introduction to statistical methods in public health

TITLEAUTHORADDRESS FORCORRESPONDENCE(incl. fax and email)KEYWORDSLEARNING OBJECTIVES(expected outcomes)MARK DIntroduction to Statistical Methods in PublicHealthLijana Zaletel-Kragelj, MD PhDInstitute of Public Health, Faculty of Medicine LjubljanaZaloška 4, 1000 Ljubljana, SLOVENIAe-mail: lijana.kragelj@mf.uni-lj.siStatistical methods, learning with comprehension, data materialand teaching toolsFor the series of modulesStatistical methods represent very important tool in public healthwork. As it is used more or less periodically, users frequentlymeet problems, especially those with less mathematicalbackground. Lack of general acquaintance with statisticalmethods most often results in a public health worker not able totranslate the results of an analysis into public health technicallanguage, which is usually followed by a complicatedexplanation which can be very hard to understand even for otherpublic health workers. Those for whoom the results are usuallymeant – decision makers or politicians - are generally even lessfamiliar with statistical methods. For the conclusions from publichealth studies and reports to be primarely understandable tothem, it is essential for public health worker to understand thetool he or she is using by himself. Therefore it is very importantto enable public health students the learning approach based oncomprehension of statistical methods.At the end of series of modules following the present one, thestudents should:- understand all principal statistical concepts starting from basicones,- understand and be able to use methods of descriptive statisticsin a proper way independently and self-reliantly,- understand the principles of statistical inference in details,- understand and be able to use majority of methods ofunivariate relationship analysis in a proper way independentlyand self-reliantly,- understand and be able to use principal methods ofmultivariate relationship analysis independently or with helpof a statistician.For the introductory moduleThe purpose of introductory module is to represent to teacher ofstatistical methods for use in public health the apparentlysuccessful way of teaching these methods in Slovenia which isbased on non-conventional distribution of teaching matter andlearning witx experience by usung precisely worked outexample.It is expected that teacher would study this module and decide touse the following modules or not regarding to abilities in his orher country.1

SYNOPSISTEACHING METHODSFor the series of modulesThe series of modules covers following subjects:1. Principles of statistical methods: statistical concepts, statisticaldescribing of data, and statistical inference2. Using statistical methods: principles of relationship analysis –univariate analysis, multivariate analysis, repeatedmeasurements, and non-parametric methodsFor the introductory moduleThe introductory module covers the principles of teaching withcomprehension and description of methods used in Slovenia forteaching the public health students statistical methods.CONTENTSFor the series of modulesMODULE 1: Introduction to statistical methods in public healthSUBTOPIC 1: Principles of statistical methodsMODULE 2: Statistical concepts and statistical describing of dataMODULE 3: Statistical inferenceSUBTOPIC 2: Using statistical methodsMODULE 4: Principles of relationship analysis – univariate analysisMODULE 5: Multivariate analysisMODULE 6: Repeated measurementsMODULE 7: Non-parametric methodsFor the introductory moduleROLE AND POSITION OF STATISTICAL METHODS IN PUBLICHEALTHPublic health, epidemiology and statisticsSTATISTICAL METHODS AS A TOOL IN DESCRIPTIVE AND ANALYTICEPIDEMIOLOGYAnalysing the relationshipOBSERVED HEALTH-RELATED PHENOMENA AND RISK FACTORSDEPENDENCY AND CAUSALITYDependencyCausalitySIMPLE AND COMPLEX ANALYSIS OF THE RELATIONSHIPLEARNING STATISTICAL METHODS WITH EMPHASIS ONCOMPREHENSIONPROPOSAL FOR TEACHING STATISTICAL METHODS FOR USE INPUBLIC HEALTHTeaching statistical methods in public health in SloveniaSEQUENCE OF TEACHING MATTERTEACHING METHODSDATA MATERIAL AND TEACHING TOOLSData materialTeaching toolsSTUDYING MATERIALEVALUATION OF METHODS BY STUDENTSStructure of contents of teaching modulesFor the series of modulesLECTURESActive discussion with students is recommended wheneverpossible, using simple blackboard or blank overheads is preferredin explaining principles of methods, a huge amount of overheadsshould be avoided.PRACTICAL WORK2

Teaching tools - using a computer is essential. Recommendationsfor hardware equipment:- optimal number of computers for a teacher not assisted by anassisting person is no more than 6,- maximal number of computers (teacher obligatory assisted byan assistant) is 10 – 12,- LCD projector is obligatory for demonstrating the methods,Recommendations for software equipment:- using an internationaly recognized statistical programme isoptimal (SPSS is recommended as it is very user friendly),- if not available the teacher shall use software at his or herdisposal but it should be a statistical programme of suitablequality,Teaching approach - learning in small groups is recommendedRecommendations for composing a group:- optimal number recommended is two students changing at thecomputer,- maximal number is three,- one student per computer is not recommended as he or shecould be less familiar with working with a computer,Recommendations for using advantages of working in smallgroups:- the discussion inside groups is stimulated as well as discussionbetween groups,- also the comparison of results between students from differentworking units is stimulated, whenever possible,Data material - learning on clear and evident examples is alsoessentialRecommendations for choosing data material:choosing the data material from the students’ working practice isrecommended (data from national or regional surveys etc..),if no data material is available at the beginning, the data materialused in modules following the present one is at disposal,Supplementary material for studentsIt is recommended to prepare:short manual for working with the computer program to enablestudents working independently as much as possible,exercises for practical work based on data material used,studying material necessary for the tasks which are to becalculated manually.3

SPECIFICRECOMMENDATIONSASSESSMENTSTUDENTS(type of examination)OFFor the series of modules1. The whole teaching materia could be taught in about 45 hours(based on the assumption that postgraduate students arefamiliar with most basic concepts of statistical methods) butmore is recommended (60 – 75 hours),2. The time for classical lectures is proposed to be shortened asmuch as possible and the time for active use of methodsprolonged as much as possible,3. The theoretical background of every single statistical methodis proposed to be placed just before using it in practice toenhance the effect of practical work,4. It is also recommended to put the lectures in a computer roomand to combine them with practical work.For the series of modules1. It is possible to assess the knowledge of practical use ofmethods during the practical work itself, through makingreports by students for each unit,2. It is possible to check the intermediate theoretical knowledgeand comprehension by short (5 – 10 minutes) test-typeassessments at the beginning or at the end of the practicalwork for each unit,3. At the end of the course there should be a global assessmentcomposed of:4. test-type assessment of theoretical knowledge,5. essay-type assessment of practical knowledge using acomplete statistical problem from description to inferenceusing appropriate statistical methods – it could be done on acomputer or on copies of the results made by a computerprogram.4

INTRODUCTION TO STATISTICAL METHODS INPUBLIC HEALTHCONTENTSROLE AND POSITION OF STATISTICAL METHODS IN PUBLIC HEALTHPublic health, epidemiology and statisticsSTATISTICAL METHODS AS A TOOL IN DESCRIPTIVE AND ANALYTIC EPIDEMIOLOGYAnalysing the relationshipOBSERVED HEALTH-RELATED PHENOMENA AND RISK FACTORSDEPENDENCY AND CAUSALITYDependencyCausalitySIMPLE AND COMPLEX ANALYSIS OF THE RELATIONSHIPLEARNING STATISTICAL METHODS WITH EMPHASIS ON COMPREHENSIONPROPOSAL FOR TEACHING STATISTICAL METHODS FOR USE IN PUBLIC HEALTHTeaching statistical methods in public health in SloveniaSEQUENCE OF TEACHING MATTERTEACHING METHODSDATA MATERIAL AND TEACHING TOOLSData materialTeaching toolsSTUDYING MATERIALEVALUATION OF METHODS BY STUDENTSStructure of contents of teaching modules5

ROLE AND POSITION OF STATISTICAL METHODS IN PUBLICHEALTHPUBLIC HEALTH, EPIDEMIOLOGY AND STATISTICSStatistical methods are important in all medical branches, thus also in public health. To putthese two terms in a relationship it is appropriate to define them, adding one more which isput between them:1. Public health is defined as one of the efforts organized by society to protect,promote, and restore the people’s health. It is the combination of sciences, skills, andbeliefs that is directed to the maintenance and improvement of the health of all thepeople through collective or social actions [1]. One of these sciences also beeing one ofimportant branches of medicine science itself is epidemiology.2. Epidemiology is defined as the study of the distribution and determinants of healthrelatedstates or events in specified populations, and the application of this study tocontrol of health problems [1]. Regarding to the aim the epidemiology as a whole can besplit to more specific branches: descriptive epidemiology, analytic epidemiology,experimental epidemiology and evaluational epidemiology. Statistical methodsrepresents one of the most powerful tools in the hands of an epidemiologist.3. Statistics is defined as the science and art of collecting, summarizing and analyzingdata that are subject to random variation [1]. It is represented by a huge set of differentmethods adequate for different situations.STATISTICAL METHODS AS A TOOL IN DESCRIPTIVE AND ANALYTICEPIDEMIOLOGYIt was already menthioned that epidemiology could be classified regarding to the aim to fourmain branches. The first two - descriptive and analytic epidemiology as well as theinvolvement of statistical methods in them it will be discussed here:1. Descriptive epidemiology is defined as activities to study occurrence of disease orother health-related characteristics in human population [1]. It is concerned in where,when and how frequent such phenomena are. The answers to these questions areobtained by the means of methods of descriptive statistics.2. Analytic epidemiology is defined as activities to examine associations, commonlyputative or hypothesized causal relationships. An analytic study is usually concerned withidentifying or measuring the effects of risk factors, or is concerned with the healtheffects of specific exposure(s) [1]. In these activities the methods of analyticalstatistics are involved.6

ANALYSING THE RELATIONSHIPBy the means of analytical statistical methods different aspects of association orrelationship between observed phenomenon and other characteristics of observedsubjects, seen as risk factors for its occurrence are assesed. Therefore the appropriatename for the whole set of various procedures also would be relationship analysis.To make all considerations about statistical methods as a tool for assessing the type andstrenght of a relationship under observation easier some of concepts should be clarifyed.OBSERVED HEALTH-RELATED PHENOMENA AND RISK FACTORSThese two already used terms should be clarifyed first:1. Observed phenomenon - disease or other health-related condition frequently calledalso an outcome and2. Risk factor – a caracteristic (an aspect of behaviour or lifestyle, an environmentalexposure, an inborn or iherited characteristic) which is on the basis of epidemiologicevidence known to be associated with health-related condition(s) considered important toprevent [1].DEPENDENCY AND CAUSALITYDependencyThe concept of dependency has different meaning in epidemiology as it has in statistics instrict sense:− in epidemiology, the dependent variable is the manifestation or outcome whose variationis to be explained by risk factors− in statistics the dependent variable is the one predicted by a regression equationIn jargon the term “dependent” is rather loosely used. Frequently it is used in sense ofcausality.CausalityBy the definition [1] causuality is relating of causes to the effects they produce. Mostlyepidemiology is concerned of causuality. The phenomenon under observation is usuallyassigned the role of “effect” and the risk factors thereof the role of "causes". Actuallycausality of the relationship is not as simple. It should be clearly stated that epidemiologicevidence of causality by itself is insufficient to establish the causality in nature. The later isusually possible to be proved only by studies in different places which could be carried out7

for more decades. However, for the statistical methods to be understandable, such settingup is very adequate. A picture (Figure 1) can offer additional help.C 1C 2C 3RISKOBSERVEDPHENOMENONC 5C 4FACTORSC 6»EFFECT«»CAUSES«Figure 1: Graphical representation of the setting up of the observed desease or other healthrelated phenomenon - observed phenomenon or "effect" and characteristics ofobserved subjects - "causes" (C1 – C6) into a relationship, as a help at relationshipanalysis.SIMPLE AND COMPLEX ANALYSIS OF THE RELATIONSHIPIn analysing the relationship between observed outcome and risk factors two kinds ofmethods could be used:1. Univariate statistical methods - the analysis of relationship of a single risk factorwith an outcome2. Complex or multivariate statistical methods – the analysis of relationship ofseveral risk factors with an outcome at a time8

It would be most appropriate to use multivariate statistical methods from the very beginning,but these methods have several limitations connected with the number of observed subjectsand statistical features of "effects" and "causes". This way of performing the analysis is mostusually not possible to be carried out as the number of observations is rarely big enough. Somostly the univariate analysis of relationship of a single "cause" with a "consequence" iscarried out, resulting in determination of statistically the most important ones. Usually it isfollowed by multivariate methods afterwards.LEARNING STATISTICAL METHODS WITH EMPHASIS ONCOMPREHENSIONUsually all users of statistical methods with less mathematical background, specially periodicones, meet big problems. Maybe in medicine these problems are even more outstanding asmedical workers usually have less expressed abstract way of thinking. Since these methodsrepresent very important tool in researches in medicine, specialy in public health, it is veryimportant to enable public health students the learning approach based on comprehensionof statistical methods not only using them as a “cook book”.For this aim to be attained, learning must be approached with consideration. It isundoubtedly important:− the teaching matter to be distributed logically and units should be smoothly associatedone to another;− not to use too many equations or mathematical expressions, especially not inprofessions with less abstract way of thinking (in medicine in particular);− to enable the students to use the methods in practice, meaning transferring theemphasis from the lectures to practical work on an example (learning with experience);− to watch carefully all the time if the students are following the explanation and practicaluse of the teaching matter; the teacher must strive for not concluding a subject until it isaccepted by the majority of students;− to use new pedagogical approaches at lecturing, for example working in smaller groups,learning with discussion etc., whenever possible;− to use adequate tools, meaning learning with the statistical program of good quality;nevertheless certain calculations shall be carried out manually or partly manually,particularly where this shall be necessary for the procedure to be easier understandable;− students shall be proposed, if not supplied with, corresponding studying material.9

The main purpose of teaching public health students statistical methods withcomprehension is for them to be able to have entire process of a public health research,from the definition of a problem as a starting point, through collecting the relevant data andanalysing them, finaly to interpretation of the results of the analysis under control. This doesnot necessarily mean to do the entire process by themselves. Lack of general acquaintancewith research tools including statistical methods most often results in a public health worker,not be able to translate the results of an analysis into technical language of his or herprofession. This is usually followed by a very complicated interpretations which can be veryhard to understand, specially to decision makers and polititians to whom the results areintended for. In other words, teaching statistical methods with comprehension means tomake future public health workers to be able to speak the same language as statisticexperts, who are responsible for technical realisation of the methods.PROPOSAL FOR TEACHING STATISTICAL METHODS FOR USEIN PUBLIC HEALTHIn teaching statistical methods in public health in Slovenia we try to follow the principles justdescribed as much as possible, specially at postgraduate level of education. It seems thiscould be the right way to attain the aim already described.In following paragraphs a short description of the teaching process in our country ispresented. At the end of this introduction also the structure of teaching modules is alsodescribed.TEACHING STATISTICAL METHODS IN PUBLIC HEALTH INSLOVENIASEQUENCE OF TEACHING MATTERThe longterm experiences show that the right sequence of teaching matter is one of the keysto success. In Table 1 the way of distribution of taeching matter we used is shown.10

Table 1: Proposal for distribution of statistical methods with regard to thematic wholes.ISTATISTICAL CONCEPTS ANDSTATISTICAL DESCRIBING OF DATAStatistical concepts− basic concepts;− concepts related to statistical activities− concepts related to statistical variables− concepts related to probability distributionsStatistical describing of data− presenting data− describing a distribution− summarizing the distribution featuresPRINCIPLES OF STATISTICAL METHODSIIPRINCIPLES OFSTATISTICAL INFERENCETheoretical probability distributions− Normal distributionSampling distributions− principles of sampling distributions− sampling distribution of mean− sampling distribution of difference between two means___________________________________________________Statistical inference techniques− confidence intervals− testing of hypothesesIPRINCIPLES OF RELATIONSHIP ANALYSISRelationship between two variables – univariate analysis− in case of two numerical variables (linear regression andcorrelation)− in case of two attributable variables (chi-square test,relative risk, odds ratio− in case of mixed variables (t-test for independentmeasurements, logistic regression)IIIREPEATED MEASUREMENTSTwo measurements− paired t-testMore than two measurements− analysis of variance for repeated measurementsUSING STATISTICAL METHODSIIMULTIVARIATE ANALYSISRelationship between more than two variables –multivariate analysis− in case of numerical dependent variable (multiple linearregression, analysis of variance)− in case of binary attributable dependent variable (multiplebinary logistic regression)−−IVNON-PARAMETRIC METHODSfor independent measurementsfor dependent (repeated) measurementsThe whole teaching process is based on the relationship analysis which is situated centrally. Bythe means of the latter, teaching starts. This is followed by construction of thinking from the mostsimple building blocs – basic concepts and methods, gradually to more complex ones. When thetechnique is absorbed we return to the relationship analysis. The realization of lessons is principallydesigned in following steps:1. Step one – getting familiar with basic statistical concepts2. Step two – getting familiar with sample distributions and their meaning in statisticalinference3. Step three – getting familiar with techniques of statistical inference using workedexamples4. Step four – transfer of basic principles of statistical methods to simple relationshipanalysis (univariate)5. Step five – extending the methods for simple relationship analysis to more complex ones,getting familiar with principles of multivariate relationship analysis11

6. Step six – transfer of all previous subjects to repeated measurements analysis7. Step seven – introduction of non-parametric methodsUp to this time the first four steps were realized in all courses and the remaining ones only insome of them.Such sequence imply one very important point of view to statistical methods – it does notrepresent classical statistical way of thinking in the sense of observing differences betweentwo groups of observed subjects. The students are for example represented that not onlyregression and correlation analysis are to analyse the relationship between two variables butalso the classical t-test is (in this test also two variables are involved one of which being theobserved phenomenon – the outcome, and the other, the one dividing the observed subjectsinto two groups – the risk factor).Based on our experiences, students also must be given enough time for basic concepts. Itis hard to say how much time would this take since groups of public health students arediffering considerably. At the beginning of single course the groups of students mostly arepossible to be of very heterogeneous background knowledge. A good teacher shall be ableto carry out the whole teaching matter with no regard to the emphasis laid to individual partsof the subject.TEACHING METHODSFor successful outcome of teaching process it is essential to use modern teaching methodswith emphasis on the active involvement of students in the process. The approach oflearning with experience in small groups based on global worked example is used.In a group there are no more than three students with optimal number of two. Every singlegroup of students, together with a computer, constitute one working unit. The students areas a rule distributed in such a way that at least one in a group is familiar with working on acomputer.This approach enables students to actively share their knowledge and help themselvesinside each group. The discussion inside groups is therefore stimulated as well as discussionbetween groups. Also the comparison of results between working units, whenever possible,is stimulated.DATA MATERIAL AND TEACHING TOOLSData material12

For already several years at teaching statistical methods in public health in Slovenia datacollection which enables learning such methods in quite a pleasant way has been used.These are the data collecting within the Perinatal Informational System of Slovenia (PISS)[2], which is considered to be one of the permanent collections of medical data of thehighest quality with the many years' tradition. It was started in 1987 when collection of datastarted on an uniform form in all Slovene maternity hospitals.Data material for teaching is only a small piece out of the whole collection PISS, preparedespecially for this purpose. Safeguard of personal data is assured so that all personalidentificators have been removed, and moreover only the data are selected from the wholecollection which shall be used for the teaching purpose. Special attention was paid to includesuch data which are possible to play the role of the "effect" as well as the data which canplay the role of "cause". Also they are chosen to have diverse statistical characteristics as tobe able to represent the majority of statistical methods.The basic data material for all statistical activities is composed of 6356 statistical units,representing the model of a population. For teaching different statistical methods, samples ofvarious size are then randomly selected from the population database. The smallest samplesis composed of 30 units and the largest one of 800 units. The students shall select some ofsuch samples from the population while performing practical work by themselves, and othersshall be prepared by the teacher. First ones are, on principle, different at each working placeand shall be, at the end of the corresponding exercise, deleted by the students or by theteacher. Others are the same for all working places, constantly present there and are usedfor many times. Data material is composed of the following permanent databases:1. Population database2. Database with a sample of 100 units – main database for teaching principles of statisticalmethods3. Database with a sample of 500 units – additional database for teaching principles ofstatistical methods4. Database with a sample of 800 units – main demonstrational database and maindatabase for teaching multivariate statistical methodsNotwithstanding the number of units in a single database, all databases are including thesame statistical variables, description of which is presented in Table 2.Table 2: Description of variables, their values and codes in basic data set for teachingstatistical methods in public health in Slovenia.COLUMN IN SHORT NAME OF A INFORMATION THE VARIABLE IS GIVINGA DATA SET VARIABLEABOUT1 IDN unit identification numberVARIABLE VALUES AND THEIRCODES IN DATA SET13

2 BWEIGHT birth weight of a child (weight in grammes)3 SEX child sex 1 = boy2 = girl4 GESTAGE gestational age of a child (age in weeks of pregnancy)5 MOTHAGE age of mother at delivery (age in years)6 SMOKING mother’s smoking habits during pregnancy 0 = no1 = to 10 cigarettes/day2 = 10 cigarettes or more/day7 HYPIRUT hyperactivity of uterus during pregnancy 0 = no1 = yes8 HBP higher blood pressure during pregnancy 0 = no1 = yes9 MEDVIT taking vitamine preparations during pregnancy 0 = no1 = yes10 MEDFE taking iron preparations during pregnancy 0 = no1 = yes11 MEDAB taking antibiotics during pregnancy 0 = no1 = yesWith the purpose of teaching, first of all representation of meaning of the reduction of aninformation for the purpose of analysis, values of some basic statistical variables stated inTable 2, have been changed (merging of values). This resulted in new variables which areadded in the databases following the basic ones. The values of the same are described inTable 3.Table 3: Description of new variables (transformation of variables from basic data set) andtheir values and codes in data material for teaching statistical methods in publichealth in Slovenia.COLUMN INA DATA SETSHORT NAME OF AVARIABLEINFORMATION THE VARIABLE IS GIVINGABOUTVARIABLE VALUES AND THEIR CODESIN DATA SET12 LBW low birth weight 0 = no (BWEIGHT 2501 grammes or more)1 = yes (BWEIGHT to including 2500grammes)13 SMOYES mother smoking during pregnancy 0 = no (SMOKING = 0)1 = yes (SMOKING 1 or more)14 PRETERM preterm delivery 0 = no (GESTAGE to including 36 weeks)1 = yes (GESTAGE 37 weeks or more)On this data most of statistical methods could be presented in an obvious way as well asnumerous possible traps of their missuse.14

Teaching toolsAdequate equipment is also very important for teaching statistical methods in a propermanner, which is carried out mostly by the means of a computer with a statistical program ofsuitable quality.At the University of Ljubljana, the statistical program SPSS (Statistical Package for SocialSciences) has been used for this purpose for already a few decades. At the beginning, it waspossible to be used only on main university computer, however for the last few years, theUniversity has hired the licence to enable the distribution of the program within its membersunder favourable conditions for each personal computer. Two main purposes are soachieved: a program of good quality is used within the University, enabling the results to becompared within the university and as this program is widely spread also enabling the resultsto be compared to other countries.However, whenever it is necessary for easier understanding of methods, the program canbe supplemented by using a calculator and statistical tables.STUDYING MATERIALStudying material prepared for students, is composed of:1. A short manual for working with the SPSS program, so that they were able to startworking by themselves with a program from the very beginning;2. Short summary of the subject, which was not intended as being the only source ofstatistical theory for the students, but to help them directing their flow of thinking and as ahelp with practical work;3. Collection of exercises for practical work4. Copies of the main results of the SPSS program, so that the students were able to markdown their comments and explanations of printouts for helping them at studying;5. Advised textbook for deepening their theoretical knowledge, which could be find in aCentral Library of Faculty of Medicine or bought for a reasonable price.EVALUATION OF METHODS BY STUDENTSAll generations of students were asked to evaluate the teaching methods. With no exeptionthe methods described above were positively evaluated. Almost at the conclusion of eachcourse, students declared that after the course statistical methods were moreunderstandable to them and they were no more afraid of using them.15

STRUCTURE OF CONTENTS OF TEACHING MODULESThe teaching material which is offered as a content under topic “Statistical methods” iscomposed from series of modules in which statistical methods are distributed in the samemanner as demonstrated in Table 1 - into two big themes/subtopics and the units/modulesthereof, all of them following the introductory module:MODULE 1: Introduction to statistical methods in public healthSUBTOPIC 1: Principles of statistical methodsMODULE 2: Statistical concepts and statistical describing of dataMODULE 3: Statistical inferenceSUBTOPIC 2: Using statistical methodsMODULE 4: Principles of relationship analysis – univariate analysisMODULE 5: Multivariate analysisMODULE 6: Repeated measurementsMODULE 7: Non-parametric methodsEach module except the introductory one is going to be composed of:− short summary of the subject covered by the unit− exercises for practical work− list of data files for practice− teaching material necessary for the tasks which are foreseen to be calculated manually− copies of the results of analysis carried out by the means of the SPSS program on asample of 800 unitsThe following is not included:− short manual for working with the SPSS program since we decided that not all users ofthe modules shall have this program at disposal or that they shall use software at theirdisposal− textbook suggestion for deepening theoretical knowledge, which shall be advised byeach teacher according to his experiences and with regard to the textbook’s availability inthe countryAs the author of these modules I declare that the teaching method and material wasdevelopped by myself during my working as a teaching assistant at Institute of biomedicalinformatics of Faculty of medicine in Ljubljana. Now it is used also at Institute for public16

health of the same faculty, where I am working at the present. Also I declare, that the onlyintention of publishing this material is to present one of possible methods for teachingstatistical methods, apparently successful one and not in any case to publish statisticaltheory. The later is very good described in numerous statistical textbooks.17