Research methodology & Biostatistics

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  • Snow ball study
  • Research methodology & Biostatistics

    1. 1. RESEARCH METHODOLOGY & BIOSTATISTICS* Few jewels from ocean Dr. Kusum Gaur Professor, PSM WHO Fellow IEC
    2. 2. Definition of Research“Research is a systematized effort to gain new knowledge”.12/08/2012 Dr. Kusum Gaur 2
    3. 3. Steps in Research (Holy 11) 1. Collect review of literature/Situation Analysis 2. Identify and prioritize health problems 3. Decide aims & objectives 4. Planning Methodology 5. Execution 6. Compilation, Classification & Presentation of data 7. Analysis 8. Test of Significance/Test of Hypothesis 9. Inferences 10. Report Writing 11. Dissemination of Report12/08/2012 Dr. Kusum Gaur 3
    4. 4. Process of Concluding 8 7 6 Reporting Inferences Analysis Data Collection 5 Execution Execution Research Problem Define 1 for Pretest Collection Data Review of Literature Methodology 4 2 3 Planning12/08/2012 Dr. Kusum Gaur 4
    5. 5. STEP-1 DEFINITION OF THE RESEARCH PROBLEM12/08/2012 Dr. Kusum Gaur 5
    6. 6. RESEARCH PROBLEM ? Research Problem refers to some difficulty which a researcher experiences and wants to obtain a solution for the same. i.e. a question or issue to be examined.12/08/2012 Dr. Kusum Gaur 6
    7. 7. Process of Defining Problem Analysis of the Situation Identify & Prioritize Problems Select & Define Problem Statement of Research Objectives12/08/2012 Dr. Kusum Gaur 7
    8. 8. CRITERIA OF SELECTION The selection of one appropriate researchable problem out of the identified problems requires evaluation of certain criteria. * Internal / Personal criteria – Researcher‟s side * External Criteria – Problem side factors12/08/2012 Dr. Kusum Gaur 8
    9. 9. INTERNAL CRITERIA OF SELECTION  Researcher‟s Interest,  Researcher‟s Competence,  Researcher‟s own Resource:  Human Resource  Money  Material  Time12/08/2012 Dr. Kusum Gaur 9
    10. 10. EXTERNAL CRITERIA OF SELECTION  Researchability of the problem,  Importance and Urgency,  Novelty of the Problem,  Feasibility,  Facilities,  Social Relevance  Public health Importance12/08/2012 Dr. Kusum Gaur 10
    11. 11. DEFINE RESEARCH PROBLEM (Title of the Research Topic) Transforming the selected research problem into a scientifically researchable statement. Problem definition or Problem statement should be clear, precise, self-explanatory and include:-  What  How  When  Where12/08/2012 Dr. Kusum Gaur 11
    12. 12. RESEARCH OBJECTIVES (Objectives) Research Objectives are the statement of the questions that is to be investigated with the goal of answering the overall research problem. Research Objectives should be clear and achievable. Generally, they are written as statements, using the word “to” (For example, „to discover …‟, „to determine …‟, „to establish …‟, „to find out -----‟, „to assess -----‟etc. ) Objectives should infer in the end of the study12/08/2012 Dr. Kusum Gaur 12
    13. 13. Hypothetical Research Question  Problem: PCR of Diabetes Mellitus is increasing very fast during last five year  Mission: Reduce the incidence of heart disease  Belief: Meditation is good to reduce stress which is an important precursor of DM  Hypothesis H- Meditation decreases the risk of DM12/08/2012 Dr. Kusum Gaur 13
    14. 14. Association of Garlic consumption with coronary Artery DiseasesAim: To Study the association of Meditation with Diabetes Mellitus in patients attending at Medical OPD of SMS Hospital, Jaipur (Raj) India.Objectives:1. To assess and compare the proportion of DM cases in individuals doing regular meditation and not doing meditation.2. To find out the risk ratio of DM in individuals not doing meditation on doing regular meditation.
    15. 15. STEP-2 REVIEW OF LITERATURE12/08/2012 Dr. Kusum Gaur 15
    16. 16. Review of literature What ? Why ? Where ?12/08/2012 Dr. Kusum Gaur 16
    17. 17. What ? REVIEW OF LITERATURE Literature Review is the documentation of a published and unpublished work from secondary sources of datain the areas of specific interest to the researcher. 12/08/2012 Dr. Kusum Gaur 17
    18. 18. Why ? - PURPOSE OF REVIEW Tofind out already investigated problems and those that need further investigation. To formulate researchable hypothesis. To gain a background knowledge To identify data sources To learn how others structured their reports. 12/08/2012 Dr. Kusum Gaur 18
    19. 19. Where ? SOURCES OF LITERATURE  Books and Journals  Databases Bibliographic Databases Abstract Databases Full-Text Databases  Govt. and NGO Records & Reports  Internet  On line journals: ww.articalbase.com …….  E. Databases – Popline, Medline …….  Research Dissertations / Thesis12/08/2012 Dr. Kusum Gaur 19
    20. 20. Step-3Methodology
    21. 21. Methodology  Study Area : Location of study - Hospital, community etc.  Study Period: Start to end of Study (maximum period available for study should be defined)  *Selection of Study Design  * Selection of Study Population  Pre-requisits of study: Study Tools, Terminologies, Orientation trainings etc. *will be taken separately12/08/2012 Dr. Kusum Gaur 21
    22. 22. Methodology……• Study Tools for data collection: subjects, proforma, examination, measurements, lab investigations• Planning  Data collection, compilation, data entry  Data cleaning  Analysis plan:• Confidentiality• Ethical clearance: Consent from  Institutional Review Board  Observational units12/08/2012 Dr. Kusum Gaur 22
    23. 23. Study Design A study design is a specific plan or protocol for conducting the study, which allows the investigator to translate the conceptual hypothesis into an operational one.12/08/2012 Dr. Kusum Gaur 23
    24. 24. Direction of StudyBackward Forward Cross -sectionalRetrospective Prospective 3 4. Ambidirectional 12/08/2012 Dr. Kusum Gaur 24
    25. 25. Decision Tree Intervention Done No Yes Observational Study Experimental Study Comparison Group Randomization No Yes No YesDescriptive Study Analytic Study NRCT Study RCT Study Direction of StudyE O E OCohort Study E = O Case-Control Study Cross-Sectional Study 12/08/2012 Dr. Kusum Gaur 25
    26. 26. Epidemiological Study Design Observational Studies  Descriptive Studies Analytic Cross-Sectional Case-Control Cohort Experimental / Interventional studies As per Control: RCT/NRCT As per Blinding: Single /Double Blind As per Design: Simple/Cross-over As per Area: Field/Clinical/Lab12/08/2012 Dr. Kusum Gaur 26
    27. 27. Descriptive Studies • Case reports • Case series • Population studies12/08/2012 Dr. Kusum Gaur 27
    28. 28. Descriptive Studies: Uses • Hypothesis generating • Suggesting associations12/08/2012 Dr. Kusum Gaur 28
    29. 29. Descriptive Type of Observational Study• Other Name Case-Series/Population• Unit of Study Case/Individuals• Study Question What is happening • Direction Of Inquiry• Study Design desired information about cases/individuals is collected12/08/2012 Dr. Kusum Gaur 29
    30. 30. Case-Series ……. Advantages• Easy to do• Excellent at identifying unusual situation• Good for generating hypotheses Disadvantages• Generally short-term• Investigators self-select (bias!)• no controls09/03/2010 Dr. Kusum Gaur 30
    31. 31. Analytical Observational Studies • Cross-sectional • Case-control • Cohort12/08/2012 Dr. Kusum Gaur 31
    32. 32. Cross-sectional Study • Data collected at a single point in time • Describes associations • Prevalence A “Snapshot”12/08/2012 Dr. Kusum Gaur 32
    33. 33. Cross-Sectional Study• Other Name Prevalence Study• Unit of Study Individual• Study Question What is happening • Direction of Inquiry• Study Design Exposed to Factor Not  Exposed Diseased to Factor Population Exposed to  Factor Non- Disease Not Exposed to12/08/2012 Dr. Kusum Gaur Factor 33
    34. 34. Objectives of a Cross-Sectional Study To find out association12/08/2012 Dr. Kusum Gaur 34
    35. 35. Cross-sectional Study Sample of Population Defined Population Regular Not doing meditation Meditation Prevalence of Prevalence of DM DM Time Frame = Present12/08/2012 Dr. Kusum Gaur 35
    36. 36. Cross-sectional StudyE.G. Out of 1000 population if 100 were doing meditation regularly &out of that only 2 were having DM. Remaining 900 were not doingmeditation at all, out of that 220 were having DM. + DM - 2 98 Meditation + - 220 68012/08/2012 Dr. Kusum Gaur 36
    37. 37. Cross-Sectional Study • Strengths – Quick – Cheap • Weaknesses – Cannot establish cause-effect09/03/2010 Dr. Kusum Gaur 37
    38. 38. Case-Control Studies  Start with people who have disease(Cases)  Match them with controls that do not have disease (Match Confounding)  Look back and assess exposures12/08/2012 Dr. Kusum Gaur 38
    39. 39. Controls A control is a standard of comparison (confounded with variability but without effect) for • Effects • Variability12/08/2012 Dr. Kusum Gaur 39
    40. 40. Case-Control Study• Other Name Retrospective Study• Unit of Study Cases/Control• Study Question What has happened • Direction of Inquiry= F O• Study Design Exposed  Cases Not Exposed Exposed Control Not Exposed12/08/2012 Dr. Kusum Gaur 40
    41. 41. Objective of a Case-Control Study To find out association To assess Risk Ratio12/08/2012 Dr. Kusum Gaur 41
    42. 42. Case-Control Study Cases Regular Meditation Patients with DM No Meditation Controls Regular Meditation Persons w/o DM No Meditation Past Present12/08/2012 Dr. Kusum Gaur 42
    43. 43. The logic of Case-Control StudiesCases differ from controls only in having the diseaseIf exposure does not predispose to having the disease, then exposure should be equally distributed between the cases and controls. The extent of greater previous exposure among the cases reflects the increased risk that exposure confers12/08/2012 Dr. Kusum Gaur 43
    44. 44. Case-Control Studies: Strengths• Good for rare outcomes: cancer• Can examine relation of exposures to disease• Useful to generate hypothesis• Fast• Cheap• Provides Odds Ratio 09/03/2010 Dr. Kusum Gaur 44
    45. 45. Case-Control Studies: Weaknesses • Cannot measure – Incidence – Prevalence – Relative Risk • Can only study one outcome • High susceptibility to bias09/03/2010 Dr. Kusum Gaur 45
    46. 46. Cohort Study • Begin with disease-free individuals • Classify patients as exposed/unexposed • Record outcomes in both groups • Compare outcomes using relative risk12/08/2012 Dr. Kusum Gaur 46
    47. 47. Cohort Study• Other Name Prospective Study / Follow-up Study/Incidence Study• Unit of Study Individual• Study Question What is happening • Direction of Inquiry F O• Study Design Diseased• Exposed to Not Non Factor Diseased Cohort Cohort Diseased Not Exposed to Factor Non-Diseased12/08/2012 Dr. Kusum Gaur 47
    48. 48. Logic of Cohort StudyCohort is a group of persons sharing a common characteristicsDifferences in the rate at which exposed and control subjects contract a disease is due to the differences in exposure, since others are known and similar.12/08/2012 Dr. Kusum Gaur 48
    49. 49. Cohort Study Prospective (usually) Controlled Can determine causes and incidence of diseases as well as identify risk factors Generally expensive, time consuming and difficult to carry out12/08/2012 Dr. Kusum Gaur 49
    50. 50. Steps for Cohort Study Identify geographically defined group Identify exposed subjects and not exposed subjects Follow over a specific time Record the fraction in each group who develop the condition of interest Compare these fractions using RR, AR or OR12/08/2012 Dr. Kusum Gaur 50
    51. 51. Objectives of a Cohort Study  To find out association  To assess Risk Ratio  To find out Relative Risk  To find out Attributed Risk12/08/2012 Dr. Kusum Gaur 51
    52. 52. Prospective Cohort Study DMNo Meditation No DM Cohort DMRegularMeditation No DM Present Future12/08/2012 Dr. Kusum Gaur 52
    53. 53. Cohort Study: Strengths • Can measure multiple outcomes • Can adjust for confounding variables • Can calculate Attributed Risk09/03/2010 Dr. Kusum Gaur 53
    54. 54. Cohort Study: Weaknesses • Expensive • Time consuming • Cannot study rare outcomes • Confounding variables09/03/2010 Dr. Kusum Gaur 54
    55. 55. Measurements of association Cohort Study Case Control Study •Significance Test •Significance Test •Relative Risk •OR •Attributable Risk •OR12/08/2012 Dr. Kusum Gaur 55
    56. 56. Measures of Association Significance Test – to test significance of difference in exposure between control and Cases Odds ratio - ratio of the odds of contracting disease in given exposure Relative Risk – Ratio between incidence among exposed and incidence among non- exposed Attributed Risk – percentage of difference between incidence among exposed and non- exposed with incidence among exposed RR or OR of 1 indicate no effect of exposure (equal odds)12/08/2012 Dr. Kusum Gaur 56
    57. 57. ‘Z’ Score of Exposure Rates Cases control Exposed a b a x 100Exposure Rates = in Cases Non- c d exposed(P2) a+c b x 100Exposure Rates = in Controls P2 – P1(P1) b+d Z Score = SEDP P1 Q 1 P 2 Q 2 SEDP = ------------- + -------- 09/03/2010 Dr. Kusum Gaur 57 N1 N2
    58. 58. ad ODD‟s Ratio = Times bc Incidence among Exposed RR = Times Incidence among Non-Exposed a/a+b a (c+d) = = c/c+d c (a+b)09/03/2010 Dr. Kusum Gaur 58
    59. 59. Attributed Risk (Incidence among Exposed - Incidence among Non-Exposed) AR = x 100 Incidence among Exposed a Incidence among Exposed= x 100 a+b c Incidence among Non-Exposed= x 100 c+d09/03/2010 Dr. Kusum Gaur 59
    60. 60. Experimental Studies Clinical trials provide the “gold standard” of determining the relationship between factor and the event12/08/2012 Dr. Kusum Gaur 60
    61. 61. Types of Experimental StudyAs per Randomization: • Randomized Control Trials (RCT) • Concurrent Parallel Design (RCT) • Sequential RCT Design • RCT with External Control • Non – Randomized Trials (NRCT)12/08/2012 Dr. Kusum Gaur 61
    62. 62. Types of Experimental Study….As per Design: • Simple • Cross-Over Study DesignAs per Study Area: • Field Trials • Clinical Trials • Lab. Trials 12/08/2012 Dr. Kusum Gaur 62
    63. 63. Quality of Experimental Study • Randomization • Blinding • Control • Cross-Over12/08/2012 Dr. Kusum Gaur 63
    64. 64. Controls in Clinical Trials A clinical trial is a comparative, prospective experiment conducted in human subjects• Historical controls are better than no controls• Patients can serve as own controls - This is usually beneficial as the comparison removes patient differences12/08/2012 Dr. Kusum Gaur 64
    65. 65. Blinding Good practice: factors that can affect the evaluation of outcome should not be permitted to influence the evaluation process Single-blind Patient or evaluator (either of one) is blinded as to intervention Double-blind design Neither patient nor outcome evaluator knows Rx to which patient was assigned12/08/2012 Dr. Kusum Gaur 65
    66. 66. Randomized Control Trials (RCT)• Before and After Comparison• Comparison with Placebo• Comparison Of two medicine/procedure/tests• Comparison Of > two medicine/procedure/tests12/08/2012 Dr. Kusum Gaur 66
    67. 67. Experimental Study• Other Name Intervention Study• Objective To know the effect of intervention• Unit of Study Individual meeting entry criteria• Study Question What is happening after intervention in both groups • Direction of Inquiry I E• Study Design 1(Intervention with Placebo) Positive Outcome Group 1/cases Intervention Negative Outcome Positive Outcome Group Placebo 2/control Negative Outcome12/08/2012 Dr. Kusum Gaur 67
    68. 68. Clinical Trial R Treatment a Outcomes Group n d Study o Population m i z Outcomes e Control Group12/08/2012 Dr. Kusum Gaur 68
    69. 69. Intervention Study - Design 2 (Comparison of Effect of Two Interventions) Cases Meeting Entry criteria Group - 1 Group -2 Intervention -1 Intervention Intervention - 2 Positive Negative Positive Outcome Negative Outcome Outcome Outcome12/08/2012 Dr. Kusum Gaur 69
    70. 70. Cross Over Design Group -1 Cases Group-2 Meeting Entry criteria Intervention - 2 Intervention - 1 Positive Negative Positive Negative Outcome Outcome Outcome Outcome Group -1 Group -2 Crossover Intervention -2 Intervention -1 Positive NegativePositive Negative Outcome Outcome OutcomeOutcome 12/08/2012 Dr. Kusum Gaur 70
    71. 71. Other Types of Experimental Study • Quincy Experimental Study • Block Experimental Study12/08/2012 Dr. Kusum Gaur 71
    72. 72. Quincy Experimental Study Cases Meeting Entry criteria Group - 1 Group -2 Intervention Intervention No Intervention Positive Negative Positive Outcome Negative Outcome Outcome Outcome12/08/2012 Dr. Kusum Gaur 72
    73. 73. Block Experimental Study Cases Meeting Entry criteria Group -3 Group - 1 Group -2 Intervention Intervention-3 Intervention -1 Intervention Intervention-2Positive Positive Negative NegativeOutcome Outcome Outcome Outcome Positive Negative Outcome Outcome 12/08/2012 Dr. Kusum Gaur 73
    74. 74. Steps of Experimental Study Drawing up a Protocol Reference Population Sample Population Exclusions Randomization Experimental Group Control Group Manipulation/Intervention Follow - up12/08/2012 Assessment of Outcome Dr. Kusum Gaur 74
    75. 75. Ideal Study Design for established causality Ethical Issues
    76. 76. STUDY QUESTIONS AND APPROPRIATE DESIGNS Type of Question Appropriate Study Design Burden of illness Field Surveys - Prevalence Cross Sectional Survey - Incidence Longitudinal survey Causation, Risk & Prognosis Case Control Study, Cohort study, RCT Treatment Efficacy Randomized Controlled study Diagnostic Test Evaluation Randomized Controlled study Cost Effectiveness Randomized Controlled study12/08/2012 Dr. Kusum Gaur 76
    77. 77. Hierarchy of Epidemiological Study Design Establish Causality RCT Cohort Case Control Cross-Sectional Case SeriesGenerate Hypothesis Case Report12/08/2012 Dr. Kusum Gaur 77
    78. 78. Methodology  Study Area : Location of study - Hospital, community etc.  Study Period: Start to end of Study (maximum period available for study should be defined)  *Selection of Study Design  * Selection of Study Population Sample Size Sampling Technique  Pre-requisits of study: Study Tools, Terminologies, Orientation trainings etc.12/08/2012 Dr. Kusum Gaur 78
    79. 79. Selection of study population Whole Population Sample Population12/08/2012 Dr. Kusum Gaur 79
    80. 80. What is Sample ?• A sample is a small representative segment of a population• Inferences drawn from a sample are expected to be applicable for the source population12/08/2012 Dr. Kusum Gaur 80
    81. 81. Why do we need a sample? To get inferences applicable to universe with minimum resources12/08/2012 Dr. Kusum Gaur 81
    82. 82. Sample – Qualities Sample is a part of population but it is true representative of whole. Qualities Adequate size Appropriate sampling technique12/08/2012 Dr. Kusum Gaur 82
    83. 83. Factors on which SAMPLE SIZE depend:• Population Factors – Type of information available• Type of study – Type of Data – Type of study design – Type of sampling – Type of Statistical Analysis for outcome needed• Determined values of research by researcher – Power – Significance level 12/08/2012 Dr. Kusum Gaur 83
    84. 84. Power: Ability to detect right answerAlpha Error: Chance to miss right answer
    85. 85. Type of Data & level of Measurements Qualitative – Counted Facts – Nominal Data Measured as Numbers expressed as proportions Quantitative- Measured Facts - Numerical Data Measured as quantity & expressed as Mean SD *Ordinal Data – Rank Order Data Measured as rank & expressed as Median Percentile12/08/2012 Dr. Kusum Gaur 91
    86. 86. Sample size for Qualitative data Z 2 PQ 4 PQ Sample Size= ------------------- -- = ------------------ L2 L2 P= Prevalence of disease Q = 100-P L = allowable error Z= 1.96 ≈ 2 for 95% CL for descriptive/case-series type of study design09/03/2010 Dr. Kusum Gaur 92
    87. 87. Sample size for Quantitative data Z 2 SD 2 4 SD 2 Sample Size= ------------------- -- =---------------------- L2 L2 SD= Standard Deviation L = allowable error Z= 1.96 ≈ 2 for 95% CL For Descriptive Studies only09/03/2010 Dr. Kusum Gaur 94
    88. 88. Finite CorrectionSample Size – Finite Population (where the population is less than 50,000) SSNew SS = _________________ ( 1 + ( SS – 1 ))Pop
    89. 89. How many controls? n k Here n0=No. of cases & 2n0  n n = expected no. of cases• k = 13 / (2*11 – 13) = 13 / 9 = 1.44• kn0 = 1.44*11 ≈ 16 controls (and 11 cases) – Same precision as 13 controls and 13 cases
    90. 90. Sampling Design factors of sample size Variance of Specified SamplingDesign Effect = Variance of Simple Random Sampling12/08/2012 Dr. Kusum Gaur 97
    91. 91. Sampling Technique effect on Sample Size Sampling Technique Design Effect Size Multiplier Simple Random Sampling 1 Systemic Random Sampling 1.2 Stratified Random Sampling 0.8 Cluster Random Sampling 2 12/08/2012 Dr. Kusum Gaur 98
    92. 92. Conventionally accepted Researcher’s Estimations Alpha Error 0.05 Power 80% Confidence Limit 95%12/08/2012 Dr. Kusum Gaur 99
    93. 93. Key Concepts: Sample size• Sampling Design - larger sample for Custer• Desired Power – more power for larger sample• Allowable error – smaller error for larger sample• Heterogeneity leads to have larger sample to cover diversities• Nature of Analysis – Complex multivariate needs larger sample 12/08/2012 Dr. Kusum Gaur 100
    94. 94. Steps -Sample Size Estimation • Stage 1- * Base Sample Size Calculation (n) • Stage 2 – Sample Size with Design Effect (d) =n*d • Stage 3- Contingency Addition (e.g. 5%) SS Estimation for study population =(n*d)+5%of n *Use appropriate equation for sample size calculation http://stat.ubc.ca/~rollin/stats/ssize/12/08/2012 Dr. Kusum Gaur 101
    95. 95. E.G. Mean 1= 5, Mean 2 = 15 & SD = 14 inputting values
    96. 96. 12/08/2012 Dr. Kusum Gaur 107
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    100. 100. 12/08/2012 Dr. Kusum Gaur 111
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    102. 102. SAMPLINGTECHNIQUES
    103. 103. SAMPLING TECHNIQUES• PROBABILITY/RANDOM SAMPLING• NONPROBABILITY SAMPLING12/08/2012 Dr. Kusum Gaur 119
    104. 104. Random sampling Techniques Aim is to give equal chance to every observation unit to be selected for study in sample.(Any Observation unit should not have Zero Probability ) 12/08/2012 Dr. Kusum Gaur 120
    105. 105. * Random Sampling TechniquesSimple Random Technique Systemic Random Technique Stratified Random Technique Multiphase Random Technique Multistage Random Technique Cluster Random Technique 12/08/2012 Dr. Kusum Gaur 121
    106. 106. Simple Random Technique • Lottery Method • Random Table Method12/08/2012 Dr. Kusum Gaur 122
    107. 107. 12/08/2012 Dr. Kusum Gaur 123
    108. 108. Steps –Use of Random Table• Stage 1- Give number to each member of population• Stage 2 – Determine total population size (N)• Stage 3- Determine Sample size (S)• Stage 4 – Drop one finger on Random Table with eyes closed• Stage 5 – Drop one finger with eyes closed on direction to be chosen – Up/Down/Rt/Lt• Stage 6- Determine first number within 0 to N• Stage 7- * Determine other numbers till Sample size (S)* Once a number is chosen do not repeat it again 12/08/2012 Dr. Kusum Gaur 124
    109. 109. Steps –Use of Random Table..e.g. N=300, M=50Random no. Selected no. (3 digits from 0-300)494684969914043 04315013 0131260033122 12294169 1698991674169 16932007 007www.evaluation wikiog/index/how_to_use_a_random_number_Table 12/08/2012 Dr. Kusum Gaur 125
    110. 110. Systemic Random TechniqueThe selection of sample follows a systematic interval of selection• Find serial interval (K) = total population/sample size• 1st observation through simple random sampling among 1to K. th• Next observation = (1st +K) Observation• Next observation = (2 nd +K)th Observation• -------------so on till No. of observations = Sample Size12/08/2012 Dr. Kusum Gaur 126
    111. 111. Systemic Random Technique PopulationN=100 (Given) 1 21 41 61 81 2 22 42 62 82S=20 (Estimated) 3 23 43 63 83K=N/S =100/20 =5 4 24 44 64 84 5 25 45 65 851st observation between 1 to 5 6 26 46 66 86 7 27 47 67 87 though SRS e.g. 3 8 28 48 68 88Every 5th observation from 3rd 9 29 49 69 89 10 30 50 70 90 observation will be included in 11 31 51 71 91 sample population 12 32 52 72 92 13 33 53 73 93So, sample population will be – 3rd 14 34 54 74 94 8th 13th 18th 23rd 28th 33rd 38th 15 35 55 75 95 16 36 56 76 96 43rd 48th 53rd 58th 63rd 68th 73rd 17 37 57 77 97 78th 83rd 88th 93rd and 98th 18 38 58 78 98 19 39 59 79 99 observation 20 40 60 80 100 12/08/2012 Dr. Kusum Gaur 127
    112. 112. Stratified Random Technique Sample selection through Simple Random/Systemic Random Technique Sample Strata 1 Sample Strata 2 Sample Strata 312/08/2012 Dr. Kusum Gaur 128
    113. 113. Multiphase Random Technique Specific test Screening Test S/SPopulation Probable cases Cases Suspected cases For study12/08/2012 Dr. Kusum Gaur 129
    114. 114. Multistage Random TechniqueEach stage Simple RT is used village district village village State 1 district Population village Study Of Population Nation village district village State 2 village district village12/08/2012 Dr. Kusum Gaur 130
    115. 115. Cluster Random TechniqueThe unit of random selection is a cluster rather than individual• CI = Total population /30 (in 30 Cluster Technique) Cluster 1 Cluster 27 Cluster 2 Cluster 28 Population Study Of Population Nation Cluster 3 Cluster 29 Cluster 30 Cluster 4 Through Simple RT12/08/2012 Dr. Kusum Gaur 131
    116. 116. Stratified Vs Cluster Technique Stratified Technique Cluster Technique• Homogenous groups • Comparable groups of are made population are made• Randomly select (usually 30) sample from each • Randomly select group sample from each• To make it more truly group representative, take sample population • More chances of error proportion to size (PPS) than simple random• Less chances of error than simple random
    117. 117. Non Probability Sampling • When random samples are not possible • Rare disease • Small population • Special population • Special Condition • Difficult to reach population12/08/2012 Dr. Kusum Gaur 133
    118. 118. Non-probability Samples Convenience  Purposive  Quota  Snow ball study12/08/2012 Dr. Kusum Gaur 134
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    122. 122. Snow ball samplingContact tracingInitial respondent helps in recruiting new populationUseful in network analysis approach12/08/2012 Dr. Kusum Gaur 138
    123. 123. Step-4 & 5 Data Collection andData Management
    124. 124. Sources of Data• Primary –Own generated data• Secondary –Already generated data Published Non-Published12/08/2012 Dr. Kusum Gaur 140
    125. 125. Primary Vs Secondary source of Data Primary data Secondary data• Need to be generated • Readily available• First hand information • Second hand information• Questionnaire • Not need of questionnaire• Purpose served • Purpose served ?• Analysis as per purpose• Require more time and • Descriptive money • Less expensive 12/08/2012 Dr. Kusum Gaur 141
    126. 126. Type of Data Collection MethodsInterview Personnel TelephonicObservationExperimentalInterview and ObservationObservation and ExperimentalInterview ,Observation and Experimental12/08/2012 Dr. Kusum Gaur 142
    127. 127. Forms of questions(Open Vs Closed) Open ended Close ended• Possible responses are • Categories are given not given. already coded• Mean, SD, Median • Proportion• For seeking opinions, • For eliciting factual attitudes ,perceptions information • Not so depth• Provides in depth info. • Investigator‟s bias• Experience of • Ease of answering, investigator and • Easy to analyse analyst required12/08/2012 Dr. Kusum Gaur 143
    128. 128. Considerations in formulating questionnaire (Questionnaire/Interview schedule)  Use simple and everyday language  Do not use ambiguous questions(?/?)  Do not ask leading questions  The order of questions:  Guideline for filling an instrument, pen-pencil Pre testing 12/08/2012 Dr. Kusum Gaur 144
    129. 129. Validity of a Research InstrumentAbility of an instrument to measure what it isdesigned to measure being measured Establish the logical link between the questions and objectives  Items/questions cover the full range of issue/attitude being measured 12/08/2012 Dr. Kusum Gaur 145
    130. 130. 1.Decide the information required. Steps 2. Define the target respondents. 3. Method(s) of reaching target 4. Decide on question content. 5. Develop the question wording. 6. Put questions into a meaningful order. 7. Check the length of the questionnaire. 8. Pre-test the questionnaire. 9. Develop the final survey form 12/08/2012 Dr. Kusum Gaur 146
    131. 131. Organization and Compilation of Data Organization and Compilation of Data in such a way (Master Chart ) to have reliable, relevant, adequate and reasonably complete data with following requisites – Simplicity Briefness Utility Distinctively Comparability Scientific Arrangement Attractive 12/08/2012 Effective Dr. Kusum Gaur 147
    132. 132. Observations
    133. 133. Steps of Observations • Entry of Observations Unites • Master Chart • Tabulation • Diagrammatic Presentation12/08/2012 Dr. Kusum Gaur 149
    134. 134. Entry of Observation Unites
    135. 135. Master Chart
    136. 136. Grouping & Classification
    137. 137. Grouping & Classification
    138. 138. Grouping & Classification
    139. 139. Grouping & Classification
    140. 140. Grouping & Classification
    141. 141. Grouping & Classification
    142. 142. Grouping & Classification
    143. 143. Grouping & Classification
    144. 144. Grouping & Classification
    145. 145. Grouping & Classification
    146. 146. Grouping & Classification
    147. 147. Grouping & Classification
    148. 148. Grouping & Classification
    149. 149. Grouping & Classification
    150. 150. Grouping & Classification
    151. 151. Master Chart for Analysis
    152. 152. Tabulation – Content of Table  Table No. Sequence in the text  Tile of Table –short, clear and self explanatory to say about for what the table is ?  Body of Table –consist of rows and columns  Rows – 1st row shows headings of columns  1st column shows headings of rows  rest of rows and columns are showing data as per required  number of rows and columns should be limited to maintained simplicity of table  source of data ( if it is other than the present study ) should be written just below the body of table  Source of Data ?  Foot Note - written just below the body of table, if there is any hidden information  Inferences –summary value of table12/08/2012 Dr. Kusum Gaur 168
    153. 153. Types of Tables As per purpose General tables –about Socio-demographic profile Specific tables –about Aims and objectives As per originality Original tables-from original Data Derived tables –from original tables As per Construction Simple tables- showing one variable at one time Complex tables – showing > one variable at one time12/08/2012 Dr. Kusum Gaur 169
    154. 154. 12/08/2012 Dr. Kusum Gaur 170
    155. 155. Tabulation
    156. 156. Diagrammatic Presentations BarQualitative Data Simple Histogram Multiple Frequency Polygon Component Cumulative Frequency Pie Polygon Line Scatter Diagram Pictogram Box and Whisker Spot Map Correlation DiagramQualitative Data Quantitative Data12/08/2012 Dr. Kusum Gaur 172
    157. 157. 12/08/2012 Dr. Kusum Gaur 173
    158. 158. Diagrammatic Presentations
    159. 159. Simple Bar diagram 12%4th Qtr 14%3rd Qtr 12%2nd Qtr 32%1st Qtr 82% 0 1 2 3 4 5 6 7 8 912/08/2012 Dr. Kusum Gaur 175
    160. 160. Multiple Bar diagram 60 50 40 (1) 1-5 Years 30 (2) 6-10 Years (3) 11 & Above Years 20 10 0 (1) Very Dissatisfied (2) Dissatisfied (3) neither satisfied (4) Satisfied (5) Very Satisfied nor dissatisfied12/08/2012 Dr. Kusum Gaur 176
    161. 161. 12/08/2012 Dr. Kusum Gaur 177
    162. 162. Pie diagram Propotion of Pie = (Proportion of that variable )(360)Degree 12% 14% 1st Qtr 2nd Qtr 82% 3rd Qtr 4th Qtr 32%12/08/2012 Dr. Kusum Gaur 178
    163. 163. Line diagram 7 6 5 4 Series 2 3 Series 1 2 1 0 2000 2001 2002 2003 2004 200512/08/2012 Dr. Kusum Gaur 179
    164. 164. Histogram ( Area Diagramme) Series 1 40 30 20 10 Series 1 0 0 to 5 yrs 5yrs to 10 10 yrs to yrs 15 yrs to 15 yrs 20 yrs to 20 yrs 25 yrs12/08/2012 Dr. Kusum Gaur 180
    165. 165. Scatter Diagram 30 25 20Duration of Diabetes 15 Duration of diabetes in yrs. Linear (Duration of diabetes in yrs.) 10 5 0 0 50 100 150 200 250 300 No. of Patients 12/08/2012 Dr. Kusum Gaur 181
    166. 166. Radar diagram 5/1/2002 40 30 20 9/1/2002 6/1/2002 10 Series 1 0 Series 2 8/1/2002 7/1/200212/08/2012 Dr. Kusum Gaur 182
    167. 167. Box & Whisker70605040 Open High30 Low20 Close10 0 5/1/2002 6/1/2002 7/1/2002 8/1/2002 9/1/2002 12/08/2012 Dr. Kusum Gaur 183
    168. 168. Step-6Analysis of Data
    169. 169. Biostatistics = Biology + Statistics• Biostatistics is application of statistics in biology i.e. science of figure in medical science• Data: Set of information, facts or figures numerically coded and from which conclusions may be drawn is called data (singular-datum).• Statistics: The collection of methods used in planning an experiment and analyzing data in order to draw accurate conclusions.
    170. 170. Type of Biostatistics• Descriptive statistics generally characterizes or describes a set of data elements• Inferential statistics tries to infer information about a population by using information gathered by sampling
    171. 171. Descriptive Analysis Qualitative Data Rates Ratios Proportions Quantitative Data Central Tendencies  Disperson Mean Standard Deviation Mode Standard Error Median Confidencial Limit Skeweness12/08/2012 Dr. Kusum Gaur 187
    172. 172. Descriptive Analysis of Qualitative Data No. of total Events in a year (A) Rate = * 1000 MYP of that Region (T) No. of total (A) Ratio = No. of total (B) No. of Specific Events (A) Percentage of Events = * 100 Total Events (T) Event of Sp. Cause (A) Proportional Rate = * 10 n Total Deaths (T)12/08/2012 Dr. Kusum Gaur 188
    173. 173. Descriptive Analysis of Quantitative Data Mean = Mathematical Average ∑X N Mode = Most commonly occurring value Median = Center value when arrange in increasing N+1 or decreasing fashion 2 Standard Deviation = It tells how much scores deviate from the mean  it is the square root of the variance  it is the most commonly used measure of spread (X-X) SD=√ N Standard Error = Deviation from mean per observation SD/ √N Skewness = Deviation of peak from median SK= 3 (Mean –Median)/SD12/08/2012 Dr. Kusum Gaur 189
    174. 174. SD from MS Excel
    175. 175. SD from MS Excel…
    176. 176. Appropriate choice of significance tests12/08/2012 Dr. Kusum Gaur 192
    177. 177. TEST OF SIGNIFICANCE OF QUALITATIVE DATA TEST OF SIGNIFICANCE OF QUALITATIVE DATA One Sample Two Sample >Two Sample Sample proportion to Independent Dependent Dependent IndependentPopulation Proportion Mc Numer Cochron’s Large Sample Small Sample (>30) (<30) Small Sample Large Sample Large Sample Small Sample Yat’s Corrected ‘Z’ Score Corrected ‘Z’ Score Chi Squire Chi Squire ‘Z’ Score Chi Squire Yat’s Corrected Chi Chi Squire12/08/2012 Dr. Kusum Gaur 193
    178. 178. TEST OF SIGNIFICANCE OF QUANTITATIVE DATA TEST OF SIGNIFICANCE OF QUANTITATIVE DATA One Sample Two Sample >Two Sample Sample Mean to Independent Dependent Dependent IndependentPopulation Mean Paired ‘T’ Test ANOVA Friedman Large Sample Small Sample (>30) (<30) Small Sample Large Sample Large Sample Small Sample ‘Z’ Test ‘T’ Test ‘Z’ Test ANOVA ANOVA 12/08/2012 Dr. Kusum Gaur 194
    179. 179. STUDY DESIGNS AND APPROPRIATE TEST Type Study Design Appropriate Significance Test Descriptive Study Analytical Case Control Study OR Qualitative ‘Z’ Score Test/Chi-Square Test Quantitative ‘Z’ Test/’t’ Test Cohort study OR, AR, & RR Qualitative ‘Z’ Score Test/Chi-Square Test Quantitative ‘Z’ Test/’t’ Test12/08/2012 Dr. Kusum Gaur 195
    180. 180. STUDY DESIGNS AND APPROPRIATE TEST Type Study Design Appropriate Significance Test Randomized Controlled study Quantitative (before and after)- Paired ‘t’ Test Quantitative (before and after >1 followup)- Freidmen ANOVA Quantitative (between two Gps)- Unpaired ‘t’ Test Quantitative (between > two Gps)- ANOVA Test Randomized Controlled study Qualitative (before and after)- Mac Numer Test Qualitative (before and after >1 followup)- Cochron’s Test Qualitative (between two Gps)- ‘Z’ Score/Chi-square Test12/08/2012 Qualitative (between > two Gps)- Chi-square Test Dr. Kusum Gaur 196
    181. 181. STATISTICAL TEST OF SIGNIFICANCE Nominal Numerical OrdinalTwo Groups ‘Z’ Score Test ‘Z’ test (n>30) Mann Whitny Chi-square Test T Test (n<30)> Two Groups Chi-square Test ANOVA Kruskal WallisPaired Two Mec Numer Paired ANOVA Wilcoxon SignMultiple Cohrane Repeated FriedmanObservation in Multivarient ANOVAsame individualAssociation of Contegency Correlation(Pearson) SpearmanTwo Variable Cofficient Regression Correlation
    182. 182. STATISTICAL TEST OF SIGNIFICANCEResearch Number and Number and Covariates Test Goal of AnalysisQuestion type of DV type of IV Nominal 1 nominal chi square determine if difference betweenGroup croupsdifferences Continuous 1 dichotomous t-test Determine significance of 1 Categorical 1 one-way ANOVA mean group 1+ one-way differences ANCOVA 2+ Categorical 1 factorial ANOVA 1+ factorial ANCOVA 2+ Continuous 1 Categorical 1 one-way MANOVA Create linear 1+ one-way MANCOVA combo of Dependent variable 2+ Categorical 1 factorial (Dvs) MANOVA to maximize 1+ factorial MANCOVA mean group differencesDegree of Continuous 1 Continuous Bivariate Determine relationship/predictionrelationship Correlation 2+ Continuous Multiple Linear combination to predict the Regression DV 1+ Continuous 2+ Continuous Path Analysis Estimate causal relations among variables 12/08/2012 Dr. Kusum Gaur 198
    183. 183. Comparing difference between Two Sample Proportions „Z‟ Score Test P2 – P1 here, P1– proportion of that event in 1st Sample „Z‟ Score = P2 - proportion of that event in 2nd Sample SEDP SEDP – Standard Error of Difference in Proportion Q1 - proportion without that event in 1st Sample i.e. Q1 = 100 – P1 Q2 - proportion without that event in P1 Q 1 P 2 Q 2 2nd Sample i.e. 100 – P2SEDP = ------- + -------- N1 - Sample Size of 1st Sample N1 N2 N2 - Sample Size of 2nd Sample 12/08/2012 Dr. Kusum Gaur 199
    184. 184. Inference of ‘Z’ Score Test If „Z‟ > 2 = Difference is Significant If „Z‟ < 2 = Difference is Not Significant If „Z‟ > 3 = Difference is Highly Significant12/08/2012 Dr. Kusum Gaur 200
    185. 185. Comparing difference between >Two Sample Proportions Chi-Square Test Indications Qualitative data Normal distribution Comparing difference between Two Sample proportions Multiple Sample proportions12/08/2012 Dr. Kusum Gaur 201
    186. 186. Comparing difference between >Two Sample Proportions Chi-Square Test Chi Square(2) = ∑all cells(O-E)2 Tr x Tc E= E T (O1-E1)2 (O2-E2)2 (O3-E4)2 (On-En)2Chi Squire = + + + ---+ E1 E2 E3 En Tr – Total of that Row here, O – Observed value of cell Tc – Total of that column E – Expected value of cell, T – Grand Total i.e. a+b+c+d considering Null Hypothesis Degree of Freedom (DF) = (C – 1) (R -1) R= No. of Rows, C = No. of Column 12/08/2012 Dr. Kusum Gaur 202
    187. 187. Inference of Chi Square(x2) Chi Square(x2 ) value is seen at Degree of Freedom DF = (R – 1) (C – 1), from Chi Square((2) Table (here R=No. of Rows &C= No. of Column) at desired level of significance Inferences If Chi Square(x2 ) Test Value is – Higher than Table value = Difference in proportions is Significant at that desired level of significance. If Chi Square(x2 ) Test Value is – Lower than Table value = Difference in proportions is Not Significant at that desired level of significance.12/08/2012 Dr. Kusum Gaur 203
    188. 188. Comparing difference between Two Sample Means (>30) „Z‟ Test Pre-requisites Quantitative data  Homogenous normally distributed Random Sample Sample Size > 30 Indications To see the Significance of any Observation in reference of Mean Value of that sample Comparing difference between Sample Mean to Population Mean Means of Two independent Samples12/08/2012 Dr. Kusum Gaur 204
    189. 189. Comparing difference between Two Sample Means (>30) „Z‟ Test X2 – X1 here, X1– Mean of that event in 1st Sample „Z‟ Test = X2 - Mean of that event in 2nd Sample SEDM SEDM – Standard Error of Difference in Means SD1 – Standard Error of 1st Sample SD2 – Standard Error of 2nd Sample N1 - Sample Size of 1st Sample SD2 1 SD2 2 N2 - Sample Size of 2nd SampleSEDM = ------- + -------- N1 N2 12/08/2012 Dr. Kusum Gaur 205
    190. 190. Comparing difference between Two Sample Means (<30) „T‟ Test Prerequisites Random Sample Quantitative data Normally Distributed Sample Size < 3012/08/2012 Dr. Kusum Gaur 206
    191. 191. Type of ‘T’ Testas per design Unpaired / Paired for inference One Tail /Two tail12/08/2012 Dr. Kusum Gaur 207
    192. 192. Unpaired ‘T’ Test Design Population -1 Population -2 S-1 S-2 Mean --1 Unpaired ‘T’ test Mean --212/08/2012 Dr. Kusum Gaur 208
    193. 193. Paired ‘T’ Test Design Intervention Population Sam Observations-1 Observations 2 ple- Mean --1 Mean --2 Paired ‘T’ test12/08/2012 Dr. Kusum Gaur 209
    194. 194. One Tail ‘T’ Test Acceptance Zone Rejection ZoneOne Tail – Results are aspect only in one direction
    195. 195. Two Tail ‘T’ TestRejection Zone Acceptance Zone Rejection Zone Two Tail – Results are aspect in both direction
    196. 196. Comparing difference between Two Sample Means (<30) „T‟ Test X2 – X1 here, X1– Mean of that event in 1st Sample „T‟ Test = --------------- X2 - Mean of that event in 2nd Sample SEDM SEDM – Standard Error of Difference in Means SD1 – Standard Error of 1st Sample SD2 – Standard Error of 2nd Sample N1 - Sample Size of 1st Sample SD2 1 SD2 2 N2 - Sample Size of 2nd SampleSEDM = ------- + -------- N1 N2 Degree of Freedom (DF) = (N1 – 1) + (N2 -1) = N1 + N2 - 2 12/08/2012 Dr. Kusum Gaur 212
    197. 197. Inference of ‘T’ Test Value „T‟ Test Value is matched at Degree of Freedom (DF) = N1 + N2 – 2 in the Table of “T” at desired level of significance. Inferences If „T‟ Test Value is – Higher than Table value = Difference in Means is Significant at that desired level of significance. If „T‟ Test Value is – Lower than Table value = Difference in Means is Not Significant at that desired level of significance.12/08/2012 Dr. Kusum Gaur 213
    198. 198. Comparing difference between >Two Sample Means ANALYSIS OF VARIENCE (ANOVA) TEST Pre-requisites Quantitative data  Homogenous normally distributed Random Sample Indications Comparing difference between more than Two Means12/08/2012 Dr. Kusum Gaur 214
    199. 199. Comparing difference between >Two Sample Means „ANOVA‟ Test MSOSI MSOS2 - Mean Sum Of Squares Within Classes ANOVA = ---------- = Total SOS – MSOSI MSOS2 T SOS = X2 – (X)2/NMSOSI – Mean Sum Of Squares Between Classes = SOSI / K-1SOSI –Sum Of Squares Between Classes (Xa)2 (Xb)2 (Xc)2 (Xk)2 (X)2 = --------- + ----------- + ----------- + ….+ ____ __ - --------- Na Nb Nc Nk N At Degree of Freedom (DF) = ( K-1) Horizontal 12/08/2012 Dr. Kusum Gaur (N – K) Vertical 215
    200. 200. Inference of ANOVA Find out Variance Ratio value at Degree of Freedom (DF) = ( K-1) Horizontal, (N – K) Vertical from the Variance Ratio Table at desired level of significance. Inferences If Test value is > Table value = Difference in Means is Significant at that desired level of significance. If Test value is < Table value = Difference in Means is Not Significant at that desired level of significance.12/08/2012 Dr. Kusum Gaur 216
    201. 201. CORRELATIONIndicationsTo find out relationship between variables12/08/2012 Dr. Kusum Gaur 217
    202. 202. Type & Degree of CorrelationCorrelation Inference Correlation (r) Inference+1 Perfect +ve -1 Perfect +ve Correlation Correlation> 0.95 About Perfect +ve > - 0.95 About Perfect +ve Correlation Correlation> 0.75 V. Good Correlation > - 0.75 V. Good Correlation0.75 – 0.5 Moderate Correlation - 0.75 to – 0.5 Moderate Correlation0.5 – 0.25 Fair Correlation - 0.5 to – 0.25 Fair Correlation0.25 - 0 No Correlation < - 0.25 No Correlation 12/08/2012 Dr. Kusum Gaur 218
    203. 203. Correlation CORRELATION Two Variables > Two Variables Un-Paired Data Paired Data Pearson‟s Spearman‟s Rank Order Multivariate Correlation Correlation Correlation12/08/2012 Dr. Kusum Gaur 219
    204. 204. Pearson’s correlation . ∑ ( X – X) ∑ ( Y – Y) ∑xy Correlation (r) = = √∑ ( X – X)2 ∑ ( Y – Y)2 √ ∑ x2 y2 Direct Method ∑ X Y - ∑ X ∑Y / N Correlation (r) = ----------------------------- √ {∑X2 – (∑X)2/N}{ ∑Y2 – (∑Y)2 /N}12/08/2012 Dr. Kusum Gaur 220
    205. 205. Pearson’s correlation ----- here, ∑ X Y = Sum of multiplication of X and Y ∑ X = Sum of all observations of X Series ∑ Y = Sum of all observations of YX Series N =Total no. of observations ∑X2 = Sum of Squares of all observations of X Series ∑Y2 = Sum of Squares of all observations of Y Series (∑X)2 = Square of Sum of all observations of X Series (∑Y)2 = Square of Sum of all observations of Y Series12/08/2012 Dr. Kusum Gaur 221
    206. 206. Spearman’s Rank Order Correlation 6∑D2• Spearman‟s Rank (rs ) = 1 - N3 - N12/08/2012 Dr. Kusum Gaur 222
    207. 207. Significance Test for Correlation (r) Standard Error (SE) of rs = rs √ N-1Inference• If difference >2 SE of r =Difference is Significant at 5% level• If difference < 2SE of r =Difference is Not Significant at 5% level12/08/2012 Dr. Kusum Gaur 223
    208. 208. REGRESSION Indication To find out causal relationship between variables REGRESSION COFFICIENT- It is a measure of change in one dependent variable (y) with one unit change in the other variable (x)12/08/2012 Dr. Kusum Gaur 224
    209. 209. Regression line with Regression Equation The regression equation of ‘Y’ on ‘X’ is expressed as follows: Here, ‘a’ is interceptor & ‘b’ is slope Yc = a + bX
    210. 210. Regression LinesRégression line of Y on X is Y = a + bX ----(1)Régression line of X on Y is X = a + bY ----(2) Here- Y = one variable X = other variable a = interceptor of X line on Y line b = slope of X line on Y line Regression 12/08/2012 Dr. Kusum Gaur 226
    211. 211. Regression – Equations Regression Equation of X on Y SD of series X (X – X)= r (Y –Y) ---- (3) SD of series Y Regression Equation of Y on X SD of series Y (Y – Y)= r (X –X) ------- (4) SD of series X12/08/2012 Dr. Kusum Gaur 227
    212. 212. Regression – coefficients Regression Coefficient of X on Y SD of series X ∑(X-X)(Y –Y) b(xy)= r = SD of series Y ∑(X – X)2 Regression Coefficient of Y on X SD of series Y ∑(X-X)(Y –Y) b(yx)= r =12/08/2012 SD of series Kusum Gaur Dr. X ∑(Y – Y)2 228
    213. 213. Relation of correlation and RegressionCo-rrelation (r) = √ bxy byx12/08/2012 Dr. Kusum Gaur 229
    214. 214. Between Tests/Procedure/TherapyFor comparison with Gold Standard: Sensitivity Specificity PPV NPV ROCFor agreement of association: KappaFor appropriate cut of value for diagnostic test: ROC 12/08/2012 Dr. Kusum Gaur 230
    215. 215. Sensitivity and Specificity Status based on gold standard test Diseased Normal Test positive True positive False positiveObservation in a bnew test Test negative False negative True negative c d Sensitivity = a /(a+c) PPV = a /(a+b) Specificity = d /(b+d) NPV = d /(c+d) 12/08/2012 Dr. Kusum Gaur 231
    216. 216. ‘ROC’ Curve
    217. 217. Kappa Statistics (Measurement of Agreement) Test Value Inference0.93 – 1 Excellent Agreement0.81 – 0.92 Very Good Agreement0.61 – 0.80 Good Agreement0.41 – 0.60 Fair Agreement0.21 – 0.40 Slight Agreement0.01 – 0.20 Poor Agreement< 0.01 No Agreement 12/08/2012 Dr. Kusum Gaur 233
    218. 218. Non-Parametric Tests Advantages Distribution free Easier to do Easier to understand/infer Disadvantages They ignore certain amount of information Indicated only ordinal or nominal data Statistically Less efficient Indicated only to test hypothesis, not for estimates12/08/2012 Dr. Kusum Gaur 234
    219. 219. Parametric Test Vs Non-ParametricTest Quality Parametric Non-Parametric Assumed Distribution Normal Any Assumed Variance Homogenous Any Data Type Interval-Continous Nominal /Ordinal Data set Relationship Independent Any Usual Centre Measure Mean Median More conclusions Easier to calculate Advantages More efficient Less affected by outliers12/08/2012 Dr. Kusum Gaur 235
    220. 220. Parametric Test Vs Non-ParametricTest Parametric Non-Parametric Correlation test Pearson Spearman Independent Independent- Mann-Whitney testmeasures, 2 groups measures t-test One-way, Independent independent- Kruskal-Wallis testmeasures, >2 groups measures ANOVARepeated measures, Matched-pair t-test Wilcoxon test 2 conditionsRepeated measures, One-way, repeated Friedmans test >2 conditions measures ANOVA Sign Test (K Test)– nonparametric test for quantitative paired data12/08/2012 Dr. Kusum Gaur 236
    221. 221. Sign test• Simplest• Based on direction(- /+/0)• Signs as per the direction are counted• Inference – if S≤K = Null hypothesis (H₀) is rejected• Here „S‟ is net sum of signs as per sign• „K‟ is constant12/08/2012 Dr. Kusum Gaur 237
    222. 222. Sign test – StepsSign K Test for Small Sample (<30) – Find out net sum of signs as per sign(S) – S = (total + signs) – (total – signs) – K = (n-1)/2 - 0.98√n• Inference – if S≤K = Null hypothesis (H₀) is rejectedSign Z Test for Large Sample (>30) – Find out no of ties with less frequent sign(X) – Z = (X – np) / √ np (1-p) here X= no. + Sign• Inference – if Z>2 = Null hypothesis is rejected12/08/2012 Dr. Kusum Gaur 238
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    228. 228. Step-7 Inferences12/08/2012 Dr. Kusum Gaur 244
    229. 229. Steps in Statistical InferenceGenerating NULL and ALTERNATIVE hypothesisTesting the hypothesis using appropriate statistical testsObtaining „p‟ valueConcluding from the p value.Obtaining Level of SignificanceComparing „p‟ value with CI. 12/08/2012 Dr. Kusum Gaur 245
    230. 230. ‘P’ Value and Inferences with Normal Curve12/08/2012 Dr. Kusum Gaur 246
    231. 231. Rejection Zone Acceptance Zone Rejection ZoneMean 1SD =68% values - Confidence Limit 68% - P Value = >0.05 - NS Mean 2SD =95% values - Confidence Limit 95% - P Value = 0.05 - S Mean 3SD =99% values - Confidence Limit 99% - P Value = 0.001 - HS
    232. 232. Rejection Zone Acceptance Zone Rejection ZoneMean 1SD =68% values - Confidence Limit 68% - P Value =/>0.05 - NS Mean 2SD =95% values - Confidence Limit 95% - P Value < 0.05 – SMean 3SD =99% values - Confidence Limit 99% P Value < 0.001 - HS 12/08/2012 Dr. Kusum Gaur 248
    233. 233. Conventionally Accepted Significance Level P Value > 0.05 LS=Not Significant P Value < 0.05 LS=Significant P Value < 0.001 LS=Highly Significant
    234. 234. Step-8 Reporting12/08/2012 Dr. Kusum Gaur 250
    235. 235. Steps of Report Writing Title of Project Abstract Introduction Aims & Objectives Methodology Observations-Compilation, Classification & Presentation of data with analysis and inferences Discussion Conclusions Recommendations Limitations Acknowledgment Bibliography12/08/2012 Dr. Kusum Gaur 251
    236. 236. DiscussionExplanation of findingsLogic and reasoning for the results as it appearsCompare and contrast with findings of other researchersBased on objectives of the studyShould answer the research questionScope & limitations of the study12/08/2012 Dr. Kusum Gaur 252
    237. 237. Recommendations & conclusions• Based on our findings• Limited to objectives of the study• Policy implications• Relevance should be emphasized• Should be exclusively limited to observations12/08/2012 Dr. Kusum Gaur 253
    238. 238. Managerial and financial aspectsProtocol developmentTime line/Gantt chartPeer reviewDevelopment of toolsTraining in data collectionBudget/ financial accountingQuality controlMonitoring & Evaluation12/08/2012 Dr. Kusum Gaur 254
    239. 239. Time Line/Gant chart/log FramActivities 1.1.12- 16.1- 1.2.12- 1.3.12- 16.5.12- 16.6.12- 16.7.12- 15.1.12 31.1 15.2.12 15.5.12 15.6.12 15.7.12 31.7.12PlanningOfficialsQue. DevTrainingPoilet SurveyCorrectionsRe-trainingResource ProcSurveyAnalysisReport WritingDisseminationof Report
    240. 240. Computer in Statistics12/08/2012 Dr. Kusum Gaur 256
    241. 241. Web sites related to Statistics• http://stattrek.com• http://vassarstat.net• http://www.scribd.com• http://www.statistixl.com• http://statistics calculators.com• http://stat.ubc.ca/~rollin/stats/ssize/• ……………………………………………………… ……12/08/2012 Dr. Kusum Gaur 257
    242. 242. Computer Softwares in Statistics• Microsoft Excel• SPSS• Epi info• Epi tab• Mini tab• Graph Pad• Primer• Medcal• ……………..12/08/2012 Dr. Kusum Gaur 258
    243. 243. Always there is room for improvement12/08/2012 Dr. Kusum Gaur 259

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