1 introduction and basic concepts
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Statistics is the study of collecting, organizing, summarizing, and analyzing data. There are two main branches of statistics: descriptive statistics and inferential statistics. Descriptive statistics involves organizing and summarizing data, while inferential statistics involves using a sample of data to draw conclusions about a population. Statistics is used across many fields, especially in research involving biological or medical data, known as biostatistics. Statistics helps effectively present research findings and evaluate research proposals.
1 introduction and basic concepts
- 2. Definition ofDefinition of StatisticsStatistics C Collecting … O Organizing … D Displaying … S Summarizing … Data Statistics is the study of the methods and procedures forStatistics is the study of the methods and procedures for and for making scientific inferences from such data
- 3. Definition of DataDefinition of Data “Data” is the plural of “Datum” Generic term for numerical information that has been obtained on a set of objects The objects can be anything… e.g., people, animals
- 4. Data: ExampleData: Example 1)1) Age, Height, WeightAge, Height, Weight 2)2) Grade in Psych 100 (A=4, B=3, etc.)Grade in Psych 100 (A=4, B=3, etc.) 3)3) Temperature (K,F, CTemperature (K,F, Coo )) 4)4) Male (0), Female (1),Male (0), Female (1), Androgynous(2)(2) 5)5) How many pens/pencilsHow many pens/pencils 6)6) Test score (e.g., SAT)Test score (e.g., SAT)
- 5. BiostatisticsBiostatistics When the data being analyzed andWhen the data being analyzed and derived from the biological sciences andderived from the biological sciences and medicine, we use the termmedicine, we use the term biostatisticsbiostatistics toto distinguish this particular application ofdistinguish this particular application of statistical tools and concepts.statistical tools and concepts.
- 6. Why Study Statistics?Why Study Statistics? Essential for people going into research or graduate study in aEssential for people going into research or graduate study in a specialized area.specialized area. Effective presentation of researcher findings in papers, inEffective presentation of researcher findings in papers, in reports for publication, and at professional meetings.reports for publication, and at professional meetings. Helpful to those who are preparing, or may be called upon toHelpful to those who are preparing, or may be called upon to evaluate, research proposals.evaluate, research proposals. A knowledge of statistics is essential for persons who wish toA knowledge of statistics is essential for persons who wish to keep their education up to date.keep their education up to date.
- 7. Why Study Statistics?....continueWhy Study Statistics?....continue Important to review and understand the writings in scientificImportant to review and understand the writings in scientific journals, which use statistical terminology and methodology.journals, which use statistical terminology and methodology. An understanding of statistics can helpAn understanding of statistics can help anyoneanyone discriminatediscriminate between fact and fancy in everyday life in reading newspapersbetween fact and fancy in everyday life in reading newspapers and watching television, and in making daily comparisons andand watching television, and in making daily comparisons and evaluations.evaluations. Finally, a course in statistics should help one know when, andFinally, a course in statistics should help one know when, and for what purpose, a statistician should be consulted.for what purpose, a statistician should be consulted.
- 8. Branches of StatisticsBranches of Statistics InferentialInferential StatisticsStatistics DescriptiveDescriptive StatisticsStatistics There are two major categories of statistics:.
- 9. DescriptiveDescriptive StatisticsStatistics Comprise those methods concerned withComprise those methods concerned with collecting, organizing, picturing, summarizing andcollecting, organizing, picturing, summarizing and describing a set of data so as to yield meaningfuldescribing a set of data so as to yield meaningful information.information.
- 10. Descriptive statistics provides information only aboutDescriptive statistics provides information only about the collected data. The construction of tables, charts,the collected data. The construction of tables, charts, graphs, falls in the area categorized as descriptivegraphs, falls in the area categorized as descriptive statistics.statistics. An exampleAn example ofof descriptivedescriptive statistics is the decennialstatistics is the decennial census in some countries, in which all the residentscensus in some countries, in which all the residents are requested to provide such information as age,are requested to provide such information as age, sex, race, and marital status. The data obtained insex, race, and marital status. The data obtained in such a census can then be compiled and arrangedsuch a census can then be compiled and arranged into tables and graphs that describe theinto tables and graphs that describe the characteristics of the population at a given time.characteristics of the population at a given time. DescriptiveDescriptive StatisticsStatistics
- 11. Inferential statisticsInferential statistics comprise those methods concerned with the analysiscomprise those methods concerned with the analysis of information from a sample or a subset of data toof information from a sample or a subset of data to draw conclusions regarding the population or thedraw conclusions regarding the population or the entire set of data.entire set of data. AnAn exampleexample ofof inferentialinferential statistics is an opinion poll,statistics is an opinion poll, such as the pre-election Poll, which attempts to drawsuch as the pre-election Poll, which attempts to draw inferences as toinferences as to the outcome of an election. In suchthe outcome of an election. In such a poll, a sample of individuals (frequently fewer thana poll, a sample of individuals (frequently fewer than 2000) is selected; their preferences are tabu-lated,2000) is selected; their preferences are tabu-lated, and inferences -are made as to how millions ofand inferences -are made as to how millions of persons would vote if an election were held that day.persons would vote if an election were held that day.
- 12. Sources of DataSources of Data Routinely kept recordsRoutinely kept records:: Hospital medical records, for example, containHospital medical records, for example, contain immense amounts of information on patients.immense amounts of information on patients. SurveysSurveys:: Methods of survey:Methods of survey: – Personal interviewPersonal interview – Telephone interviewTelephone interview – QuestionnairesQuestionnaires ExperimentsExperiments:: for example, the effect of specific medication on specificfor example, the effect of specific medication on specific disease.disease. ObservationsObservations attained by naked eyes or through video camera etc.attained by naked eyes or through video camera etc. External sourcesExternal sources:: e.g. published reports, commercially available datae.g. published reports, commercially available data banks, or the research literature.banks, or the research literature.
- 13. VariablesVariables The variable is the characteristic of the people orThe variable is the characteristic of the people or object included in a study to be measured orobject included in a study to be measured or observed.observed. Examples:Examples: Age, weight, height, marital status, or blood groupAge, weight, height, marital status, or blood group
- 14. Types of VariablesTypes of Variables Qualitative orQualitative or categoricalcategorical variablesvariables are thoseare those variables that yield observations on whichvariables that yield observations on which individualsindividuals can be categorized according to some characteristic,can be categorized according to some characteristic, examples include; occupation, sex, marital status, andexamples include; occupation, sex, marital status, and education level.education level. (Nonnumeric in nature)(Nonnumeric in nature) Quantitative variablesQuantitative variables are those variables that yieldare those variables that yield observations that can be measured, example include;observations that can be measured, example include; weight, height, and serum cholesterol.weight, height, and serum cholesterol. (numeric values)(numeric values)
- 15. Quantitative variables can be further classified asQuantitative variables can be further classified as discrete or continuous.discrete or continuous. Discrete variablesDiscrete variables A variable is called discrete if it has only a countable number ofA variable is called discrete if it has only a countable number of values. Usually these will be whole numbers (integers) such as 3, 5,values. Usually these will be whole numbers (integers) such as 3, 5, 9, and 23 and none in between (i.e. they usually don’t have decimal9, and 23 and none in between (i.e. they usually don’t have decimal values). For example, the number of patients in a hospital may bevalues). For example, the number of patients in a hospital may be 178 or 179, but it cannot be any value between these two.178 or 179, but it cannot be any value between these two. The number of children in one familyThe number of children in one family The number of time you visit a doctor.The number of time you visit a doctor. The number of missing teeth are termed discrete variablesThe number of missing teeth are termed discrete variables
- 16. ContinuousContinuous Continuous variable is one which has any value within aContinuous variable is one which has any value within a certain interval of values. They are measured on somecertain interval of values. They are measured on some scale in terms of some measurement unit such asscale in terms of some measurement unit such as kilograms, meters, mmol/l, degree Centigrade, weight,kilograms, meters, mmol/l, degree Centigrade, weight, height, length…..etc. they may take on for example,height, length…..etc. they may take on for example, fractional values (e.g., 37.8, 56.2, and 112.9).fractional values (e.g., 37.8, 56.2, and 112.9). Quantitative variables can be further classified asQuantitative variables can be further classified as discrete or continuous.discrete or continuous.
- 17. Scale (level) of MeasurementScale (level) of Measurement Nominal Ordinal Interval Ratio Degree of ambiguity in interpreting numbers decreases. Information content increases Use the mnemonic NOIR to remember these scales in order.
- 18. The lowest level of the measurement.The lowest level of the measurement. Nominal scale data are divided into qualitative categories or groups.Nominal scale data are divided into qualitative categories or groups. Example:Example: male/female, black/white, Well/sick, Child/adult, Single/ marriedmale/female, black/white, Well/sick, Child/adult, Single/ married Numbers, when used, it will be mereNumbers, when used, it will be mere labellabel and have no numericaland have no numerical meaning such as telephone or car numbers.meaning such as telephone or car numbers. Example: Gender Data Male, Female, Androgenous (0,1,2) or (-3,50,23.983) The arithmetic operations of addition, subtraction, multiplication, and division are not performed for nominal data. Nominal MeasurementNominal Measurement
- 19. Ordinal Measurement Data may be arranged in some order, but actual differences between data values either cannot be determined or are meaningless. Example: class rank; 1st 2nd 3rd 95% 88%90% More examples include, •the degree of pain (severe, moderate, mild, none), •the age group (baby, infant, child, adult, geriatric ).
- 20. Interval Measurement Like the ordinal level, in that they can be arranged in some order but it has addition property that meaningful intervals (differences) between data values can be computed. Example: Temperature Difference between 100 and 90°C is the same as the difference between 50°C and 40°C.
- 21. However, interval-level dataHowever, interval-level data have no absolute zero pointhave no absolute zero point oror starting point. Consequently, differences are meaningful butstarting point. Consequently, differences are meaningful but ratiosratios ofof data are not.data are not. For example, on the Celsius scale it is not correct to say 20 °C isFor example, on the Celsius scale it is not correct to say 20 °C is twice as hot as 10 °C or 100°C is not twice as hot as 50°C, becausetwice as hot as 10 °C or 100°C is not twice as hot as 50°C, because 0°C does not represent the point at which there is no heat, but the0°C does not represent the point at which there is no heat, but the freezing point of water.freezing point of water. Calendar times are also interval measurements, since the date 0Calendar times are also interval measurements, since the date 0 A.D. does not signify “no time”.A.D. does not signify “no time”. An IQ “Intelligent Quotient of zero would not mean no intelligence atAn IQ “Intelligent Quotient of zero would not mean no intelligence at all, but serious intellectual or perceptual problem in using materialsall, but serious intellectual or perceptual problem in using materials of the test.of the test. “The summer is 50% percent warmer than the spring” Interval Measurement
- 22. Ratio Measurement Has the same properties as an interval scale; but because it has an absolute zero, meaningful ratios do exist. Example: biomedical variables weight in grams or pounds, time in seconds or days, Kelvin scale blood pressure in millimeters of mercury and pulse rate are all ratio scale data. Pulse rate of 120 is twice as fast as a pulse rate of 60.
- 23. Populations and SamplesPopulations and Samples AA populationpopulation is a set of persons (or objects)is a set of persons (or objects) having a common observable characteristic.having a common observable characteristic.
- 24. SampleSample AA samplesample is a subset of data selected from ais a subset of data selected from a population,population, selected so as to beselected so as to be representativerepresentative ofof the larger population.the larger population. The number of elements in the sample is called theThe number of elements in the sample is called the sample sizesample size.. The primary objective for selecting a sample from aThe primary objective for selecting a sample from a population is to drawpopulation is to draw inferencesinferences about thatabout that population.population.
- 25. Statistics and parameters A parameterA parameter isis a characteristic of or a facta characteristic of or a fact about a population.about a population. A statisticA statistic is a characteristic of or a factis a characteristic of or a fact about a sample.about a sample.
- 26. Definition of samplingDefinition of sampling Procedure by which some membersProcedure by which some members of a given population are selected asof a given population are selected as representatives of the entire populationrepresentatives of the entire population
- 27. Why do we use samples ?Why do we use samples ? Why notWhy not study the entirestudy the entire population?population? It is impossibleIt is impossible to obtain the weight of every tuna in theto obtain the weight of every tuna in the Pacific Ocean.Pacific Ocean. It is too costly.It is too costly. Need long period of time.Need long period of time. It is labour-intensiveIt is labour-intensive Some testing is inherently destructiveSome testing is inherently destructive: We can't drain: We can't drain all the blood from a person and count every white cell.all the blood from a person and count every white cell.
- 28. How Samples Are Selected?How Samples Are Selected? Simple random samples Systematic sampling Stratified sampling Cluster sampling Convenience Sampling Judgment Sampling
- 29. Sample typeSample typeSample typeSample type Probability samplesProbability samplesNon-probability samplesNon-probability samples ClusterClusterClusterClusterSystematicSystematicSystematicSystematic StratifiedStratifiedStratifiedStratifiedSimple RandomSimple RandomSimple RandomSimple Random ConvenienceConvenienceConvenienceConveniencePurposivPurposiv ee PurposivPurposiv ee SnowballSnowballSnowballSnowball Sampling TechniquesSampling Techniques
- 30. Probability Samples Random samplingRandom sampling – Each subject has a known probability of being selected – Allows application of statistical sampling theory to results to: Generalise and Test hypotheses. Probability samples are the best Ensure – Representativeness – Precision 3030
- 31. Non-probability samples Probability of being chosen is unknownProbability of being chosen is unknown Cheaper- but unable to generaliseCheaper- but unable to generalise Potential for biasPotential for bias 3131
- 32. Simple random samplesSimple random samples It is a sample drawn so that every element in theIt is a sample drawn so that every element in the population has an equal probability of being included.population has an equal probability of being included. Two ways for selecting simple random sampleTwo ways for selecting simple random sample Lottery methodLottery method ProcedureProcedure – Number all unitsNumber all units – Randomly draw unitsRandomly draw units Random number tableRandom number table
- 33. Example:Example: evaluate the prevalence of toothevaluate the prevalence of tooth decay among the 850 children attending adecay among the 850 children attending a schoolschool List of children attending the schoolList of children attending the school Children numerated from 1 to 850Children numerated from 1 to 850 Sample size = 10 childrenSample size = 10 children Random sampling of 10 numbers between 1Random sampling of 10 numbers between 1 and 850and 850 How to randomly select? Simple random samplingSimple random sampling
- 35. How to select a Random Sample?How to select a Random Sample? UsingUsing random number table Selecting a random sample involves three steps:Selecting a random sample involves three steps: (1)(1) Define the population.Define the population. (2)(2) Enumerate it.Enumerate it. (3)(3) Use a random number table to select the sample.Use a random number table to select the sample.
- 36. Example:Example: evaluate the prevalence of toothevaluate the prevalence of tooth decay among the 850 children attending adecay among the 850 children attending a schoolschool List of children attending the schoolList of children attending the school Numerate children from 1 to 850Numerate children from 1 to 850 Sample size = 10 childrenSample size = 10 children Random sampling of 10 numbers between 1Random sampling of 10 numbers between 1 and 850and 850 Simple random samplingSimple random sampling
- 37. Random number tableRandom number table Many calculators andMany calculators and computers also generatecomputers also generate random numbers.random numbers. The digits 0 through 9 occurThe digits 0 through 9 occur randomly throughout a randomrandomly throughout a random number table withnumber table with each digiteach digit having an equal chance ofhaving an equal chance of occurringoccurring.. To use a random numberTo use a random number table, first randomly select atable, first randomly select a starting positionstarting position and thenand then move in any directionmove in any direction toto select the numbers.select the numbers. 13962 70992 65172 28053 02190 83634 66012 70305 66761 88344 43905 46941 72300 11641 43548 30455 07686 31840 03261 89139 00504 48658 38051 59408 16508 82979 92002 63606 41078 86326 61274 57238 47267 35303 29066 02140 60867 39847 50968 96719 43753 21159 16239 50595 62509 61207 86816 29902 23395 72640 83503 51662 21636 68192 84294 38754 84755 34053 94582 29215 36807 71420 35804 44862 23577 79551 42003 58684 09271 68396 19110 55680 18792 41487 16614 83053 00812 16749 45347 88199 82615 86984 93290 87971 60022 35415 20852 02909 99476 45568 05621 26584 36493 63013 68181 57702 49510 75304 38724 15712 06936 37293 55875 71213 83025 46063 74665 12178 10741 58362 84981 60458 16194 92403 80951 80068 47076 23310 74899 87929 66354 88441 96191 04794 14714 64749 43097 83976 83281 72038 49602 94109 36460 62353 00721 66980 82554 90270 12312 56299 78430 72391 96973 70437 97803 78683 04670 70667 58912 21883 33331 51803 15934 75807 46561 80188 73440 29317 27971 16440 62843 84445 56652 91797 45284 25842 40938 73504 21631 81223 19528 15445 77764 33446 41204 70067 16926 70680 66664 75486 16737 01887 50934 43306 75190 86997 24057 79018 34273 25196 99389 06685 45945 62000 76228 60645 66318 46329 46544 95665 36160 38196 77705 28891 12106 56281 29579 66116 39626 06080 05505 45420 44016 79662 92069 27628 07440 32540 19848 27319 85962 19758 92795 00458 71289 05884 97407 23322 73243 98185 28763 04900 54460 22083 89279 43492 82470 40857 86568 49336 42222 40446 82240 79159 44168 38213 43797 26598 29983 67645 43626 40039 51492 36488 70280 24218 53872 04744 89336 35630 97761 43444 95895 24102 07006 71923 17132 32062 41425 66862 49275 44270 52512 03951 21651 53867 36136 70073 45542 22831 15797 75134 39856 73527 78417 36208 11283 76913 22499 68467 04497 24853 43879 07613 26400 17180 93285 66083 02196 10638
- 38. Random number table 13962 70992 65172 28053 02190 83634 66012 70305 66761 88344 43905 46941 72300 11641 43548 30455 07686 31840 03261 89139 00504 48658 38051 59408 16508 82979 92002 63606 41078 86326 61274 57238 47267 35303 29066 02140 60867 39847 50968 96719 43753 21159 16239 50595 62509 61207 86816 29902 23395 72640 83503 51662 21636 68192 84294 38754 84755 34053 94582 29215 36807 71420 35804 44862 23577 79551 42003 58684 09271 68396 19110 55680 18792 41487 16614 83053 00812 16749 45347 88199 82615 86984 93290 87971 60022 35415 20852 02909 99476 45568 05621 26584 36493 63013 68181 57702 49510 75304 38724 15712 06936 37293 55875 71213 83025 46063 74665 12178 10741 58362 84981 60458 16194 92403 80951 80068 47076 23310 74899 87929 66354 88441 96191 04794 14714 64749 43097 83976 83281 72038 49602 94109 36460 62353 00721 66980 82554 90270 12312 56299 78430 72391 96973 70437 97803 78683 04670 70667 58912 21883 33331 51803 15934 75807 46561 80188 73440 29317 27971 16440 62843 84445 56652 91797 45284 25842 40938 73504 21631 81223 19528 15445 77764 33446 41204 70067 16926 70680 66664 75486 16737 01887 50934 43306 75190 86997 24057 79018 34273 25196 99389 06685 45945 62000 76228 60645 66318 46329 46544 95665 36160 38196 77705 28891 12106 56281 29579 66116 39626 06080 05505 45420 44016 79662 92069 27628 07440 32540 19848 27319 85962 19758 92795 00458 71289 05884 97407 23322 73243 98185 28763 04900 54460 22083 89279 43492 82470 40857 86568 49336 42222 40446 82240 79159 44168 38213 43797 26598 29983 67645 43626 40039 51492 36488 70280 24218 53872 04744 89336 35630 97761 43444 95895 24102 07006 71923 17132 32062 41425 66862 49275 44270 52512 03951 21651 53867 36136 70073 45542 22831 15797 75134 39856 73527 78417 36208 11283 76913 22499 68467 04497 24853 43879 07613 26400 17180 93285 66083 02196 10638
- 39. Systematic random sampleSystematic random sample We randomly select a first case and thenWe randomly select a first case and then proceed by selecting everyproceed by selecting every nnthth (say(say nn = 30) case= 30) case thereafter.thereafter. WhereWhere nn is determined by dividing the number ofis determined by dividing the number of items in the sampling frame or population by theitems in the sampling frame or population by the desired sample size.desired sample size.
- 40. ExampleExample If for example you want to select a sample of 50 children fromIf for example you want to select a sample of 50 children from the 850 children attending a schoolthe 850 children attending a school SolutionSolution Divide the 850 children by 50 (sample size) =Divide the 850 children by 50 (sample size) = 1717.. so every 17th children is sampled.so every 17th children is sampled. Select a number randomly betweenSelect a number randomly between 11 andand 1717 first, and wefirst, and we then select every 17th children.then select every 17th children. Suppose we randomly select the numberSuppose we randomly select the number 88 from a randomfrom a random number table.number table. Then, the systematic sample consists of children with IDThen, the systematic sample consists of children with ID numbersnumbers 8, 25, 42, 59, 768, 25, 42, 59, 76, and so on; each subsequent, and so on; each subsequent number is determined by adding 17 to the last ID number.number is determined by adding 17 to the last ID number.
- 42. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 151 2 3 4 5 6 7 8 9 10 11 12 13 14 15 31 32 33 34 35 36 37 38 39 40 41 42 43 44 4531 32 33 34 35 36 37 38 39 40 41 42 43 44 45 16 17 18 19 20 21 22 23 24 25 26 27 28 29 3016 17 18 19 20 21 22 23 24 25 26 27 28 29 30 46 47 48 49 50 51 52 53 54 55 ……..46 47 48 49 50 51 52 53 54 55 ……..
- 43. Systematic samplingSystematic sampling Example: systematic sampling
- 44. Stratified Random sampleStratified Random sample StrataStrata are groups or classes inside a populationare groups or classes inside a population that share a common characteristic.that share a common characteristic.
- 45. The population is first divided into at least twoThe population is first divided into at least two distinct strata or groups.distinct strata or groups. Then a random sample of a certain size is drawnThen a random sample of a certain size is drawn from each stratum.from each stratum. The groups or strata are often sampled inThe groups or strata are often sampled in proportion to their actual percentageproportion to their actual percentage of occurrenceof occurrence in the overall population.in the overall population. Combine results of all strata.Combine results of all strata. Procedure for selecting of stratifiedProcedure for selecting of stratified samplingsampling This stratification results in greater representativeness.
- 46. ExampleExample Drawing one sample ofDrawing one sample of 10 people10 people from a total populationfrom a total population ofof 10001000 person, consisting ofperson, consisting of 500 black500 black andand 500 white500 white peoplepeople, two random samples of five could be taken from, two random samples of five could be taken from each racial group (or stratum) separately, thuseach racial group (or stratum) separately, thus guaranteeing the racial representativeness of theguaranteeing the racial representativeness of the resulting overall sample of 10.resulting overall sample of 10. Other strata might beOther strata might be men or women and so on.men or women and so on. departmentdepartment locationlocation ageage industry type, etc.industry type, etc.
- 47. Cluster samplingCluster sampling In cluster samplingIn cluster sampling we begin by dividing the demographic (or geographic)we begin by dividing the demographic (or geographic) area into sections.area into sections. Then we randomly select sections or clusters.Then we randomly select sections or clusters. The selected clusters may be completely sampled or aThe selected clusters may be completely sampled or a random sample may be obtained from the selectedrandom sample may be obtained from the selected clusters.clusters. Every member of the cluster is included in the sample.Every member of the cluster is included in the sample.
- 48. Example: Cluster samplingExample: Cluster sampling Section 4 Section 5 Section 3 Section 2Section 1
- 49. In conducting a survey of school children in a largeIn conducting a survey of school children in a large city, we could first randomly select 5 schools andcity, we could first randomly select 5 schools and then include all the children from each selectedthen include all the children from each selected school.school. This technique is more economical than theThis technique is more economical than the random selection of persons throughout the city.random selection of persons throughout the city. Cluster samplingCluster sampling ExampleExample
- 50. Convenience SamplingConvenience Sampling Convenience sampling is very easy to do, but it's probablyConvenience sampling is very easy to do, but it's probably the worst technique to use. In convenience sampling,the worst technique to use. In convenience sampling, readily available data is used. That is,readily available data is used. That is, the first people thethe first people the surveyor runs intosurveyor runs into.. ExampleExample: A professor conducting research might use student: A professor conducting research might use student volunteersvolunteers to constitute a sample.to constitute a sample.
- 51. Judgment SamplingJudgment Sampling The person most knowledgeable on the subjectThe person most knowledgeable on the subject of the study selects elements of the populationof the study selects elements of the population that he or she feels are most representative ofthat he or she feels are most representative of the population.the population. ExampleExample: A reporter might sample three or four: A reporter might sample three or four senators, judging them as reflecting the generalsenators, judging them as reflecting the general opinion of the senate.opinion of the senate.
- 52. Snowball SampleSnowball Sample sample is selected from elements of a population that are related to each other in certain manner, It could be classified into: Horizontal: friend of friend….etcHorizontal: friend of friend….etc Vertical: Son, father, grandfather, …etc
- 53. Errors in sample There are two main sources of error in sampling: 1. Systematic error (or bias) Inaccurate response (information bias). Selection bias. 2. Random Sampling Error (random error) Variability. Sampling method. Sample size.