collecting data 2

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STX 1110 STX 1110 INTRODUCTION TO INTRODUCTION TO

QUANTITATIVE QUANTITATIVE METHODSMETHODS

LECTURE 2LECTURE 2

COLLECTING DATA 2COLLECTING DATA 2

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CONTENTSCONTENTS1. Main Stages in a Statistical Investigation

2. Data - Overview - Definitions

3. Survey (Data Collection Method) - Interviews - Postal Questionnaire

4. Survey Guidelines - Questionnaire Design - Pilot Survey - Errors in Surveying - Validity and Precision

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MAIN STAGES IN A MAIN STAGES IN A STATISTICAL INVESTIGATIONSTATISTICAL INVESTIGATION

Pose a question

Collect relevant data

Summarise and present the data

Analyse and interpret the results

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OVERVIEW OF DATAOVERVIEW OF DATAData

Types Attributes(categorical) Variables(Numerical)

Data Source Primary Data Secondary Data

Example ofCollection Method

Survey Document extraction

InterviewPostal

Questionnaire

PublishedStatistics

AnnualReport

Discrete Continuous

Nominal* Ordinal*

* Not under the syllabus of this Module.

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DEFINITIONSDEFINITIONSData (raw materials of statistics) is simply a scientific term for facts, figures, information and measurement, both numerical and non-numerical.

Attribute (Categorical or Qualitative) is something an object has either got or not got. E.g. gender (male or female); blood group (A; AB; B; O); T-Shirt size (S; M; L; XL).

Qualitative data describes characteristics that cannot be measured.

Data collected are stored as variables and consist of qualitative and quantitative in nature.

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DEFINITIONS (Cont’d)DEFINITIONS (Cont’d)

Discrete variables are represented by whole numbers only (mainly counts). E.g. number of children.

Continuous variables may take on any value and are typically measured rather than counted. E.g. distance; height.

Numerical (Quantitative) is something can be measured or counted. E.g. children (number); height (in cm); weight (in kg).

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DEFINITIONS (Cont’d)DEFINITIONS (Cont’d)

Primary data are data collected especially for the purpose of whatever survey is being conducted.

Secondary data are data which have already been collected elsewhere, for some other purpose, but which can be used or adapted for the survey being conducted. E.g. financial figures extracted from published annual report.

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SURVEY SURVEY (DATA COLLECTION METHOD)(DATA COLLECTION METHOD)

In the absence of suitable secondary data, primary data will be generated through survey or experiment.

Survey

Observation

(Observe people’s behaviours)Questionnaire

(Ask people questions)

Conducted through

Interviews PostalQuestionnaire

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INTERVIEWSINTERVIEWS

Face to Face (Personal) Interviews

Telephone Interviews

Type

Advantages

Disadvantages

High response rateMore reliable in general

Time consumingHigh costInterviewer biasRespondents might not talk freely

Rapid responseCheaper cost

Some people do not have telephoneHigher refusal rateRespondents might not talk freely

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POSTAL QUESTIONNAIREPOSTAL QUESTIONNAIRE

Advantages:• Cheap and easy to organise• No interviewer bias• Respondents might express more freely

Disadvantages: • Low response rate• No clarification on respondents’ doubt is possible

Reasonable expectation on response rate for a survey is generally 20%.

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QUESTIONNAIRE DESIGNQUESTIONNAIRE DESIGN

• as short as possible• simple, easy and clear (unambiguous)• avoiding technical jargon• following a logical sequence• not offensive or leading• not involving calculations or tests of memory• avoiding open questions where possible – should have answer categories• relevant to the survey

Questions should be: -

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PILOT SURVEYPILOT SURVEY

Pre-testing the questionnaire i.e. to trial it on a few respondents before using it to collect the required data.

Revise the questionnaire if any problems discover in the pilot survey.

The final version of questionnaire will gather the required data.

It may save lots of time and cost later.

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ERRORS IN SURVEYINGERRORS IN SURVEYING• Sampling Error

• Response Error

• Non Response Error

- Arises when the sample selected is not representative of the population.

- Occurs when respondents are unable to response (may be couldn’t understand the questions) or answer incorrectly.

- Occurs when respondents refuse to take part in the survey.

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VALIDITY AND PRECISIONVALIDITY AND PRECISIONData Quality: -

• Validity - The data obtained in the survey should be relevant, i.e. related to the objectives of the survey.

• Precision - The data obtained in the survey should be reliable and accurate. - Precision of recording data can affect calculations and cause rounding errors.

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Some Survey QuestionsSome Survey Questions• Do you often go to pubs and restaurants?

• Do you like Klinko coffee?

• How old are you?

• Are you angry about the government’s current plans to deal with housing?

• How much money do you have?

• How often do your parents visit the doctor?

• How did you travel to work today?

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STX 1110 STX 1110 INTRODUCTION TO INTRODUCTION TO

QUANTITATIVE QUANTITATIVE METHODSMETHODS

LECTURE 2LECTURE 2SUMMARISING AND SUMMARISING AND PRESENTING DATA 1PRESENTING DATA 1

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CONTENTSCONTENTS• Ways/Methods of Presenting Data• Format of Tables, Charts and Graphs• Use Percentages to Compare Counts• Interpretation of Tables, Charts and Graphs• Advantages and Disadvantages of Each

Method of Presenting Data

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WAYS/METHODS OF WAYS/METHODS OF PRESENTING DATAPRESENTING DATA

1. Frequency Table or Frequency Distribution2. Cross Tabulation / Contingency Table3. Pie Chart4. Bar Chart5. Pareto Chart6. Pictogram7. Group Frequency Distribution (to be discussed in Week 3)

8. Histogram (to be discussed in Week 3)

9. Frequency Polygons (to be discussed in Week 3)

10. Line Graph (to be discussed in Week 3)

11. Stem and Leaf Display (to be discussed in Week 4)

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FREQUENCY TABLE / FREQUENCY TABLE / FREQUENCY DISTRIBUTIONFREQUENCY DISTRIBUTION

Gender Frequency Relative Frequency %Male 12 0.8 80

Female 3 0.2 20Total 15 1.0 100

A tabular summary of a set of data showing the frequency(or number) of data items in each category.

Gender for a Workforce

For discussion purpose

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FREQUENCY TABLE / FREQUENCY TABLE / FREQUENCY DISTRIBUTION (Cont’d)FREQUENCY DISTRIBUTION (Cont’d)

Gender for a Workforce

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FREQUENCY TABLE / FREQUENCY TABLE / FREQUENCY DISTRIBUTION (Cont’d)FREQUENCY DISTRIBUTION (Cont’d)

Exercise

Construct a frequency table for number of children in a family based on the following data obtained from 23 families: -

0 1 2 0 3 0 1 1 0 2 3 2 1 1 2 4 3 2 2 21 0 3

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FREQUENCY TABLE / FREQUENCY TABLE / FREQUENCY DISTRIBUTION (Cont’d)FREQUENCY DISTRIBUTION (Cont’d)

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CROSS TABULATION /CROSS TABULATION /CONTINGENCY TABLECONTINGENCY TABLE

A table showing data of two variables simultaneously, which reflects the relationship of the two tabulated variables.

Marital Status Gender Total Male Female Single 1 1 2Married 10 2 12Widowed 1 0 1 Total 12 3 15

Workforce by Gender and Marital Status

For discussion purpose

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CROSS TABULATION /CROSS TABULATION /CONTINGENCY TABLE (Cont’d)CONTINGENCY TABLE (Cont’d)

A cross tabulation can be summarised by calculating percentage of the row or column totals.

If one variable (the explanatory variable) is believed to influence the other (the response variable), then one normally takes percentages of the totals for the explanatory variable.

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CROSS TABULATION /CROSS TABULATION /CONTINGENCY TABLE (Cont’d)CONTINGENCY TABLE (Cont’d)

Marital Status Gender Total Male Female Single 8% 33% 13% Married 84% 67% 80%Widowed 8% 0% 7%Total 100% 100% 100%

Workforce by Gender and Marital Status

Single 50% 50% 100%Married 84% 16% 100%Widowed 100% 0% 100%Total 80% 20% 100%

To identify “Explanatory Variable” and “Response Variable” for each table.

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CROSS TABULATION /CROSS TABULATION /CONTINGENCY TABLE (Cont’d)CONTINGENCY TABLE (Cont’d)

Example 1

Production shift against type of defect for a furniture manufacturing process

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CROSS TABULATION /CROSS TABULATION /CONTINGENCY TABLE (Cont’d)CONTINGENCY TABLE (Cont’d)

Comparison of type of defect by shift

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CROSS TABULATION /CROSS TABULATION /CONTINGENCY TABLE (Cont’d)CONTINGENCY TABLE (Cont’d)

Example 2

Cross tabulation of the quality of a meal by price

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CROSS TABULATION /CROSS TABULATION /CONTINGENCY TABLE (Cont’d)CONTINGENCY TABLE (Cont’d)

Comparison of the quality of a meal by price

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PIE CHARTPIE CHART

A pie chart is used to show pictorially the relative sizes of component elements of a total.

Factory A

Materials35%

Labour15%

Overheads45%

Admin5%

Production Costs of Two FactoriesFactory B

Materials20%

Labour50%

Overheads20%

Admin10%

For discussion purpose

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PIE CHARTPIE CHART(Cont’d)(Cont’d)

Pie charts are very good for comparing the relative sizes of elements of a total.

Disadvantages:•Actual numbers or % associated with each category need to presented on the diagram.•They are not a very good presentation method if there are too many different categories.•The impression they can give is easily distorted, by presenting a 3 dimensional pie chart for example.

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BAR CHARTBAR CHART

A chart in which quantities are shown in the form of bars.

3 main types: -• Simple bar chart• Component bar chart, including Percentage component bar chart• Multiple/Compound bar chart

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BAR CHART (Cont’d)BAR CHART (Cont’d)

Simple bar chart is a chart consisting of one or more bars, in which the length of each bar indicates the magnitude of the corresponding data items.

0

2

4

6

8

10

12

14

Apple Compaq Gateway IBM PackardBell

Fre

qu

ency

Number of Computers Sold by Each Company

For discussion purpose

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BAR CHART (Cont’d)BAR CHART (Cont’d)

Component bar chart is a bar chart that gives a breakdown of each total into its components.

Component bar chart

0

50

100

150

200

250

Foothills General Southern Heathview St Johns

Psychiatric

Medical

Surgical

Maternity

Category of Beds in Each HospitalPercentage component bar chart

0%

20%

40%

60%

80%

100%

Foothills General Southern Heathview St Johns

Psychiatric

Medical

Surgical

Maternity

For discussion purpose

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BAR CHART (Cont’d)BAR CHART (Cont’d)

Multiple/Compound bar chart is a bar chart in which two or more separate bars are used to present sub-divisions of data.

Gender

MaleFemale

Count

60

50

40

30

20

Marital status

Unmarried

Married

Analysis of Marital Status by Gender

For discussion purpose

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PARETO CHARTPARETO CHART

Essentially a bar chart in which the categories are arranged according to frequency with the tallest bar is at the left.

0

2

4

6

8

10

12

14

Apple Compaq Packard Bell IBM Gateway

Fre

quen

cy

Number of Computers Sold by Each Company

For discussion purpose

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PICTOGRAMPICTOGRAM

A form of visual presentation in which data is represented by picture/s.

1997

1998

1999

2000

2001 = 5000 chairs

Number of Chairs Sold by ABC Limited

For discussion purpose

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PICTOGRAM PICTOGRAM (Cont’d)(Cont’d)

•Very elementary form of visual representation.

•Can be informative and more effective than other methods of presenting data to the general public.

•Not accurate forms of presentation.

•Provide lots of scope for confusion or misleading interpretations of the data.