Collection of Data and Graph of Statistics2

8/13/2019 Collection of Data and Graph of Statistics2

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STATISTICS -the science (and art) of

COLLECTING,

ORGANIZING,

ANALYZING, and

INTERPRETING data


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data


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CLASSIFICATION OF QUANTITATIVE DATA

I. DISCREET VARIABLEII.CONTINUOUS VARIABLE


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A discrete variable is a variable whose

values can be counted using integral

values.

Examples:

Number of employees, number of students

in classroom, number of cars owned,number of siblings



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A continuous variable is a variable that

can assume any numerical value over an

interval or intervals. It yields fractions or

decimals.

Examples:

Height, weight, temperature, time



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1. Non-Probability Samples

Samples are obtained haphazardly, selected

purposively or are taken as volunteers Probabilities of selection are unknown

May not be used for statistical inference

Results from the use of judgement sampling,

accidental sampling, purposively sampling,

etc.


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2. Probability Samples Samples are obtained using some objective

chance mechanism, thus involvingrandomization

Requires the use of a complete listing of theuniverse called the sampling frame

Probabilities of selection are known

Generally referred to as random samples Allows one to make valid generalizations

about the universe/population


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TYPES OF PROBABILITY SAMPLING METHODS:

1. Simple Random Sampling

2. Stratified Random Sampling

3. Systematic Random Sampling

4. Cluster Sampling5. Simple TwoStage Sampling


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SIMPLE RANDOM SAMPLING

Most basic method of drawing a probability sample

Assigns equal probabilities of selection to each possible sample

Results to obtaining a simple random sample

Types of SRS:

1. SRS Without Replacementdoes not allow repeats in the selection of the

sample

2. SRS With Replacementallows repeats in the selection of the sample


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STRATIFIED RANDOM SAMPLING

The universe is divided into L mutually exclusive sub-universes

called strata

Independent simple random samples are obtained from each stratum

Illustration:

I

II

III

IV V

Stratified

Sample

Note:

1

1

L

h

h

L

h

h

N N

n n


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ADVANTAGES OF STRATIFICATION:

1. Gives a better cross-section of the population

2. Simplifies the administration of the survey/data

gathering

3. The nature of the population dictates some inherent

stratification

4. Allows one to draw inferences for varioussubdivisions of the population

5. Generally increases the precision of estimates


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SYSTEMATIC SAMPLING

Adopts a skipping pattern in the selection of

sample units

Gives a better cross-section if the listing is

linear in trend but has high risk of bias if there

is periodicity in the listing of units in the

sampling frame

Allows the simultaneous listing and selection

of samples in one operation


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CLUSTERSAMPLING

Considers a universe divided into N mutually exclusive sub-

groups called clusters

A random sample of n clusters is selected and are completely

enumerated

Administratively convenient and has simpler frame

requirements

Illustration:

From the ten clusters(enumeration areas) delineated

within the barangay, four are

completely enumerated.


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SIMPLE TWO-STAGE SAMPLING

In the first stage, the units are grouped into N sub-groups, called

primary sampling units (psus) and a simple random sample of n

psus are selected

In the second stage, each of the n psus selected with Mielements

will be independently sampled by getting a simple random sample of

miunits (called secondary sampling units or ssus)

Illustration:

Two-stage sample


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DATA COLLECTION


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METHODS OF DATA COLLECTION

1. Objective Method

makes use ofobservation and measurement in gathering thedata. Observation may be done as participatory ornon-participatory observation.

2. Subjective Method the information isdirectly obtained from the respondent; consistsmainly of the different forms of interview.

3. Use of Existing Records the data iscopied/requested from existing databasesmaintained by certain agencies.


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FORMS OF INTERVIEW

1. Personal Interviews

Advantages:

- Respondents tend to respond more if the questions areasked by an interviewer

- Interviewer can note specific reactions- Interviewer can eliminate misunderstandings about the

questions being asked

Disadvantages:

- Cost due to hiring of interviewers

- If not properly trained, interviewers can deviate from theprotocol and thus introduce bias

- The qualities of the interviewer can also affect theresponse obtained


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FORMS OF INTERVIEW

2. Telephone Interviews

Advantages:

-Applicable especially for controversial survey topics

- Interviewer can place any number of calls for a fixedmonthly rate

- Less expensive compared to personal interview because ofcut in travel cost.

Disadvantages:

- Visual verification of the response is not possible

- Interviews are kept short and impersonal

- Restricts the data gathering to those who have telephones


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FORMS OF INTERVIEW

3. Self-Administered Questionnaires

Advantages:

- Big savings in the cost of the survey (may now be done

using the Internet)

- A large area may be easily and quickly covered

Disadvantages:

- Low response rates- Follow-up letters and communications with the respondents

are needed to minimize the bias due to the low response rate


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STEPS IN QUESTIONNAIRE

CONSTRUCTION1. Determination of questionnaire content (items)

2. Organization of items

3. Framing the questions and accompanyinginstructions

4. Composing the form by deciding thearrangement and layout

5. Constructing the questionnaire6. Pre-testing of the draft questionnaire

7. Printing or reproduction of the finalquestionnaire


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What to consider in determining questionnaire

content:Validity and Reliability of Items

Validity - the items should measure what theyintend to measure

Reliability - the items should accurately

measure what they intend to measure


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How to ascertain validity:

* Define the variable of interest clearly

conceptually and operationally


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Line graphsare typically used to show the change or

trend in a variable over time.

A Bar Chartcan be used to depict the distribution ofvariables falling under any level of measurement

(nominal, ordinal, interval, or ratio)

A Pie Chartis useful for displaying a relative frequency

distribution. A circle is divided proportionally to the relative

frequency and portions of the circle are allocated for the

different groups.

GRAPHS


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Category 1 Category 2 Category 3 Category 4

Series 1

Series 2

Series 3

LINE GRAPH


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Category 1

Category 2

Category 3

Category 4

Series 3

Series 2

Series 1

BAR GRAPH


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Series 1

Series 20

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20

30

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1/5/2002

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Series 1

Series 2

AREA GRAPH


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Series 1

Series 2

Series 3

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Category 1Category 2

Category 3

Category 4

4-5

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0-1

SURFACE GRAPH


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0.5

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1.5

2

2.53

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0 0.5 1 1.5 2 2.5 3 3.5

Y-Values

Y-Values

BUBBLE GRAPH


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351/5/2002

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1/7/20021/8/2002

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Series 1

Series 2

RADAR GRAPH


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Sales

1st Qtr

2nd Qtr

3rd Qtr

4th Qtr

DOUGHNUT GRAPH


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Y-Values

Y-Values

SCATTER GRAPH


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REFERENCE:

Advanced Algebra, Trigonometry, and

Statistics; Esparrago, et al.

(2004)


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END

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Collection of Data and Graph of Statistics2

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