventilation and daily bowel movements among patients S.No . Bowel movements Mode of ventilation N=60 f (%) χ 2 value Spontaneous ventilation f (%) Mechanical ventilation f (%) Present 391 (64.0) 32 (29.4) 423 45.87* Absent 220 (36.0) 77 (70.6) 297 Total 611 109 720 df =1 9/8/2021 POOJA GODIYAL

26. Types of the table Multiple Response Tables: When classification of the cases is to be done into categories that are neither exclusive nor exhaustive (observation cannot be beyond these categories), a multiple response table is used For example, a patient can have two or more complaints. In such cases sum total of frequencies would exceed the total number of subjects and may lead to confusion Therefore, the total number of subjects in cases of multiple responses is given as base, and from this we calculate the percentages. 9/8/2021 POOJA GODIYAL

27. Types of the table Table 10.3 Factors contributing to sleep deprivation among patients * Each patient has more than one factor S.No . Factors* N=60 f (%) 1 Blood sampling 35 (58.3) 2 Diagnostic test 33 (55.0) 3 Medication 33 (55.0) 4 Vital signs monitoring 32 (53.3) 5 Noise 32 (53.3) 6 Bright lights 30 (50.0) 9/8/2021 POOJA GODIYAL

28. Types of the table Miscellaneous tables: When the presentation of data cannot be classified under any other type These tables are used to present data other than frequency or percentage distributions such as mean, median, mode, range, standard deviation and so on 9/8/2021 POOJA GODIYAL

29. GRAPHS AND DIAGRAMS Graphical presentation of data There are certain rules to effectively present the information in the graphical representation. They are: Suitable Title: Make sure that the appropriate title is given to the graph which indicates the subject of the presentation. Measurement Unit: Mention the measurement unit in the graph. Proper Scale: To represent the data in an accurate manner, choose a proper scale. Index: Index the appropriate colours, shades, lines, design in the graphs for better understanding. Data Sources: Include the source of information wherever it is necessary at the bottom of the graph. Keep it Simple: Construct a graph in an easy way that everyone can understand. Neat: Choose the correct size, fonts, colours etc in such a way that the graph should be a visual aid for the presentation of information. 9/8/2021 POOJA GODIYAL

30. Constructing Diagrams / Graphs While constructing a diagram or graph the following points should be considered: They must have a title and an index. The proportion between width and height should be balanced Footnotes must be appropriate principal of simplicity must be kept in mind Neatness and cleanliness in construction of graph must be ensured 9/8/2021 POOJA GODIYAL

31. Types of Diagrams and Graphs Commonly used diagrams and graphs are: Bar diagram Pie chart Histogram Frequency polygon Line graphs Cumulative frequency curve Scattered diagrams Pictograms Map diagrams 9/8/2021 POOJA GODIYAL

32. BAR DIAGRAM Useful for displaying nominal and ordinal data Easy method for visual comparison of the magnitude of different frequencies The width of the bars should be uniform throughout the diagram The gap between one bar and another should be uniform throughout Bars may be vertical or horizontal 9/8/2021 POOJA GODIYAL

33. Types of Bar Diagram Simple Bar Diagram Multiple Bar Diagram Proportion bar Diagram 9/8/2021 POOJA GODIYAL

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37. Pie Diagram A pie chart is a type of graph that represents the data in the circular graph. The slices of pie show the relative size of the data. It is a type of pictorial representation of data. A pie chart requires a list of categorical variables and the numerical variables. Here, the term “pie” represents the whole, and the “slices” represent the parts of the whole. 9/8/2021 POOJA GODIYAL

38. Formula To work out with the percentage for a pie chart, follow the steps given below: Categorize the data Calculate the total Divide the categories Convert into percentages Finally, calculate the degrees Therefore, the pie chart formula is given as (Given Data/Total value of Data) × 360° 9/8/2021 POOJA GODIYAL

39. How to Create a Pie Chart? I magine a teacher surveys her class on the basis of their favourite Sports Step 1: First, Enter the data into the table. Football Hockey Cricket Basketball Badminton 10 5 5 10 10 9/8/2021 POOJA GODIYAL

40. Step 2: Add all the values in the table to get the total. i .e. Total students are 40 in this case. Step 3: Next, divide each value by the total and multiply by 100 to get a per cent: Football Hockey Cricket Basketball Badminton (10/40) × 100 =25% (5/ 40) × 100 =12.5% (5/40) ×100 =12.5% (10/ 40) ×100 =25% (10/40)× 100 =25% 9/8/2021 POOJA GODIYAL

41. Step 4: Next to know how many degrees for each “pie sector” we need, we will take a full circle of 360° and follow the calculations below: The central angle of each component = (Value of each component/sum of values of all the components)✕360° Now you can draw a pie chart. Football Hockey Cricket Basketball Badminton (10/40) × 360° =90° (5/ 40) × 360° =45° (5/40) × 360° =45° (10/ 40) × 360° =90° (10/40) × 360° =90° 9/8/2021 POOJA GODIYAL

42. Step 5: Draw a circle and use the protractor to measure the degree of each sector. 9/8/2021 POOJA GODIYAL

43. Histogram A histogram is a graphical representation of a grouped frequency distribution with continuous classes H istogram is a diagram involving rectangles whose area is proportional to the frequency of a variable and width is equal to the class interval. 9/8/2021 POOJA GODIYAL

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45. How to Make Histogram? You need to follow the below steps to construct a histogram. Begin by marking the class intervals on the X-axis and frequencies on the Y-axis. The scales for both the axs have to be the same. Class intervals need to be exclusive. Draw rectangles with bases as class intervals and corresponding frequencies as heights. A rectangle is built on each class interval since the class limits are marked on the horizontal axis, and the frequencies are indicated on the vertical axis. The height of each rectangle is proportional to the corresponding class frequency if the intervals are equal. The area of every individual rectangle is proportional to the corresponding class frequency if the intervals are unequal. 9/8/2021 POOJA GODIYAL

46. Histogram Example Question: The following table gives the life times of 400 neon lamps. Draw the histogram for the below data. Lifetime (in hours) Number of lamps 300 – 400 14 400 – 500 56 500 – 600 60 600 – 700 86 700 – 800 74 800 – 900 62 900 – 1000 48 9/8/2021 POOJA GODIYAL

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48. Frequency Polygon A frequency polygon is almost identical to a histogram Frequency polygons are the pictorial or graphical representation of data set It is used to compare sets of data or to display a cumulative frequency distribution. Frequency polygons are a visually substantial method of representing quantitative data and its frequencies. 9/8/2021 POOJA GODIYAL

49. Steps to Draw Frequency Polygon To draw frequency polygons, first we need to draw histogram and then follow the below steps: Step 1- Choose the class interval and mark the values on the horizontal axes Step 2- Mark the mid value of each interval on the horizontal axes. Step 3- Mark the frequency of the class on the vertical axes. Step 4- Corresponding to the frequency of each class interval, mark a point at the height in the middle of the class interval Step 5- Connect these points using the line segment. Step 6- The obtained representation is a frequency polygon. 9/8/2021 POOJA GODIYAL

50. Example Example 1: In a batch of 400 students, the height of students is given in the following table. Represent it through a frequency polygon. Height (cm) No. of students (Frequency) 14 0 – 15 74 150 - 160 163 160 - 170 135 170 - 180 28 Total 400 9/8/2021 POOJA GODIYAL

51. Solution: Following steps are to be followed to construct a histogram from the given data: The heights are represented on the horizontal axes on a suitable scale as shown. The number of students is represented on the vertical axes on a suitable scale as shown. Now rectangular bars of widths equal to the class- size and the length of the bars corresponding to a frequency of the class interval is drawn. ABCDEF represents the given data graphically in form of frequency polygon as: 9/8/2021 POOJA GODIYAL

52. Frequency polygons can also be drawn independently without drawing histograms. For this, the midpoints of the class intervals known as class marks are used to plot the points. 9/8/2021 POOJA GODIYAL

53. Line Graph It is mostly used where data is collected over a long period of time On x-axis, values of independent variables are taken and values of dependent variables are taken on y-axis 9/8/2021 POOJA GODIYAL

54. Cumulative frequency curve or Ogive This graph represents the data ofa cumulative frequency distribution For drawing ogive, an ordinary frequency distribution table is converted into cumulative frequency table The cumulative frequencies are then plotted corresponding to the upper limits of the classes The points corresponding to cumulative frequency at each upper limit of the classes are joined by a free hand curve The diagram made is called Ogive 9/8/2021 POOJA GODIYAL

55. Height of 50 students Height (cm) Frequency Cumulative frequency 145 - 155 3 3 155 - 165 9 12 165 - 175 21 33 175 - 185 13 46 185 - 195 4 50 9/8/2021 POOJA GODIYAL

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57. Scattered or Dotted diagram It is a graphic presentation that shows the nature of correlation between two variable characters x and y on the similar features or characteristics E.g. height and weight in men 20yrs old 9/8/2021 POOJA GODIYAL

58. Scattered or Dotted diagram The following table gives the height and weight of 10 students in a class Height (cm) 180 150 158 165 175 163 145 195 180 155 Weight (Kg) 65 154 55 61 60 54 50 63 65 50 9/8/2021 POOJA GODIYAL

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60. Pictograms or Picture diagram This method is used to impress the frequency of the occurence of events to common people, such as attacks, deaths, number of operations, admissions, accidents etc. 9/8/2021 POOJA GODIYAL

61. Map diagram or Spot map These maps are prepared to show geographical distribution of frequency of characteristics 9/8/2021 POOJA GODIYAL