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DATA TYPES AND QUANTITATIVE DATA ANALYSIS

PRESENTED TOTHIRD-TRIMESTER YEAR 1

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DATA

Information expressed qualitatively or quantitatively

Data are measurements of characteristics Measurements are functions that assign

values in quantitative or quantitative form

Characteristics are referred to as variablesEg. Height, weight, sex, tribe, etc

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VARIABLES AND DATA TYPES

Variable as characterization of event

Classification of Variables Qualitative: usually categorical; values/members fall

into one of a set of mutually exclusive & collectively exhaustive classes. eg. Sex, crop variety, animal breed, source of water, type of house

Quantitative: numeric values possessing an inherent order.

Discrete: eg. # of children/farmers/animals, etc Continuous: height, weight, distance, etc

– Random and Fixed

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Data Types Scales of measurements

Nominal Ordinal

Interval Ratio

Levels of measurement distinguished on the basis of the following criteria:

Magnitude or size; Direction Distance or interval; Origin Equality of points; Ratios of intervals; Ratio of points

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NOMINAL DATA

Example: Sex (Gender) coded M,F or 0,1 ‘Numbers’ simply identify, classify, categorize or

distinguish. The score has no size or magnitude Score has equality because two subjects are similar

(equal) if they have same number Weakest level of measurement; poor Arithmetic operations CANNOT be performed on

nominal data types

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ORDINAL DATA

Associated with qualitative random variables Generated from ranked responses (or from a

counting process). Have properties of nominal-data, in addition to

DIRECTION Numeric or non-numeric Next to nominal in terms of weakness Arithmetic operations must be avoided Egs: knowledge (low, average, high), socio-

economic status, attitude, opinion (like, dislike, strongly dislike), etc.

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INTERVAL and RATIO

INTERVAL – Numeric, have magnitude or size, direction, distance or interval,

and origin– Interval scale has no absolute 0 that is NOT independent of

system of measurement [0oC not same temperature as 0oF]– Eg. Temperature in degrees Fahrenheit or Celsius

RATIO • Weight of cassava in kilogram or pounds weight– Numeric, have magnitude or size, direction, distance or interval,

and origin– Absolute origin exists and not system dependent

All arithmetic operations can be performed on such data types

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DATA COLLECTION PROCESSES

Processes include (not mutually exclusive)– Routine Records; – Survey Data;

– Experimental data;

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ROUTINE (MONITORING) DATA

Data periodically recorded essentially for administrative use of the establishment and for studying trends or patterns.

Examples – medical records, meteorological data

Some statistical analysis of data possible on description and prescription

Cheap data, and planning could be haphazard

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EXPERIMENTAL DATA

Treatments are the investigated factors of variation Treatments are controlled by the designer Treatment levels may be fixed, random, qualitative,

quantitative Comparative experimental data require inductive

analysis Emphasis on inference including estimation of

effects and test of hypotheses.

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SURVEY DATA COLLECTION

Information on characteristics, opinions, attitudes, tendencies, activities or operations of the individual units of the population

Based on a small set of the population Can be planned; preference for random surveys

Researcher or investigator has no (or must not exercise) control over the respondent or data

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Which procedure to use?

Depends on study objectives

All 3 procedures are possible while in the community

Monitoring and Survey procedures will be most used during the first year.

We discuss SURVEY further

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SAMPLING (SURVEY) METHODS Ensure units of population have same chance of

being in the sample.

Sampling Types

Probability sampling - the selection of sampling units is according to a probability (random & non-random) scheme.

Non-probability sampling - selection of samples not objectively made, but influenced a great deal by the sampler. Example – haphazard and use of volunteers

Preference is for probability sampling, but situation may determine otherwise

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SYSTEMATIC SAMPLING Procedure

Sampling units are selected according to a pre-determined pattern.

For instance, given a sampling intensity of 10% from a population of 100 numbered trees or units (strips etc) might require your observing every 1 out of 10 trees (units, strips) in an ordered manner or sequence

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Selection in Systematic Procedure

E.g. if by some process, random or non-random, the 3rd tree (unit or strip) is selected first, then the 13th, 23rd, 33rd, 43rd,..., 93rd trees (unit, strips) will accordingly be selected. Strictly, this type of selection as illustrated with the population of 100 trees (units) involves only one sample.

Improve by selecting 1st unit randomly from 1 to 10, or 1 to 100, and by MULTIPLE random starts

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Applications of Systematic Sampling

_ Population is unknown

_ Baseline studies on spatial distribution patterns of population

_ Baseline studies on extent/distribution of pests, pathogens, etc.

_ Mapping purposes

_ Regeneration studies

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Advantages of Systematic Sampling

_ Easy to set-up_ Relative speed in data collection_ Total coverage of population assured_ Good base for future designs, as position of characters can easily be mapped (with known coordinates)_ Demarcation of units not necessary, as sampling units are defined by first unit.

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Disadvantages of Systematic Sampling

With only one random observation, sampling error not valid

Unknown trend(s) in population can influence results adversely [Examples: topography, season of sampling interval]

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Avoiding the disadvantages

The first major disadvantage on sampling error can be rectified by introducing several multiple random starts through stratification of the population

The second problem of trend is more difficult but simply relates to the choice of the sampling interval.

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Simple/Unrestricted Random Sampling

Unlike the systematic sampling, sampling units need not be equally spaced.

We shall define this as that sampling procedure which ensures equal probability for all samples of the same size (without any restriction imposed on the selection process).

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Illustration of SRS

Given a pop. Size of N from which a sample of size n will be drawn, the number of possible ways of obtaining the sample is

Supposing a population is known to have 5 units, and a sample size of 3 is required.

From this population of 5 units, there are 10 possible ways of obtaining a sample of size 3. [The formula is 5C3= 5!/{(5-3)! 3!} = 10].

Each of these combinations is unique and has the same chance (1/10) of being selected.

Thus SRS is a random sampling procedure where each sample of size n has the same probability of selection.

}!)!{(!nnN

N

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SRS selection process

(i) Select randomly one 'sample combination' from the number 1 to 10 (as there are 10 possible combinations).

(ii) Use the table of random numbers to select 3 numbers from 1 to 5 or select three numbers from a 'hat' containing all the five numbers. This option seems easier and more practicable than (i).

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Summary - SRS

Application: Applied when the population is known to be homogeneous. Procedure is suitable for units defined by plot sizes.

Advantage: Easy to apply, though not as easy as the systematic procedure.

Disadvantage: Requires knowledge of all the units in the population (construction of the frame is necessary)

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STRATIFIED RANDOM SAMPLING

Requires dividing the population into non-overlapping homogeneous units, which we are called STRATA.

SRS is then applied to each stratum, hence stratified random sampling (STRS).

Examples of strata types or criteria are ages of plantation, species types, aspect, topography/ altitude, farm types, habitat

Dividing the population into such homogeneous units usually

leads to better estimates of the desired population parameters.

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Where/when to apply Stratified RS

Very suitable for heterogeneous areas (or units) that can be identified and classified into homogeneous entities.

Supplementary information, e.g. rem sensing aerial photographs, useful for stratification.

Choice of strata should ensure variation between units within strata is less than the variation between strata.

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Advantages/Disadvantages of STRS

Advantages Estimates are more precise Separate estimates and inferences for strata are

possible

Disadvantages Sample size depends on type of allocation to be used Sampling likely to be efficient in some strata than others Errors in strata classification affect overall estimate Frame construction for each stratum is required.

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Allocation of units (n) to strata

Equal allocation - Equal (same) number of units are collected from each stratum.

Proportional allocation - The number of units per strata is proportional to the size of the strata.

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ANALYSING QUALITATIVE DATA

Qualitative data are essentially labels of a categorical variable

Statistical Analyses involve totals, percentages and conversion to pie-charts and bar charts (bar-graphs).

Sophisticated analyses include categorical modelling

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0

5

10

15

20

25

30

35

40

1 2 3

Series1

Chart of A,B,C

1

2

3

HseFreque

ncyPercen

tDegree of 360

A=1 36 72% 260

B=2 10 20% 72

C=3 4 8% 28

EXAMPLE

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0

5

10

15

20

25

30

35

40

1 2 3

Male

Female

0

10

20

30

40

50

60

70

80

1 2 3

Female

Male

You can have multiple bar graphs (i.e, can have more than one variable illustrated on a bar chart. Example is given below:

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This involves count summaries for 2 or more categories placed in row-column format:Example of a 2 by 3 contingency table:

Group

Gender A B C

Male 36 10 4

Female 34 28 2

Contingency Table

Assess association between Gender & Group

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ANALYSING QUANTITATIVE DATA

Basic analyses involve determining the CENTRE and SPREAD of data.

Inferential, probability and non-probability based

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Measuring Centre

Statistics include

– MODE (most frequently occurring observation)– MEDIAN (observation lying at the centre of an

ordered data) – best for INCOME data– MEAN (a sufficient, consistent, unbiased statistic,

utilising ALL observations)

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EXAMPLE

Consider that we selected RANDOMLY 10 houses out of 50, and observed the number of school-aged children who do not go to school as follows:

1 2 4 4 1 1 6 0 5 2

Find MEDIAN, MODE, MEAN

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MODE: 1 as it appeared most often (most households have at least 1 child of school-going age not in school) MEDIAN: Centremost observation after ordering data lies between the 4th and 5th data, i.e., between 2 and 2 (= 352)

0 1 1 1 2 2 4 4 5 6

Interpretation: 50% of the sampled population have up to 2 children of school-going age not in school)

MEAN: We use the arithmetic mean = sum of data divided by no. of observations, = (0+1+1+1+ 2+2+4+4+5+6)/10=2.6

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Measuring Spread

Statistics include– MINIMUM, MAXIMUM (ie EXTREME data)– RANGE (a single statistic calculated as

MAXIMUM minus MINIMUM value)– MEAN of the sum of the ABSOLUTE DEVIATION– STANDARD DEVIATION (SD, but use the divisor

n-1, not n as in most calculators). – STANDARD ERROR

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EXAMPLE

Consider that we selected RANDOMLY 10 houses out of 50, and observed the number of school-aged children who do not go to school as follows:

1 2 4 4 1 1 6 0 5 2

Find STANDARD DEVIATION, STANDARD ERROR and CONFIDENCE LIMITS

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X DeviationSquare Dev

1 -1.6 2.56

1 -1.6 2.56

1 -1.6 2.56

0 -2.6 6.76

2 -0.6 0.36

2 -0.6 0.36

4 1.4 1.96

4 1.4 1.96

5 2.4 5.76

6 3.4 11.56

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Standard Deviation:

1

)( 2

n

XXSD

n

ii

9

4.36SD = 2.01

1

)( 22

nn

XX

SD

n

i

ii

CALCULATING SPREAD: STANDARD DEVIATION

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RangeASD = (6-0)/4 = 1.5 (valid if sample is large and distribution is normal)Approximate SD =

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Sampling fraction (f) and Finite Population Correction Factor (fpc)

Sampling fraction= f = n/N = 10/50 = 0.20 (represents the proportion of the population that is sampled, i.e. observed)

If f < 0.05, fpc is ignored. In our case, f > 0.5 (indeed equals 0.20), fpc must be calculated and used for the sampling error computation fpc = (N-n)/N = 1– n/N = 1- 0.20 = 0.80

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80.010

01.2xfpc

n

SDSE = 0.57

)1(1

)( 2

N

n

n

n

XX

SE

n

ii

CALCULATING SPREAD: STANDARD ERROR

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Confidence (Fiducial) Limits

Given a level of significance, 5%, can obtain a 95% confidence limit on the mean number of non-school going children by multiplying SE by 1.96, that is:

P(2.6-1.96*0.57 < true number < 2.6+1.96*0.57) =1-0.05= 0.95

P(1.5 < true number per household < 3.7) = 0.95

Interpretation: 95% certain that true number of children in community who are of school-age but at home is between 1.5 (1) and 3.7 (4).

OR can conclude (after multiplying by the total 50 households

75 to 185 school-aged children in the community are not in school

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Combining Spread and Centre

BOX PLOT HISTOGRAM

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Further Analysis of Quantitative Data

Histograms give idea of the distribution of the data; very useful for quantitative data

An excellent alternative to histogram is the stem-leaf diagram.

Measures of association – correlation analysis, dependence (cause-effect) relations (regression procedures) – 2006/2007

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DATA ANALYSIS IS ENDLESS!!!

ENJOY YOUR TIME DURING TTFPP

END

KS Nokoe, PT Birteeb, IK Addai, M Agbolosu, L Kyei,