METODE PENELITIANMETODE PENELITIAN

MFK 601MFK 601 2 SKS2 SKSMFK 601 MFK 601 2 SKS2 SKS

Dib PDib PDibyo PramonoDibyo Pramonodibyo_pramono@yahoo.comdibyo_pramono@yahoo.com

dibyopramono@gadjahmada.edudibyopramono@gadjahmada.eduMagister Epidemiologi LapanganMagister Epidemiologi Lapangan

((Field Epidemiology Training Program Field Epidemiology Training Program FETPFETP))

Program Pascasarjana Program Pascasarjana FK FK UGMUGM

There are three kinds of lies: lieskinds of lies: lies, damned lies anddamned lies and

statistics

B j i Di li (1804 1881)Benjamin Disraeli (1804-1881)

STATISTIKA:ALAT UNTUK MENGHASILKAN INFORMASI DARI SUATU DATAINFORMASI DARI SUATU DATA

KECAMATAN LUKAMENINGGAL PDDK RUSAK RMH GAKIN KK

SEDAYU 49 3 44759 243 6634 2586 9581

BANGUNTAPAN 1009 236 80209 5557 21241 4336 17560

KASIHAN 1035 57 79496 1790 18393 3390 15736

PIYUNGAN 705 243 38403 5514 13450 4594 10241

SEWON 350 462 76811 8281 22781 4483 24857

PAJANGAN 131 36 30538 1228 6054 2394 7219

PLERET 4855 519 34377 8139 11899 3042 10912

BANTUL 239 247 59309 4708 15347 3072 14063

DLINGO 581 18 36836 1377 9477 2825 9680

JETIS 223 830 50483 11356 14630 3138 13969

PANDAK 933 112 48561 2966 12795 4178 12147

IMOGIRI 748 318 56850 5664 22799 4752 13948

BAMBANG LIPURO 100 607 43262 6587 10135 2339 9933

SRANDAKAN 48 5 27425 342 6902 1818 7576

PUNDONG 758 422 33080 6793 9196 1980 7684

SANDEN 32 2 34216 97 6799 2538 8783

KRETEK 230 26 31312 1121 8272 2267 7810

KECAMATAN LUKA/1000 MENINGGAL/1000 % RUSAK % GAKIN/ /

SEDAYU 1,09 0,07 3,66 26,99

BANGUNTAPAN 12,58 2,94 26,16 24,69

KASIHAN 13,02 0,72 9,73 21,54

PIYUNGAN 18,36 6,33 41,00 44,86

SEWON 4,56 6,01 36,35 18,04

PAJANGAN 4,29 1,18 20,28 33,16

PLERET 141,23 15,10 68,40 27,88

BANTUL 4,03 4,16 30,68 21,84

DLINGO 15,77 0,49 14,53 29,18

JETIS 4,42 16,44 77,62 22,46

PANDAK 19,21 2,31 23,18 34,40

IMOGIRI 13,16 5,59 24,84 34,07

BAMBANG LIPURO 2,31 14,03 64,99 23,55

SRANDAKAN 1,75 0,18 4,96 24,00

PUNDONG 22,91 12,76 73,87 25,77

SANDEN 0,94 0,06 1,43 28,90

KRETEK 7,35 0,83 13,55 29,03

DISTRIBUSI PROPORSI PENDUDUK YANG MENINGGAL (PER 1000) DI KECAMATAN-

KECAMATAN KABUPATEN BANTUL

141.23

DISTRIBUSI PROPORSI PENDUDUK YANG LUKA (PER 1000) DI KECAMATAN-

KECAMATAN KABUPATEN BANTUL

STATISTIKSTATISTIKSTATISTIKSTATISTIK

1.1. DataData22 Parameter (Indikator)Parameter (Indikator)2.2. Parameter (Indikator)Parameter (Indikator)

3.3. Metode (Ilmu)Metode (Ilmu)

DEFINISI STATISTIKADEFINISI STATISTIKA

StatisticsStatisticsStatisticsStatistics

The science of statistics is essentially a branch of Applied The science of statistics is essentially a branch of Applied Mathematics, and may be regarded as mathematics Mathematics, and may be regarded as mathematics applied to observational data that may be regarded as applied to observational data that may be regarded as (i) study population (ii) study of variation (iii) study(i) study population (ii) study of variation (iii) study(i) study population, (ii) study of variation (iii) study (i) study population, (ii) study of variation (iii) study methods of reduction datamethods of reduction data

(Fisher, 1950)(Fisher, 1950)

Statistics is concerned with inferential process, in Statistics is concerned with inferential process, in particular with the planning and analysis of experiments particular with the planning and analysis of experiments or surveys, with the nature of observational errors and or surveys, with the nature of observational errors and sources of variability that obscure underlying patternssources of variability that obscure underlying patternssources of variability that obscure underlying patterns, sources of variability that obscure underlying patterns, and with the efficient summarizing sets of dataand with the efficient summarizing sets of data

(Kruskal, 1968)(Kruskal, 1968)

St ti tiSt ti tiStatisticsStatistics

Science and art concerning the development Science and art concerning the development d th li ti f th d t ll td th li ti f th d t ll tand the application of methods to collect, and the application of methods to collect,

organize/summarize, present, analyze and organize/summarize, present, analyze and li tit ti d t i hli tit ti d t i hgeneralize quantitative data, in such a way generalize quantitative data, in such a way

so that uncertainty in the decision making so that uncertainty in the decision making b l l t d b i th tib l l t d b i th tican be calculated by using mathematics can be calculated by using mathematics

probabilityprobability

STATISTIKASTATISTIKASTATISTIKASTATISTIKA

Statistika adalah ilmu dan seni Statistika adalah ilmu dan seni tenten--tang pengembangan dan tang pengembangan dan aplikasi metode pengumpulan, aplikasi metode pengumpulan, pengolahan, penyajian, analisis pengolahan, penyajian, analisis dan interpretasi data kuantitatif dan interpretasi data kuantitatif sedemikian rupa, sehingga sedemikian rupa, sehingga kesalahan dalam pengamkesalahan dalam pengam--bilan bilan keputusan dapat diperhitungkeputusan dapat diperhitung--kan kan secara matematik probabilitas.secara matematik probabilitas.

Elements of StatisticsElements of StatisticsElements of StatisticsElements of Statistics

Collecting Summarizing Presenting Analyzing GeneralizingCollecting Summarizing Presenting Analyzing gData

El St ti tikEl St ti tikElemen StatistikaElemen Statistika

1. Pengumpulan1. Pengumpulan2 P l h2 P l h2. Pengolahan2. Pengolahan3. Penyajian3. Penyajian4 A li i4 A li i4. Analisis4. Analisis5. Interpretasi5. Interpretasi

Bidang Kajian StatistikaBidang Kajian Statistika

1. Statistika Deskriptif1. Statistika Deskriptif

2. Statistika Inferens2. Statistika Inferens

Biostatistics

Descriptive Statistics Inferential StatisticsDescriptive Statistics Inferential Statistics

Collecting

CollectingSummarizing

PresentingA l i

CollectingSummarizing

PresentingAnalyzing

Analyzing Generalizing

Draw conclusion only to Draw conclusion that applies to s bjects or gro ps hich is biggerythe subject we have studied subjects or groups which is biggerthan we have observed

INFERENSI STATISTIKINFERENSI STATISTIKINFERENSI STATISTIKINFERENSI STATISTIK

POPULASIPOPULASIPOPULASIPOPULASIRataRata--ratarata

Deviasi StandarDeviasi Standar Inferensi Inferensi Parameter PopulasiParameter Populasi StatistikStatistik

Pengambilan Pengambilan SAMPELSAMPELSampelSampel RataRata--ratarataSampelSampel RataRata ratarata

Deviasi StandarDeviasi StandarStatistik SampelStatistik Sampel

DATADATADATADATA

Data are collections of facts about an object, things, or a situationj , g ,

Types of Data1 Quantitative1. Quantitative

Discrete

ContinuousContinuous

2. Qualitative

DATADATA

Data diartikan sebagai keterangan Data diartikan sebagai keterangan atau fakta mengenai suatu benda, atau fakta mengenai suatu benda, g ,g ,persoalan atau keadaan.persoalan atau keadaan.

Ratio

Quantitative

Interval

Data

Continuous Discrete

NominalNominal

Ordinal

Qualitative

SKALA PENGUKURANSKALA PENGUKURAN

1. Data Nominal1. Data Nominal1. Data Nominal1. Data Nominal2. Data Ordinal2. Data Ordinal3. Data Interval3. Data Interval4 Data Ratio4 Data Ratio4. Data Ratio4. Data Ratio

Scale of Meas ementScale of Meas ementScale of MeasurementScale of Measurement

1. Ratio1. RatioOn a ratio scale measurement begins at a trueOn a ratio scale measurement begins at a trueOn a ratio scale, measurement begins at a true On a ratio scale, measurement begins at a true zero point and the scale has equal intervalzero point and the scale has equal interval

2 Interval2 Interval2. Interval2. IntervalAn interval scale assign each measurement to An interval scale assign each measurement to one of an unlimited number of categories thatone of an unlimited number of categories thatone of an unlimited number of categories that one of an unlimited number of categories that are equally spaced. The scale has no true zero are equally spaced. The scale has no true zero pointpointpointpoint

Scale of Meas ementsScale of Meas ementsScale of MeasurementsScale of Measurements

3. Nominal 3. Nominal A nominal scales uses names numbers or otherA nominal scales uses names numbers or otherA nominal scales uses names, numbers or other A nominal scales uses names, numbers or other symbols to assign each measurement to one of symbols to assign each measurement to one of a limited numbers of category that can not be a limited numbers of category that can not be g yg yordered one above the otherordered one above the other

4. Ordinal4. OrdinalAn ordinal scale assign each measurement to An ordinal scale assign each measurement to one of a limited number of categories that are one of a limited number of categories that are ggranked in terms of graded orderranked in terms of graded order

Identify the scale measurements of these Identify the scale measurements of these variables :variables :

1. ARI Status1. ARI Status1. ARI Status1. ARI Status2. Body temperature2. Body temperature3 Rationality of drug use3 Rationality of drug use3. Rationality of drug use3. Rationality of drug use4. Creatinine clearance4. Creatinine clearance5 Length of stay5 Length of stay5. Length of stay5. Length of stay6. Blodd glucose level 2 hours pp6. Blodd glucose level 2 hours pp7 Malaria type7 Malaria type7. Malaria type7. Malaria type8. Serum retinol level8. Serum retinol level9 D l t d bl9 D l t d bl9. Drug related problems9. Drug related problems

10. Sputum conversion status10. Sputum conversion status

11. Resistence of P falciparum to chloroquine11. Resistence of P falciparum to chloroquine12. Nutritional status12. Nutritional status13. Immunoglobuline level13. Immunoglobuline level14. Body mass index14. Body mass index15. Hb level15. Hb level16. Hepatitis type16. Hepatitis type17. Nosocomial infection17. Nosocomial infection18. Side effect18. Side effect19. Number of drugs per prescription19. Number of drugs per prescriptiong p p pg p p p20. Antituberculosis drug type20. Antituberculosis drug type

HOW TO SUMMARIZE DATA ?HOW TO SUMMARIZE DATA ?

1. Ordered Array1. Ordered Array2. Frequency Distribution2. Frequency Distribution3. Descriptive Measures3. Descriptive Measures

Desc ipti e Meas esDesc ipti e Meas esDescriptive MeasuresDescriptive Measures

Two major mathematical descriptions to Two major mathematical descriptions to describe the shape of the distribution of describe the shape of the distribution of ppobservations :observations :1 Central Tendencies1 Central Tendencies1. Central Tendencies1. Central Tendencies

mean, median, modemean, median, mode2 Di i / V i bilit2 Di i / V i bilit2. Dispersion/ Variability2. Dispersion/ Variability

range, variance, standard deviationrange, variance, standard deviation

DESCRIPTIVE MEASURES :DESCRIPTIVE MEASURES :

1. Central Tendency1. Central Tendency

2. Dispersion2. Dispersion

KECENDERUNGAN SENTRALKECENDERUNGAN SENTRAL

1. Mean1. Mean2. Median2. Median2. Median2. Median3. Modus3. Modus

SGOT level of 10 subjectsSGOT level of 10 subjects

NNumberumber SGOT levelSGOT level

11 881. 1. 882.2. 993. 3. 10104. 4. 665.5. 101066 776. 6. 777. 7. 888.8. 111199 12129. 9. 1212

10.10. 1010

USIA PENDERITA (KASUS BARU) TB BTA+USIA PENDERITA (KASUS BARU) TB BTA+USIA PENDERITA (KASUS BARU) TB BTA+ USIA PENDERITA (KASUS BARU) TB BTA+ DI PUSKESMAS DEPOK I DAN PUSKESMAS GODEANDI PUSKESMAS DEPOK I DAN PUSKESMAS GODEAN

PenderitaPenderita UsiaUsia PenderitaPenderita UsiaUsia

11 4848

22 5555

33 4949

11 3535

22 2828

33 252533 4949

44 4848

55 5252

33 2525

44 4040

55 5656

66 4949

77 5151

88 5050

66 5050

77 5454

88 585888 5050

99 4848

1010 5050

88 5858

99 7575

1010 6262

1111 6060

1212 5757

PENYEBARAN (DISPERSI)PENYEBARAN (DISPERSI)

1. Rentang1. Rentang2. Deviasi rata2. Deviasi rata--ratarata2. Deviasi rata2. Deviasi rata ratarata3. Variansi3. Variansi4. Deviasi standar4. Deviasi standar4. Deviasi standar4. Deviasi standar5. Jarak interkuartil5. Jarak interkuartil

MeanMeanMeanMean

M f t l i l l t d bM f t l i l l t d b Mean of a set values is calculated by Mean of a set values is calculated by adding up all the values and dividing this adding up all the values and dividing this

b th b f l i th tb th b f l i th tsum by the number of values in the setsum by the number of values in the set

+++n

xxxxx n...321 +++=

xn

ii

1

nx i== 1

MedianMedianMedianMedian Median is the middle of data which have Median is the middle of data which have

b d db d dbeen put in an ordered arraybeen put in an ordered array The median is similar to the mean if the data The median is similar to the mean if the data

k d t th l ftk d t th l ftare skewed to the leftare skewed to the left

If i ddIf i dd b tib ti(n+1)th

If n is odd : If n is odd : oobservationbservation

If n is evenIf n is even

(n 1)2

Median is the arithmatic meanMedian is the arithmatic meanof of and and observationobservationn

2n2+1 th

th

2 2

ModeModeModeModeMode

Mode is the value that Mode is the value that occurs most occurs most

Mode

frequently in a data frequently in a data setset

p

e

o

p

l

e

N

u

m

b

e

r

o

f

Type of Measurement Advantages Disadvantagesypof Central Tendency

g g

Mean Uses all data valuesAlgebraically defined

Distorted by outliersDistorted by skewedAlgebraically defined

and so mathematically manageableKnown sampling

Distorted by skewed data

distribution

Median Not distorted by outliersNot distorted by skewed

Ignores most of the informationNot distorted by skewed

datainformationNot algebraically definedComplicated Sampling Distribution

Mode Easily determined for categorical data

Ignores most of the informationNot algebraicallyNot algebraically

definedUnknown Sampling Distribution

RangeRangeRangeRange

Range is the difference between the Range is the difference between the largest and the smallest observation in largest and the smallest observation in ggdata setdata set

Range=Maximum Minimum

Range provides a misleading measure of Range provides a misleading measure of spread if there are outliersspread if there are outliers

Va ianceVa ianceVarianceVariance

More representatives measure of More representatives measure of variability than range because it use all variability than range because it use all y gy gmeasurement in the set and their measurement in the set and their individual distances from the mean of the individual distances from the mean of the distributiondistribution

( )2( )1

2

2

=

nxx

S i

Standa d De iationStanda d De iationStandard DeviationStandard Deviation

Standard deviation is the square root of Standard deviation is the square root of the variancethe variance

We can assume standard deviation as a We can assume standard deviation as a sort of average of the deviations of thesort of average of the deviations of thesort of average of the deviations of the sort of average of the deviations of the observations from the meanobservations from the mean

( )1

2= n

xxS i

1n

Measure of dispersion Advantages Disadvantages

RangeRange Easily determinedEasily determined Uses only two Uses only two observationobservationobservationobservationDistorted by outliersDistorted by outliersTends to increase with Tends to increase with increasing sample sizeincreasing sample size

VarianceVariance Uses every observationUses every observationAlgebraically definedAlgebraically defined

Units of measurement Units of measurement are the square of the are the square of the unit of raw dataunit of raw dataSensitive to outliersSensitive to outliersSensitive to outliersSensitive to outliers

Inappropriate for Inappropriate for skewed dataskewed data

Standard deviationStandard deviation Same advantages as Same advantages as Sensitive to outliersSensitive to outliersStandard deviationStandard deviation Same advantages as Same advantages as variancevarianceUnits of measurement Units of measurement are the same as raw are the same as raw d td t

Sensitive to outliersSensitive to outliersInappropriate for Inappropriate for skewed dataskewed data

datadataEasily interpretedEasily interpreted

ExampleExampleSerum level of alanine aminotransferase (ALT) was measured Serum level of alanine aminotransferase (ALT) was measured in all study participants to determine the effects of alcohol in all study participants to determine the effects of alcohol consumption on ALT and were recorded in the following tableconsumption on ALT and were recorded in the following table

ALT level (U/l) Frequency

25 18

40 25

36 836 8

60 34

52 25

24 1524 15

15 6

26 32

30 22

85 15

Example

Problems :Problems :1.1. Compute mean, median, mode of serum Compute mean, median, mode of serum

ALT levelALT level2.2. Compute range, variance and standard Compute range, variance and standard

deviation of serum ALT leveldeviation of serum ALT leveldeviation of serum ALT level deviation of serum ALT level

MeanMeanMeanMeanALT level (U/l) Frequency Frequency x ALT level (fx)

1515 66 90902424 1515 3603602525 1818 4504502626 3232 8328322626 3232 8328323030 2222 6606603636 88 2882884040 2525 100010004040 2525 100010005252 2525 130013006060 3434 204020408585 1515 12751275

n = 200 fx = 8295

8295 fxMean = =

2008295

41.48=nf

MedianMedianALT level (U/l) Frequency Cumulative

Frequency15 6 6

100th

624 15 2125 18 3926 32 71

100

101th30 22 9336 8 10140 25 12652 25 15152 25 15160 34 18585 15 200

n = 200 even

122

thnthn

++

101100 thth

222 =

2101100 thth += = 36Median

ModeModeModeModeALT level (U/l) Frequency = the most frequent value= the most frequent valueMode

15 624 1525 18

qq= = 6060

25 1826 3230 2236 836 840 2552 2560 34 Most frequent value60 3485 15

Mostfrequentvalue

RangeRangeRangeRange

Maximum value Maximum value Minimum ValueMinimum Value= 80= 80 1515

Range=

80 80 1515= = 6565

VarianceVarianceVarianceVariance

1)( 22 = xxs i

1n199

67,379.88=199

338 59= 338.59=

Standa d De iationStanda d De iationStandard DeviationStandard Deviation

2ss =59.338=

40.18=