Biostatistics
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This document provides an introduction to biostatistics and statistical concepts. It discusses descriptive statistics, which are used to describe data through measures like mean, median and mode. Inferential statistics are used to make inferences about populations based on sample data. Key terms are also defined, such as parameter (a population characteristic), statistic (a quantity calculated from a sample), population (the entire group being studied), and sample (a subset of a population). The document also covers topics like frequency distributions, graphical representation of data through graphs and diagrams, and how to construct tables and frequency distributions.
Biostatistics
- 1. Lecture 1 Introduction to Biostatistics Biostatistics=biology+statistics Other definitionsfor“Statistics” Frequentlyusedtoreferredtorecordeddata Denotescharacteristicscalculatedforaset of data : sample mean Statistical procedurescanbe dividedintotwomajorcategories:descriptive statisticsandinferential statistics. Descriptive statistics Descriptive statisticsincludesstatistical proceduresthatwe use to describe the populationwe are studying.The data couldbe collectedfromeitherasample ora population,butthe resultshelpusorganize anddescribedata. Descriptive statisticscanonlybe usedtodescribe the groupthat isbeingstudying.Thatis,the resultscannotbe generalizedtoanylargergroup. Frequencydistributions, measuresof central tendency (mean,median,andmode),andgraphslike pie chartsandbar charts that describe the dataare all examplesof descriptive statistics. Inferential Statistics Inferentialstatisticsisconcernedwithmakingpredictionsorinferencesaboutapopulationfromobservationsand analysesof a sample.Thatis,we can take the resultsof ananalysisusinga sample andcan generalizeittothe larger populationthatthe sample represents.Inordertodothis,however,itisimperativethatthe sample is representative of the grouptowhichitis beinggeneralized. Examplesof inferentialstatisticsincludelinearregressionanalyses, ANOVA,correlationanalyses,andsurvival analysis,toname a few. Parameter A parameterisa value,usuallyunknown(andwhichtherefore hastobe estimated),usedtorepresentacertain populationcharacteristic.Forexample,the populationmeanisaparameterthatisoftenusedto indicate the average value of a quantity. Withina population,aparameterisafixedvalue whichdoesnotvary.Eachsample drawnfromthe populationhas itsown value of anystatisticthat isusedto estimate thisparameter.Forexample,the meanof the datain a sample isusedto give informationaboutthe overallmeaninthe populationfromwhichthatsample wasdrawn. Parametersare oftenassignedGreekletters(e.g.µ ) Statistic A statisticisa quantitythat iscalculatedfroma sample of data.It is usedtogive informationaboutunknownvalues inthe correspondingpopulation.Forexample,the average of the dataina sample isusedtogive informationabout the overall average inthe populationfromwhichthatsample wasdrawn. Statisticsare oftenassignedRomanletters(e.g.mands) Population A populationisanyentire collectionof people,animals,plantsorthingsfromwhichwe maycollectdata.It isthe entire groupwe are interestedin,whichwe wishtodescribeordraw conclusionsabout. The numberof observationsinapopulationiscalledthe size of the populationandisdenotedbythe letterN.
- 2. Example The populationfora studyof infanthealthmightbe all childrenborninthe UK inthe 1980's. The sample mightbe all babiesbornon 7th May in any of the years. Sample A sample isa groupof unitsselectedfromalargergroup(the population).Bystudyingthe sample itishopedtodraw validconclusionsaboutthe largergroup. A sample isgenerallyselectedforstudybecause the populationistoolarge tostudyin itsentirety.The sample shouldbe representativeof the general population.Thisisoftenbestachievedbyrandomsampling.Also,before collectingthe sample,itisimportantthatthe researchercarefullyandcompletelydefinesthe population,includinga descriptionof the memberstobe included. The numberof observationsinasample iscalledthe size of the sample andisdenotedbythe letter n. Example The populationfora studyof infanthealthmightbe all children borninthe UK inthe 1980's. The sample mightbe all babiesbornon 7th May in any of the years. Lecture 2 Data: The raw material of Statistics is data. We may define data as figures. Figures result from the process of counting or from taking a measurement. For example: 1. When a hospital administrator counts the number of patients (counting). 2. When a nurse weighs a patient (measurement) We search for suitable data to serve as the raw material for our investigation. Such data are available from one or more of the following sources: 1- Routinely kept records. For example: 1. Hospital medical records contain immense amounts of information on patients. 2. Hospital accounting records contain a wealth of data on the facility’s business activities. 2- External sources. The data needed to answer a question may already exist in the form of published reports, commercially available data banks, or the research literature, i.e. someone else has already asked the same question. 3- Surveys: The source may be a survey, if the data needed is about answering certain questions. For example: If the administrator of a clinic wishes to obtain information regarding the mode of transportation used by patients to visit the clinic, then a survey may be conducted among patients to obtain this information. 4- Experiments. Frequently the data needed to answer a question are available only as the result of an experiment. For example:If a nurse wishes to know which of several strategies is best for maximizing patient compliance, she might conduct an experiment in which the different strategies of motivating compliance are tried with different patients. Applications ofbiostatistics
- 3. It has particular applications to medicine and to agriculture, public health, including epidemiology, health services research,nutrition, and environmental health, Design and analysis of clinical trials in medicine Statistical methods are beginning to be integrated into medical informatics, public health informatics, and bioinformatics Presentation ofdata Massive volume of data It is Difficult to learn data by examining unorganized data Data should be organized and condensed into a form that can be more rapidly and easily understood and interpreted Classification Process of dividing a set of observations or objects into classes or groups in such a way that 1. Observations or objects in the same class or group are similar 2. Observations or objects in each class or group are dissimilar to observations or objects in other class or group. Types ofclassification 1. Data are sorted according to one criterion … one way classification 2. When data are sorted according to two criteria… two way classification. 3. When data are sorted according to severalcriteria… manifold classification. Data may be classified according to qualitative, temporal and geographic characteristic. Arrangement of data according to the values of a variable characteristic is called DISTRIBUTION. When the defining variable is expressed in terms of location ….spatial or geographical distribution. Temporal arrangement of values is called a time series. Tabulation Systematic presentation of data classified under suitable heads and subheads , and placed in columns and rows. Data is easy to understand, facilitate comparison,and effective way to conveyinformation to a reader. Types oftables 1. general purpose table..large in size,are extensive with vast coverage and are constructed for for reference purpose. 2.specific purpose table….simple in structure and deal with one or two criteria of classification .. Used ton analyse or to assist in analyzing data. Parts of a table A statistical table has at least four major parts and some other minor parts. (1) The Title (2) The Box Head (column captions) (3) The Stub (row captions) (4) The Body (5) Prefatory Notes (6) Foots Notes (7) Source Notes Main parts of table and its construction Title : table must have a self explanatory title. It should be brief in the form of phrases.
- 4. Abbreviations shouldn’t be used Should be in capitals throughout The different parts of a title should be separated by commas but no full stop at the end If in two or more lines .. Inverted pyramid arrangement of the lines should be used. Column captions and boxhead The heading of each column is called column caption while the section of a table that contains the column aption is called boxhead The heading should be clear but concise Most important characteristic is placed in 1st column Only first word in each column caption shoud be capitalized. No full stop should be put at the end. Row caption and Stub The heading or title for a row caption is called a row caption and the section containing the row caption is called stub. The principles of column caption s apply to row caption in the sub Prefatory notes and footnotes Explanatory notes incorporated in the table bene ath the title and below the bdy is calledPrefatory notes and footnotes respectively. Prefatory note give additional specification of the data indicative of items included and excluded for all data of the table, statements of the box etc. Footnotes are used to clarify anything in the table by giving a fuller description Source notes Every table should have a source note unless the table is an original tabulation and its source is clear from the context It is placed immediately below the table and below the footnote. Body and arrangement of data The most important part. Taking in consideration the basis of classification arrangement of data is made. The data may be arranged according to o alphabetical order o time of occurance o location o magnitude o by customary arrangement i.e men,women and children Spacing and ruling Thick or double lines are used for emphasis and for separating the title, the boxhead, the stub,etc General Rules ofTabulation: A table should be simple and attractive. There should be no need of further explanations (details). Proper and clear headings for columns and rows should be need. Suitable approximation may be adopted and figures may be rounded off. The unit of measurement should be well defined. If the observations are large in number they can be broken into two or three tables. Thick lines should be used to separate the data under big classes and thin lines to separate the sub classes of data. Lecture 3 FrequencyDistribution
- 5. A frequencydistributionisanorderlyarrangementof dataclassifiedaccordingtothe magnitude of the observations. Whenthe data are groupedintoclassesof appropriate size indicatingthe numberof observationsineachclasswe geta frequencydistribution.Byformingfrequencydistribution,we cansummarize the dataeffectively.Itisa methodof presentingthe dataina summarizedform.FrequencydistributionisalsoknownasFrequencytable. Usesof FrequencyDistribution 1. Frequencydistributionhelpsustoanalyze the data. 2. Frequencydistributionhelpsustofacilitate the computationof variousstatisticalmeasures UngroupedFrequencyDistribution A frequencydistributionwithan interval widthof 1is refferedtoanungroupedfrequencydistribution.Ungroped frequencydistributionisanarrangementof the observedvaluesinascendingorder.The ungroupedfrequency distributionare those data,whichare notarrangedin groups.They are knownasindividual series.Whenthe ungroupeddataare grouped,we getthe groupedfrequencydistribution. GroupedFrequencyDistributionTable Frequencydistributiontable (alsoknownasfrequencytable) consistsof variouscomponents. Classes:A large numberof observationsvaryinginawide range are usuallyclassifiedinseveralgroupsaccordingto the size of theirvalues.Eachof these groupsisdefinedbyaninterval calledclassinterval.The classinterval between 10 and 20 is definedas10-20. Class limits:The smallestandlargestpossible valuesineachclassof a frequencydistributiontableare knownas classlimits.Forthe class10-20, the classlimitsare 10 and 20. 10 iscalledthe lowerclasslimitand20 iscalledthe upperclass limit. Class mark: Classmark is the midmostvalue of the classinterval.Itisalsoknownasthe midvalue. Midvalue of each class= (lowerlimit+Upperlimit) If the classis 0-10, lowerlimitis0 and upperlimitis10. So the midvalue is (0+10)2 = 102 = 5. Magnitude of a class interval: The difference betweenthe upperandlowerlimitof aclassis calledthe magnitude of a class interval. Class frequency:The numberof observationfallingwithinaclassinterval iscalledclassfrequencyof thatclass interval. Creatinga GroupedFrequencyDistribution Findthe largestand smallestvalues Compute the Range = Maximum - Minimum Selectthe numberof classesdesired.Thisisusuallybetween5and20. Findthe classwidthby dividingthe range bythe numberof classesandroundingup.There are twothingsto be careful of here.Youmust round up,notoff.Normally3.2wouldroundto be 3, butin roundingup,itbecomes4. If the range dividedbythe numberof classesgivesanintegervalue (noremainder),thenyoucaneitheraddone tothe numberof classesor addone to the classwidth.Sometimesyou're lockedintoacertainnumberof classesbecause of the instructions.The Blumantextfailstomentionthe case whenthere isnoremainder. Picka suitable startingpointlessthanorequal tothe minimumvalue.Youwill be able tocover:"the classwidth timesthe numberof classes"values.Youneedtocoverone more value thanthe range.Follow thisrule andyou'll be okay:The starting pointplus the numberof classestimes the class width mustbe greaterthan the maximumvalue. Your startingpointisthe lowerlimitof the firstclass.Continue toaddthe class widthtothislowerlimittogetthe restof the lowerlimits.
- 6. To findthe upperlimitof the firstclass,subtractone from the lowerlimitof the secondclass.Thencontinue toadd the class widthtothisupperlimittofindthe restof the upperlimits. Findthe boundariesbysubtracting0.5 unitsfromthe lowerlimitsandadding0.5 unitsfrom the upperlimits.The boundariesare alsohalf-waybetweenthe upperlimitof one classandthe lowerlimitof the nextclass.Depending on whatyou're tryingto accomplish,itmaynot be necessarytofindthe boundaries. Tallythe data. Findthe frequencies. Findthe cumulative frequencies.Dependingonwhatyou're tryingto accomplish,itmaynotbe necessarytofindthe cumulative frequencies. If necessary,findthe relativefrequenciesand/orrelativecumulative frequencies LECTURE 4 Graphical representation The visual displayof statistical datainthe formof points, lines,areasandothergeometrical formandsymbolsis calledgraphical representation Two maingroups;Graphs & diagrams Difference betweenagraph and a diagram Graph is a representationof databya continuouscurve usuallyshownona graphpaper. Diagram isany otherone, twoor three dimensional formof visual representation. Diagrams Bestsuitedtospatial series anddatasplitintodifferentcategories For comparisonof same type of data at differentplaces Advantages More attractive thanfigures. Beinga visual display,leave alonglastingandmore effective impressiononthe mindof a reader Comparisoniseasierwithdiagrams. Disadvantage isthat itis lessaccurate than tables. Drawing a diagram An appropriate scale shouldbe chosen Must have a title,akeyfootnote or source note is alsonecessary It shouldbe shaded,coloredorcrosshatchedto show the differentparts,if any.
- 7. Types ofdiagram 1. Simple barchart 2. Multiple barchart 3. Componentbarchart 4. Rectanglesandsubdividedrectangles 5. Pictograms 6. Pie diagrams Simple bar chart Consistsof horizontal orvertical barsof equal widthsor lengthsproportional tothe valuestheyrepresent. The space separating the barsshouldn’texceedthe width of the bar and shouldn’tbe lessthanhalf of itswidth. The bar shouldneitherbe exceedinglylongandnarrow nor shortand broad. Multiple bar chart It showstwoor more characteristicscorrespondingtothe value of a commonvariable inthe formsof groupedbars, whose lengthsare proportional tothe valuesof characteristics,andeachof whichisshadedor coloreddifferentlyto aididentification. It isa gooddevice forthe comparisonof twoor three kindsof information. Componentbar chart It isan effective technique inwhicheachbarisdividedintotwoormore sections,proportional insizetothe componentpartsof a total beingdisplayedbyeach bar. Variouscomponentsare shadedorcoloreddifferentlyto increase the overall effectivenessof the diagram It isusedto representthe accumulationof the variouscomponentsof dataandthe percentages. Theyare alsoknownas subdividedbars. Rectanglesand subdividedrectangles The area of rectangle isequal tothe productof itslengthandbreadth. To representaquantitybya rectangle,bothlengthandbreadthof the rectangle are used. Subdividedrectanglesare drawnforthe data where the quantitiesalongwiththeircomponentsare tobe compared. For construction: Change eachcomponentintothe percentage of the correspondingtotal. Draw one rectangle foreachtotal,takingequal lengthsandbreadthsproportional tothe total.
- 8. Pictograms It isa device forportrayingstatistical databymeansof picturesorsmall symbols. Representaunitvalue of the data by a standardsymbol or a picture andthe whole quantitybybyanappropriate numberof repetitionsof symbolconcerned. A quantitylessthana unitisrepresentedbyapart of the symbol used. Pie diagrams/sector diagrams It consistsof a circle dividedintosectorsorpie shapedpieceswhose areasare proportional tothe variouspartsinto whichthe whole quantityisdivided. Sectorsare shadedor coloreddifferentlytoshow the relationshipof partsto whole.