Evaluasi Statistik I

8/18/2019 Evaluasi Statistik I

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Data Collection andPreparation

(Swan, ARH., Sandil ands , M., 1995, Introduction to Geologicaldata Analysis , Blackwell Science Ltd)

Asep HP Kesumajana

ET-3104 Evaluasi Statistik dalam Eksplorasi Mineral


1. Data Collection and preparation

A. Data QualityPrecision :

repeated measurements are similar.replicates are identical prepared from the somesource.the error involved is random.

Accuracy :close to the true value



Precision vs Accuracy:

Precision

High Low

Accuracy (True value=50)

High 49 50 50 52 50 49 51 50 55 47 50 52 44 53 57 47

Low 54 55 55 57 55 54 56 55 60 52 55 57 49 58 62 52



B. Handling DataObject and variables:

Each model will be a measurement of aspecified property of one particular entity.

Entity: some geological object or sample:hand specimens of granite

a soil sample

a thin sector of sandstone

trilobite specimens


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Entity



B. Handling Data A single data set:

contain information on many variables and many

objects.Column = variableRow = objects

The entire column will be analysis togethermust be same comparing like with likeMust be measured under the same strict definition ofvariable

unit must be same of every entrythe same data retrieval procedureunique to paleontology : problem homology



Visualization: Effects Scale Changesdata display can be change by changing scale

data original:



Effects Scale Changes :


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Effects Scale Changes :Log-Normal vs Normal-Normal



Effects Scale Changes :Compare 2 curve:

different vertical scale


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C. Types of Geological Data1. Ratio s cale data :

e.g. length, weight, porosity, density

2. Interval scale data :the 0 not a fundamental termination of scale e.g. C, F

3. Closed data:(%)/ppm expression of proportion of fix total (in geochemistry)

4. Directional data :in angle bearing, strike, dip

5. Ordinal scale data :constant interval scale data the scale not regular.to place observation in relative order (not valid -, +, /, *)

e.g. Mho’s hardness scale, Richter, time in stratigraphic positionused non parametric methodanalyse data on basis of rank order only



Concept of Data Type

0 1 2 3 4 5 6 7 8 9 10

1 2 3 4 5 6 7 8 9 10 11

0% 10% 2 3 4 5 6 7 8 9 100% 0% 0% 0% 0% 0% 0% 0% 0%

-3 0 1 2 3 4 5 6 7 8 9 10 -2 -1

N

EW

S

360 0o o

Ratio

Interval

Closed

Ordinal

Directional

ET-3104 Evaluasi Statistik dalam EksplorasiMineral


Directional data



Ordinal scale: Mohs ScaleMineral Knoop Vickers Mohs'

Talc NA 1 1 Gypsum 61 3 2 Calcite 141 9 3

Fluorite 181 21 4 Apatite 483 48 5

Orthoclase 621 72 6

Quartz 788 100 7 Topaz 1190 200 8

Corundum 2200 400 9 Diamond 8000 1600 10

From: http://www.geocities.com/unforbidden_geology/rock_properties.htm


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Ordinal scale: Richter Scale (Power of Ten)1 1 1 x 10 0 2 10 1 x 10 1 3 100 1 x 10 2 4 1,000 1 x 10 3 5 10,000 1 x 10 4 6 100,000 1 x 10 5 7 1,000,000 1 x 10 6 8 10,000,000 1 x 10 7

9 100,000,000 1 x 10 8 Source: http://www.nyu.edu/projects/mstep/amnh/earthquake.htm



Types of Geological Data(cont.)

6. Discrete data :has a special frequency distribution

e.g. number of fossils in a 1m 2

7. Nominal or categorical data :e.g. list of minerals or fosils

information presented in the form of namesConverted to numerical value 1 present 0 absent



Continous and Discrete data



Nominal or categorical data

Fossils Depth interval

No Name F.A L.A 300 330 360 370 380

1 Globigerinoides ruber 9.5 0.0 1 1 1 1 1

2 Globigerina bulloides bulloides 8.3 0.0 1 13 Globorotalia (T.) obesa 31.6 0.0 1 1 1

4 Globorotalia (T.) acostaensis acostaensi 9.5 1.8 1

5 Orbulina universa 15.2 0.0 1 1

6 Globoquadrina altispira altispira 25.2 1.8 1 1 1

7 Globigerina praebulloidess 38.2 5.3

8 Globigerinoides extremus 9.5 1.8 1 1 1

9 Pulleniatina primalis 7.0 3.8 1 1 1

10 Globoquadrina baroemoensis 25.2 3.8 1

11 Hastigerina aequilateralis 12.0 0.0 1

12 Sphaeroidinella dehiscens dehiscens 4.7 0.0

13 Sphaeroidinellopsis seminulina seminulin 18.7 3.8


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D. Type of AnalysisStatistic and data analysis :

must always be aware that the general data analyticalmethod do not give definitive answers,leave some interpretation to the user

Univariate :Statistical with one variable

Bivariate :Statistical with two variable

Time/space series :some can be treated as simple bivariate data with one astime or space



Univariate : Bivariate :

0 5 10 15 20 25x

0 5 10 15 20 25

45

40

35

30

2520

15

10

5

y

x

0.335

0.34

0.345

0.35

0.355

0.36

0.365

0.37

1 2 3 4 5 6 7 8 9 1 0 1 1 12 1 3 1 4 15 1 6 1 7 1 8 1 9 20 2 1 2 2 23 24 2 5

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

0 0.1 0.2 0.3 0.4

Porosity (fraction)

D e p

t h ( f t )



Time/space series

4.03.53.02.52.01.51.00.5

0

x

Time



D. Type of analysisSpatial :

3 or 4 variable analysis together with 2 or 3 are spatialcoordinate;grid refference

logitude/latitude with or without depth

Multivariate : > 3 variablethe prime object is to reduce the dimensionality so theshape of data scatter can be viewedrelationship between variable can also be investigated.


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Spatial



E. Population and Samplenot primarily interested in the properties of the bits of rock that measured.interested in the properties of the large body of rockmeasurements are representative of the population.

The population:is the total set of measurementshypothetically be taken from the entity being s tudies.the limit of the population defined by the geologist at the beginning of theproject.

The statistical :sample is the collection of objects or measurementsare a subset of the population of interestare taken to represent that population.

Bias :For any data analytical investigation to be valid it is essential that the sampleis an unbiasedsubset of the population.There are always a pitfalls in the measurement process due to instrumentalor procedural error.



Defining the geological population



Sampling StrategySample size

Depends on the degree of subtlety of the problems beingaddressed and often not known in advanceIt is good practice to investigate the properties of a smallpilot sample before deciding on the definitive sample sizerequired.

Spatial sampling schemeRandomUniformRegular or griddedClusteredTraverse


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Spatial sampling scheme

Regular

Random

Uniform

Clustered Traverse



Characteristic o verall population parameters

Geological population may have internal variation: randomly orsystematic variationMust be concentrate to overall characteristics of the populationExamples:

Coal mineCopper ore body with opencast bulk extraction

Characteristic variation with in population

if heterogeneity in the population is visible in advance should bebroken into subpopulation and sampled and analyzed separately.

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Evaluasi Statistik I