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BIOSTATISTICS Dr Lohith D 1st year MDS Department of orthodontics V S dental college.Bengaluru 1 CONTENTS • Introduction • History • Applications • Measures of central tendency • Measures of dispersion • Steps in statistical methods • Methods of presentation of data • Types of studies • Sampling 2 • Null hypothesis • Parametric and non –parametric tests • Softwares-Statistical packages • Conclusion • References 3 INTRODUCTION Statistics as a singular noun is “a science of figures” Where as plural noun it means “figures” or numerical data or information. 4 BIOSTATISTICS BIOSTATISTICS can be defined as art and science of collection, compilation, presentation, analysis and logical interpretation of biological data affected by multiplicity of factors “An ounce of truth produces tons of statistics” 5 STATISTICS The word ‘statistic’ is derived from an Italian word statista meaning statesman. OR the German word ‘statistik’ which means political state Zimmerman introduced the word statistics in England. 6 HISTORY OF STATISTICS During the outbreak of plague in england, in 1532 they started publishing the weekly death statistics.This practice continued and by 1632 published the bills of mortality and they listed births and deaths. 7 8 HISTORY OF STATISTICS.. In 1662, John graunt used 30 years of these bills to make predictions about the number of people who would die from various diseases and proportions of male and female births that could be expected. John graunt(1620-1674) 9 father of health statistics KNOWLEDGE OF STATISTICAL METHODS 1. Enables us to make intelligent use of the current literature. 2. Opens up new paths of experimental procedures 3. Enables a research worker to collect, analyze and present his data in the most meaningful manner. 4. Allows a bioinformatics professional to use statistical softwares in a meaningful manner 10 LIMITATIONS Statistic laws are not exact laws like mathematical or chemical laws but are only true in majority of cases. Ex: when we say that the average height of an adult indian is 5’ 6’’ , it does not indicate the height of an individual but of a group of individuals. 11 SUBDIVISIONS OF STATISTICS They can be seperated into two broad categories: 1. Descriptive statistics 2. Inferential statistics 12 MEASURES OF CENTRAL TENDENCY Three common types • MEAN • MEDIAN • MODE 13 MEAN • The arithmetic mean is widely used in statistical calculation. It is sometimes simply called Mean. • To obtain the mean, the individual observations are first added together, and then divided by the number of observations. • The operation of adding together is called 'summation' and is denoted by the sign or S. The individual observation is denoted by the sign and the mean is denoted by the sign (called "X bar"). • = Sum of observations No of observations • = X1+X2+X3……………..+Xn n 14 • The mean (x) is calculated thus : the age of 10 orthodontic patients was 15, 14, 16, 12, 18, 16, 17, 19, 21,23. The total was 171. The mean is 171 divided by 10 which is 17.1. 15 MEDIAN • The median is an average of a different kind, which does not depend upon the total and number of items. • To obtain the median, the data is first arranged in an ascending or descending order of magnitude, and then the value of the middle observation is located, which is called the median. E.g.1)seven subjects are arranged in ascending order . 3, 4, 4, (5), 5, 6, 7. the fourth observation (5) is median in this series E.g.2) 3, 4, 5, 6, 7, 8, 9, 10. 6+7= 13 median is 13/2= 6.5 16 MODE (z) • The mode is the commonly occurring value in a distribution of data. It is the most frequent item or the most "fashionable" value in a series of observations. • Selection of Mode = The Observation having highest repetition. • mode of the following data: 10, 11, 12, 26, 20, 40, 20, 10, 12, 10. As 10 is repeating 3 times 10 is the mode. 17 DISPERSION It is necessary to study the variation. This variation is also known as dispersion. It gives us information, how individual observations are scattered or dispersed from the mean of large series. 18 MEASURES OF DISPERSION • There must be individual variations. If we examine the data of blood pressure or heights or weights of a large group of individuals, we will find that the values vary from person to person. Even within the same subject, there may be variation from time. The questions that arise are : What is normal variation ? And how to measure the variation ? • There are several measures of variation (or "dispersion” as it is technically called) of which the following are widely known: (a) The Range (b) The Mean or Average Deviation (c) The Standard Deviation 19 THE RANGE • The range is by far the simplest measure of dispersion. It is defined as the difference between the highest and lowest figures in a given sample. For example, from the following record of diastolic blood pressure of 10 individuals – • 83, 75,81, 79, 71,90, 75,95, 77,94. • It can be seen that the highest value was 95 and the lowest 71. The range is expressed as 71 to 95 or by the actual difference (24). • If we have grouped data, the range is taken as the difference between the mid-points of the extreme categories. The range is not of much practical importance, because it indicates only the extreme values between the two values and nothing about the dispersion of values 20 between the two extreme values. THE MEAN DEVIATION • It is the average of the deviations from the arithmetic mean. It is given by the formula: • M.D. = (x- ) / • Example : The diastolic blood pressure of 10 individuals was as follows : 83, 75, 81, 79, 71, 95, 75, 77, 84 and 90. 21 22 The Standard Deviation • The standard deviation is the most frequently used measure of deviation. In simple terms, it is defined as "Root-Means- Square -Deviation." It is denoted by the Greek letter sigma or by the initials S.D. The standard deviation is calculated from the basic formula : 23 • When the sample size is more than 30, the above basic formula may be used without modification. For smaller samples, the above formula tends to underestimate the standard deviation, and therefore needs correction, which is done by substituting the denominator ( -1) for . The modified formula is as follows : 24 • The steps involved in calculating the standard deviation are as follows : (a) First of all, take the deviation of each value from the arithmetic mean, (x- ) (b) Then, square each deviation - ·(x(c) Add up the squared deviations- )2 (x- )2 (d) Divide the result by the number of observations [or] ( -1) in case the sample size is less than 30] (e) Then take the square root, which gives the standard deviation. 25 Example : The diastolic blood pressure of 10 individuals was as follows : 83, 75, 81, 79, 71, 95, 75, 77, 84, 90. Calculate the standard deviation. 26 STEPS IN STATISTICAL METHODS 1. Collection of data 2. Classification 3. Tabulation 4. Presentation by graphs 5. Descriptive statistics 6. Establishment of relationship 7. Interpretation 27 DATA Whenever an observation is made, it will be recorded and a collective recording of these observations, either numerical or otherwise, is called a data. Ex: recording the sex of a person in a group of persons 28 VARIABLE In each of cases a certain observation is made for a characteristic and this characteristics varies from one observation to other observation and is called a variable 29 TYPES OF DATA 1. Qualitative 2. Quantitative a)Discrete b)continuous 3. Grouped / ungrouped 4. Primary / secondary 5. Nominal / ordinal 30 TYPES OF CLINICAL DATA THAT CAN BE SUPPORTED BY STATISTICS • Statistics can be used to help the reader make a critical evaluation of virtually any quantitative data. • It is important that the statistical techniques used are appropriate for the given experimental design. 31 NEED FOR ORGANISING THE DATA • Data collected and compiled from experimental work, surveys, registers or records are raw data. • These are unsorted and not very helpful in understanding the underlying trends or its meaning. • The objective of classification of data is to make data simple, concise, meaningful, interesting and helpful in further analysis. 32 METHODS OF PRESENTATION OF DATA •Tabulation •Charts and diagrams 33 TABLES • Tables are devices for presenting data simply from masses of statistical data. • Tabulation is the first step before the data is used for analysis or interpretation. • A table can be simple or complex, depending upon the number or measurement of a single set or multiple sets of items. 34 GUIDELINES FOR PRESENTATION OF TABLES 1. The tables should be numbered e.g., Table 1, Table 2, etc. 2. A title must be given to each table. The title must be brief and self explanatory. 3. The headings of columns or rows should be clear and concise. 4. The data must be presented according to size or importance; chronologically, alphabetically or geographically. 5. If percentages or averages are to be compared, they should be placed as close as possible. 35 6. No table should be too large. 7. Most people find a vertical arrangement better than a horizontal one because, it is easier to scan the data from top to bottom than from left to right. 8. Foot notes may be given, where necessary. 9. providing explanatory notes or additional information 36 TYPES OF TABLES • Simple table: they are one way tables which supply answer to questions about one characteristic of data only. 37 FREQUENCY DISTRIBUTION TABLE • In a frequency distribution table, the data is first split up into convenient groups (class intervals) and the number of items (frequency) which occur in each group is shown in the adjacent column. 38 CHARTS AND DIAGRAMS • Charts and diagrams are one of the most convincing and appealing ways of depicting statistical results. Diagrams and graphs are extremely useful because: 1. They are attractive to the eyes. 2. They give a bird’s eye view of entire data 3. They have lasting impression on the mind of layman 4. They facilitate comparison of relating to different time periods and regions. 39 BAR CHARTS • Bar charts are merely a way of presenting a set of numbers by the length of a bar. The length of the bar is proportional to the magnitude to be represented. • Bar charts are a popular media of presenting statistical data because they are easy to prepare, and enable values to be compared visually. 40 41 HISTOGRAM • It is. a pictorial diagram of frequency distribution. It consists of a series of blocks . • The class intervals are given along the horizontal axis and the frequencies along the vertical axis. The area of each block or rectangle is proportional to the frequency. 42 FREQUENCY POLYGON • A frequency distribution may also be represented diagrammatically by the frequency polygon. It is obtained by joining the mid-points of the histogram blocks. 43 LINE DIAGRAM • This diagram is useful to study the changes of valuables in the variable over the time and is simplest of the diagram. • On the x axis the time such as hours, days, weeks, months or years are represented and the value of any quantity pertaining to this is represented along the y axis. 44 Pie charts • These are so called because the entire graph looks like a pie and its components represent slices cut from a pie. • The total angle at the the centre of the circle is equal to 360 degree and it represents the total frequency. • It is divided into different sectors corresponding to the frequencies of variables in the distribution. 45 PICTOGRAM • Pictograms are a popular method of presenting data to the "man in the street" and to those who cannot understand orthodox charts. Small pictures or symbols are used to present the data. 46 STATISTICAL MAPS • When statistical data refer to geographic or administrative areas, it is presented either as "Shaded Maps“ or "Dot maps" according to suitability. • The shaded maps are used to present data of varying size. The areas are shaded with different colours, or different intensities of the same colour, which is indicated in the key. 47 TYPES OF STUDIES 48 COHORT STUDY Cohort study is another type of analytical (observational) study which is usually undertaken to obtain additional evidence to refute or support the existence of an association between suspected cause and disease. Cohort study is known by a variety of names : prospective study, longitudinal study, incidence study, and forward-looking study. The most widely used term, however, is "cohort study“. The distinguishing features of cohort studies are : • The cohorts are identified prior to the appearance of the disease under investigation • the study groups, so defined, are observed over a period of time to determine the frequency of disease among 49 them. • the study proceeds forward from cause to effect. CONCEPT OF COHORT • In epidemiology, the term "cohort" is defined as a group of people who share a common characteristic or experience within a defined time period (e.g., age, occupation, exposure to a drug or vaccine, pregnancy, insured persons, etc). Thus a group of people born on the same day or in the same period of time (usually a year) form a "birth cohort". All those born in 2010 form the birth cohort of 2010. • Persons exposed to a common drug, vaccine or infection within a defined period constitute an "exposure cohort". • The comparison group may be the general population from which the cohort is drawn, or it may be another cohort of persons thought to have had little or no exposure to the substance in question, but otherwise 50 similar. Indications for cohort studies • when there is good evidence of an association between exposure and disease, as derived from clinical observations and supported bydescriptive and case control studies. • when exposure is rare, but the incidence of disease high among exposed, e,g., special exposure groups like those in industries, exposure to X-rays, etc. • when attrition of study population can be minimized, e.g., follow-up is easy, cohort is stable, cooperative and easily accessible. • when ample funds are available. 51 INTERVENTIONAL STUDIES These are also known as experimental studies or clinical trials. In these studies the investigator decides which subject gets exposed to a particular treatment (or placebo). These studies may be cohort or case-control. Ex-animal experiments,isolated tissue experiments,in vitro experiments. 52 INTERVENTIONAL STUDIES •Randomized controlled trials/clinical trials-with patients as unit of study •Field trials/community intervention studies-with healthy people as unit of study •Community trials-with communities as unit of study 53 SAMPLING • When a large proportion of individuals or items or units have to be studied, we take a sample. • It is easier and more economical to study the sample than the whole population or universe. • Great care therefore is taken in obtaining a sample. It is important to ensure that the group of people or items included in the sample are representative of the whole population to be studied 54 SAMPLE SELECTION-GUIDELINES I. EFFICIENCY II. REPRESENTATIVENESS III. MEASURABILITY IV. SIZE V. COVERAGE VI. GOAL ORIENTATION VII. FEASIBILITY VIII.ECONOMY AND COST EFFICIENCY 55 DIFFERENT SAMPLING DESIGNS 1. Simple random sampling 2. Systematic random sampling 3. Stratified random sampling 4. Cluster sampling 5. Sub sampling/ multistage sampling 6. Multiphase sampling 56 DETERMINATION OF SAMPLE SIZE Quantitative data N= 4 SD2 L2 SD= Standard deviation L = allowable error Journal of orthodontics Vol 31:2004,107-114 57 PRECISION Individual biological variation, sampling errors and measurement errors lead to random errors,which lead to lack of precision in the measurement. This error can never be eliminated but can be reduced by increasing the size of the sample 58 PRECISION PRECISION= square root of sample size standarad deviation Standard deviation remaining the same, increasing the sample size increases the precision of the study. 59 EXPERIMENTAL VARIABILITY ERROR/ DIFFERENCE / VARIATION There are three types 1. Observer- subjective / objective 2. Instrumental 3. Sampling defects or error of bias 60 BIAS IN THE SAMPLE This is also called as systematic error. This occurs when there is a tendency to produce results that differ in a systematic manner from the true values. A study with small systematic error is said to have high accuracy.Accuracy is not affected by the sample size. 61 BIAS IN THE SAMPLE.. Accuracy is not affected by the sample size. There are as many as 45 types of biases, however the important ones are: 1. Selection bias 2. Information bias 3. Confounding bias 62 ERRORS IN SAMPLING SAMPLING ERRORS NON SAMPLING ERRORS Faulty sampling design Coverage error -due to non response or non cooperation of the informant Small size of the sample Observational error -due to interviewers bias,imperfect design Processing error -due to errors in statistical analysis 63 DISTRIBUTIONS When you have a collection of points you begin the initial analysis by plotting them on a graph to see how they are distributed 64 DISTRIBUTION-TYPES 1. Normal or gaussian 2. Binomial 3. Poisson 4. Rectangular or uniform 5. Skewed 6. Log normal 7. Geometric 65 NORMAL OR GAUSSIAN DISTRIBUTION • When data is collected from very large number of people and a frequency distribution is made with the narrow class intervals, the resulting curve is smooth, symmetrical and it is called normal curve. 66 In a normal curve • (a). the area between one standard deviation on either side of the mean ( x ± 1 ) will include approximately 68 per cent of the values in the distribution • (b) the area between two standard deviations on either side of the mean( x ± 2 ) will cover most of the values, i.e., approximately 95 per cent of the values. • (c) the area between ( x ± 3 ) will include 99. 7 per cent of the values. These limits on either side of the mean are called "confidence limits" 67 STANDARD NORMAL CURVE 1. The standard normal curve is bell shaped 2. The curve is perfectly symmetrical based on an infinitely large number of observations. The maximum number of observations is at the mean and the number of observations gradually decrease on either side with few observations at the extreme points. 3. The total area of the curve is one, its mean is zero and standard deviation one. 4. All the three measures of central tendency, the mean, median, and mode coincide. 68 BINOMIAL DISTRIBUTION The binomial distribution is used for describing discrete not the continuous data. These values are as a result of an experiment known as bernoulli’s process.They are used to describe 1. One with certain characteristic 2. Rest without this characteristic The distribution of the occurrence of the charactreristic in the population is defined bythe binomial distribution. 69 THE POISSON DISTRIBUTION If in a binomial distribution the value of probability of success and failure of an event becomes indefinitely small and the number of observation becomes very large, then binomial distribution tends to poisson distribution. This is used to describe the occurrence of rare events in a large population. 70 CRITICAL RATIO, Z SCORE It indicates how much an observation is bigger or smaller than mean in units of SD Z ratio = Observation – Mean Standard Deviation The Z score is the number of SDs that the simple mean depart from the population mean. As the critical ratio increases the probability of accepting null hypothesis decreases. 71 NULL HYPOTHESIS It is a hypothesis which assumes that there is no difference between two values such as population means or population proportions. When you are subjecting to null hypothesis certain terminologies should be clear. 72 NULL HYPOTHESIS….. POPULATION CONCLUSION BASED ON SAMPLE NULL HYPOTHESIS NULL HYPOTHESIS REJECTED ACCEPTED NULL HYPOTHESIS TRUE TYPE I ERROR CORRECT DECISION NULL HYPOTHESIS FALSE CORRECT DECISION TYPE II ERROR 73 Parametric or Non-parametric? • If the information about the population is completely known by means of its parameters then statistical test is called parametric test • • Eg: t- test, f-test, z-test, ANOVA Parametric Test If there is no knowledge about the population or parameters, but still it is required to test the hypothesis of the population. Then it is called non-parametric test • Eg: mann-Whitney, rank sum test, Kruskal-Wallis test Nonparametric test 74 Parametric Non Parametric 1 Student paired T test 1 Wilcoxan signed rank test 2 Student unpaired T test 2 Wilcoxan rank sum test 3 One way Anova 3 Kruskal wallis one way anova 4 Two way Anova 4 Friedman one way anova 5 Correlation coefficient 5 Spearman’s rank correlation 6 Regression analysis 6 Chi-square test 75 STUDENT’S ‘t’ TEST This test is a parametric test described by W.S.Gossett whose pen name was “student”.Hence called as student’s t test. It is used for small samples, i.e Less than 30. T Test can be: Paired t test Unpaired t test 76 Unpaired ‘t’ TEST This test is applied to unpaired data of independent observations made on individuals of two different or separate groups or samples drawn from two populations, to test if the difference between the mean is real or it can be attributed to sampling variability. Ex: comparing intermolar width in boys and comparing intermolar width in girls. 77 Paired “t” test • It is applied to paired data of independent observations from one sample only when each individual gives a pair of observations. • Ex: comparison of intermolar width in mixed dentition period and intermolar width in permanent dentition period of the same sample. 78 ANALYSIS OF VARIANCE (ANOVA) when 3 more or more groups of individuals with the objective of determining whether any true differences in mean performance exist among the conditions under the study. Ex: comparing the curve of spee, curve of Wilson, curve of monsoon in 3 different groups. 1st group: control. 2nd group: serial extraction. 3rd group: late premolar extraction. 79 CHI- SQUARE(ᵡ2) TEST The letter “x” in Greek represents “chi”. As it is “x2” or square of “x” it is called as “Chisquare test.” It was first introduced by a famous statistician “Karl Pierson” in 1889. 80 • When the data is measured in terms of attributes or qualities, and it is intended to test whether the difference in the distribution of attributes in different groups is due to sampling variation or not, the chi square test is applied. • It is used to test the significance of difference between two proportions and can be used when there are more than two groups to be compared. 81 • For example , if there are two groups, one which has received oral hygiene instructions and other has not received any instructions and if it is desired to test if the occurrence of new cavities is associated with the instructions. group Occurrence of new cavities Present Absent total No. who received instruction s 10 40 50 No.who did not receive instruction s 32 8 40 total 42 48 90 82 STEPS 1. Test the null hypothesis: to test whether there is an association between oral hygiene instructions received and the occurrence of new cavities, state the null hypothesis as ‘there is no association between oral hygiene instructions received in dental hygiene and occurrence of new cavities’. 2. X2 statistics is calculated as: x2 = (O-E)2 / E Where O = observed frequency and E = expected frequency Proportion of people with caries=42/90= 0.47 Proportion of people without caries=48/90=0.53 83 • Among those who received instructions: expected number attacked=50x0.47= 23.5 expected number not attacked=50x0.53=26.5 • Among those who did not receive instructions expected number attacked=40x0.47= 18.8 expected number not attacked=40x0.53= 21.2 GROUP ATTACKED NOT NOT ATTACKED ATTACKED NO. who received instructions O=10 E= 23.5 O-E=13.5 O=40 E=26.5 O-E=13.5 NO. who did not O =32 E= 18.8 O-E= 13.2 O=8 E=21.2 O-E=13.2 84 APPLYING THE X2 TEST • X2= (O-E)2/E (13.5)2/23.5 +(13.5)2/18.8 + (13.2)2/21.2 =7.76+6.88+9.27+8.22 =32.13 • FINDING THE DEGREE OF FREEDOM it depends upon the number of column and rows in the original table. d.f=(column-1) (row-1) (2-1) (2-1) =1 85 • Probability tables: in the probability table, with a degree of freedom of 1, the X2 value for a probability of 0.05 is 3.84. since the observed value 32 is much higher it is concluded that the null hypothesis is false and there is a difference in caries occurrence in the two groups with caries being lower in those who received instructions. 86 COMPARABLE PARAMETRIC and NON PARAMETRIC TESTS use parametric Non parametric To compare two paired samples for equality of means Paired ‘t” test Wilcoxan signed rank test To compare two independent samples for equality of means Unpaired ‘t” test Mann Whitney test To compare more than two samples for equality of means ANOVA Kruskal-Wallis Chi square test 87 Miscellaneous :- Fisher’s exact test : A test for the presence of an association between categorical variables. Used when the numbers involved are too small to permit the use of a chi- square test. Friedman’s test : A non- parametric equivalent of the analysis of variance. Permits design. the analysis of an unreplicated randomized 88 Kruskal wallis test : A non-parametric test. Used to compare the samples. medians of several independent It is the non-parametric equivalent of the one way ANOVA. Mc Nemar’s test : A variant of a chi squared test, used when the data is paired. 89 MANN –WHITNEY TEST • It is non parametric test equivalent to ‘t’ test. • Used to compare the medians of 2 independent sampling. ex: comparison of cervical vertebral maturation index at the pre and post treatment stages of 2 different groups. pre treatment. Group 1 Fixed functional appliance Group 2 Premolar extraction 1 2 2 2 1 1 3 14 8 4 5 13 5 1 1 6 0 0 90 Post treatment Group 1 Fixed functional appliance Group 2 Premolar extraction 1 1 1 2 0 0 3 2 0 4 11 10 5 4 9 6 5 5 91 DISCRIMINANT FUNCTION ANALYSIS It is used to classify cases into the values of a categorical dependent, usually a dichotomy.If discriminant function analysis is effective for a set of data, the classification table of correct and incorrect estimates will yield a high percentage correct. 92 META ANALYSIS • Gene glass(1976) coined the term ‘meta analysis’. • Meta-analysis is a statistical technique for combining the findings from independent studies. • Meta-analysis is most often used to assess the clinical effectiveness of healthcare interventions; it does this by combining data from two or more randomised control trials. • Meta-analysis of trials provides a precise estimate of treatment effect, giving due weight to the size of the different studies included. 93 AIMS OF META ANALYSIS • Good meta-analyses aim for complete coverage of all relevant studies. • look for the presence of heterogeneity. • explore the robustness of the main findings using sensitivity analysis. 94 Systematic reviews • Systematic review methodology is at the heart of meta- analysis. This stresses the need to take great care to find all the relevant studies (published and unpublished), and to assess the methodological quality of the design and execution of each study. • The objective of systematic reviews is to present a balanced and impartial summary of the existing research, enabling decisions on effectiveness to be based on all relevant studies of adequate quality. • Frequently, such systematic reviews provide a quantitative (statistical) estimate of net benefit aggregated over all the included studies. • Such an approach is termed a meta-analysis. 95 BENEFITS OF META-ANALYSES Overcoming bias: The danger of unsystematic (or narrative) reviews, with only a portion of relevant studies included, is that they could introduce bias. Meta-analysis carried out on a rigorous systematic review can overcome these dangers – offering an unbiased synthesis of the empirical data. Precision: The precision with which the size of any effect can be estimated depends to a large extent on the number of patients studied. • Meta-analyses, which combine the results from many trials, have more power to detect small but clinically significant effects. • Furthermore, they give more precise estimates of the size of any effects uncovered. • This may be especially important when an investigator is looking for beneficial (or deleterious) effects in specific subgroups of 96 patients. TRANSPARENCY: good meta-analyses should allow readers to determine for themselves the reasonableness of the decisions taken and their likely impact on the final estimate of effect SIZE. REQUIREMENTS FOR META-ANALYSIS:The main requirement for a worthwhile meta-analysis is a wellexecuted systematic review. • However competent the meta-analysis, if the original review was partial, flawed or otherwise unsystematic, then the metaanalysis may provide a precise quantitative estimate that is simply wrong. • The main requirement of systematic review is easier to state than to execute: a complete, unbiased collection of all the original studies of acceptable quality that examine the same therapeutic question. • There are many checklists for the assessment of the quality of systematic reviews;however, the QUOROM statement (quality of reporting of meta-analyses) is particularly recommended. 97 CONDUCTING META-ANALYSES • Location of studies • Quality assessment • Calculating effect sizes • Checking for publication bias • Sensitivity analyses • Presenting the findings 98 HETEROGENEITY • A major concern about meta-analyses is the extent to which they mix studies that are different in kind (heterogeneity). • One widely quoted definition of meta-analysis is: ‘a statistical analysis which combines or integrates the results of several independent clinical trials considered by the analyst to be “combinable”. • The key difficulty lies in deciding which sets of studies are ‘combinable’. Clearly, to get a precise answer to a specific question, only studies that exactly match the question should be included. 99 LIMITATIONS • Assessments of the quality of systematic reviews and meta-analysis often identify limitations in the ways they were conducted. • Flaws in meta-analysis can arise through failure to conduct any of the steps in data collection, analysis andpresentation described above. 100 YANCEY’S 10 RULES -Evaluating Scientific literature 1. Be skeptical 2. Look for the data 3. Differentiate between descriptive and inferential statistics 4. Question the validity of descriptive statistics 5. Question the validity of inferential statistics 101 AJODO-1996 559-563 YANCEY’S 10 RULES -Evaluating Scientific literature 6. Be weary of correlation and regression analyses 7. Identify the population sampled 8. Identify the type of study 9. Look for the indices of probable magnitude of treatment effects 10.Draw your own conclusions. 102 AJODO-1996 559-563 SOFTWARES-STATISTICAL PACKAGES SPSS(Statistical package for the social sciences) Developed in 1968 and current version is IBM SPSS, popular in health sciences. MINITAB-It access complete set of statistical tools,including descriptive statistics,Hypothesis tests and normality tests. 103 EPIINFO-Statistical software for epidemiology developed by Centers for disease control and prevention in Atlanta. -It is used worldwide for the rapid assessment of disease and helps in public health education MICROSOFT EXCEL-It is similar to SPSS but provides an extensive range of statistical functions,that perform calculations from basic mean,median,mode to the more complex stastistical distributions and probability tests. 104 Conclusion Biostatistics is an integral part of research protocols. In any field of investigation ,data obtained is subsequently classified, analyzed and tested for accuracy by statistical methods.A good understanding of biostatistics can improve clinical decision making, program evaluation and research with regard to both individuals and groups of people. 105 REFERENCES • Park K, Park’s text book of preventive and social medicine, 23rd edition. • Soben edition. Peter S, essential of public health dentistry, 4th • Basic epidemiology 2nd edition R Bonita, R Beaglehole, T Kjellstrom. • Mahajan BK, methods in biostatistics. 6th edition • Rao K Visweswara, Biostatistics – A manual of statistical methods for use in health, nutrition & anthropology. 2nd edition.2007 • Determination of sample size-Journal of orthodontics Vol 31:2004,107-114 • Ten rules for reading clinical research reports. John M . Yancey AJODO may 1996. vol 109. • Selection of Statistical Software for Solving Big Data Problems: A Guide for Businesses, Students, and Universities. Ceyhun osgur, Michelle kleckner, Yang Li. SAGE OPEN. May 12, 2015. • What is meta-analysis? Iain K Crombie PhD FFPHM Professor of Public Health, University of Dundee. Huw TO Davies PhD Professor of Health Care Policy and Management, University of St Andrews. 107 THANK YOU 108