BUILDING MATHEMATICAL ABILITY

PRESENTED BY:• Parth Nagpal (11332576)• Krati Goyal (11332550)• Sonali Kalra (1133260)• Arun (11332485)• Pratibha Sharma (11332559)• Akash Verma (11332529)• Rahul (11332487)• Pankaj Kumar (11332532)• Dhirendra Jaiswal (11332484)• Mridul Patel (11332490)

DATA COLLECTION TECHNIQUESSub Heads• Methods to collect data –

questionnaire, observations, recording, etc.• Population and sampling

DATA Data are values of quantitative or qualitative variables, belonging to a set of items.Eg: Data regarding the no. of seats for some of the science courses in a college

Course No. of SeatsMathematics 120Physics 95Chemistry 78Statistics 50

TYPES OF DATA

Quantitative data are measurements that are recorded on a naturally occurring numerical scale.

IDENTIFICATIONMeasured on a numeric scale.• Number of defective items in a lot.• Salaries of CEOs of oil companies.• Ages of employees at a company.

3

52

71

4

8

943

120 1221

Qualitative data are measurements that cannot be measured on a natural numerical scale; they can only be classified into a group of categories.

IDENTIFICATIONClassified into categories.• College major of each student in a class.

•Gender of each employee at a company.

• Method of payment (cash, check, credit card).

SOURCES OF DATA COLLECTION

PRIMARY DATAPrimary data is a type of information that is obtained directly from first-hand sources by means of surveys, observation or experimentation. It is the data that has not been previously published and is derived from a new or original research study and collected at the source such as in marketing.

METHODS OF COLLECTING PRIMARY DATA

• Interview •Questionnaire•Observations

SECONDARY DATASecondary data is any information collected by someone else other than it's user. It is data that has already been collected and is readily available for use. Secondary data saves on time as compared to primary data which has to be collected and analysed before use.

METHODS OF COLLECTING SECONDARY DATA Published Sources • International Publication – UNO,WTO,etc.• Government Publications – Central and State

Govt.• Publication- Municipal Corporations,boards, etc.

Unpublished Sources• Research Works• Records of Private Firms

A series of questions asked to individuals to obtain information statistically useful about a certain topic.

QUESTIONNAIRE

ADVANTAGES• They can be easily be fed back to

employees.• Questionnaires can be standard or

customized.• Large amounts of information can be gathered.• Can be analyzed easily.• Simple and quick to fill up by the

respondent.• Can be used for sensitive topics.• Respondents have time to think about their answers.• Format is familiar to most respondents.

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DISADVANTAGES

• Respondents don’t always answer honestly.• No additional questions can be asked.• Appear impersonal.• Respondents may misunderstand.• Unsuitable for some kind of respondents.• Respondents may ignore questions.• Different respondents may interpret

differently.• Danger of questionnaire fatigue.

KEY POINTS FOR MAKING AN IDEAL QUESTIONNAIRE• Keep it as short as possible.• Ask short, simple, clearly worded questions.• Start with demographic questions.• Use open ended questions cautiously.• Place the questions in logical order.• Try to minimize effort to be put in by the

respondent.• Put in more open ended questions.

INTERVIEWS• This method of collecting data involves

presentation or oral-verbal stimuli and reply in terms of oral-verbal responses.

• Interviews are probably the most widely used technique for collecting data.

• They permit the interviewer to ask the respondent direct questions.

TYPES OF INTERVIEW• Structured: Pre-established

questions• Unstructured: Draw out information

without the use of pre-established questions• Semi-Structured: A mixture of both

strategies

FORMAL AND INFORMAL INTERVIEW

Formal: A formal interview is just that, formal. It includes: the office setting; the formal handshake; appropriate attire; order and structure; and best professional behavior.

Informal: An informal interview attempts to ignore the rules and roles associated with interviewing in an attempt to gain trust and create a more natural environment for an open and honest communication.

INTERVIEWING TIPS• Keep language pitched to that of

respondent• Avoid long questions • Create comfort• Establish time frame for interview• Avoid leading questions• Sequence topics• Be respectful• Listen carefully

ADVANTAGES AND DISADVANTAGES OF INTERVIEWS

Advantages Disadvantages

Deep and free response Costly in time and personnel

Flexible, adaptable Requires skill

Glimpse into respondent’s tone, gestures

May be difficult to summarize responses

Ability to probe, follow-up Possible biases: interviewer, respondent, situation

EXAMPLE

Suppose IBN7 Managing Editor Ashutosh comes to KMC to interview our Principal, Dr. SP Gupta.

Now, by interviewing Dr. SP Gupta, he can get data about our college like,

• What is the total budget allotted by DU to KMC?

• What is the the total strength of the teaching/Non-teaching staff?

• How many rooms are available for the lectures?

And so on……

OBSERVATION• Observation: A systematic method of

data collection that relies on a researcher’s ability to gather data through their senses

 • Observe: To notice using a full range of

appropriate senses. To see, hear, feel, taste, and smell

ADVANTAGES TO OBSERVATION:

• They are free from the biases inherent in the self-report data.

• They put the practitioner directly in touch with the behaviors in question.

• They involved real-time data, describing behavior occurring in the present rather than the past.

PROBLEMS WITH OBSERVATION• Difficulties interpreting the meaning underlying

the observations.• Observers must decide which people to

observe; choose time periods, territory and events

• Failure to attend to these sampling issues can result in a biased sample of data.

EXAMPLESSee what is happening• traffic patterns• land use patterns• layout of city and rural areas• quality of housing• condition of roads• conditions of buildings • who goes to a health clinic

INFORMALEXAMPLE

During our Manali tour, I observed some things that can provide a kind of data regarding the tour. The observations are as follows:• There were 3 teachers, 9 -1st year, 2 -2nd year and 31- 3rd

students.• Only 1 student among 45 demanded onion/garlic less food.• Most rooms were booked on triple sharing basis and 3-4

rooms on quad sharing basis.• Only 1 student among 45 was a minor.

THINGS TO CONSIDER• All data collection methods are capable of gathering

quantitative and qualitative data, although some may be better suited towards one task or the

• There is no single data collection method that can guarantee credible data

• All data collection methods can be consciously manipulated

• All data collection methods can be ‘contaminated’ by unrecognized bias

• All data collection methods require conscious deliberation on the part of the researcher to ensure credibility

POPULATION

WHAT IS A POPULATION?

• A population is any complete group with at least one characteristic in common. 

• Populations are not just people.• Populations may consist of people,

animals, businesses, buildings, motor vehicles, farms, objects or events.

WHY DO YOU NEED TO KNOW WHO OR WHAT ARE IN A POPULATION?

• When looking at data, it is important to clearly identify the population being studied or referred to, so that you can understand who or what are included in the data.

• For example, if you were looking at some Indian farming data, you would need to understand whether the population, the data refers to, is all farms in India, just farms that grow crops, those that only have livestock, or some other type of farm.

SAMPLINGSampling is the process of selecting a number of individuals for a study in such a way that the individuals represent the larger group from which they were selected

Sample

The representatives selected for a study whose characteristics match the larger group from which they were selected.

SAMPLING FRAME

• A sampling frame is the source material from which a sample is drawn.

•  It is a list of all those within a population who can be sampled, and may include individuals, households or institutions

SAMPLING BREAKDOWN

BASIC METHODS OF SAMPLING

Probability sampling

Nonprobability sampling

Cluster Sampling

Simple Random Sampling

Probability Sampling

Systematic Random Sampling

Stratified Random Sampling

SIMPLE RANDOM SAMPLING• It is the basic random sampling

technique where a group of subjects (a sample) is selected for study from a larger group (a population).

• Every experimental unit is chosen entirely by chance and each member of the population has an equal chance of being included in the sample.

Examples: Lottery, generation of random numbers/digits.

LOTTERY SAMPLINGProcedures:1. Write down the name of each

member of the population on pieces of paper.

2. Place these papers in a box or a container drum.

3. The box or lottery drum must be shaken thoroughly to prevent some pieces of paper from sinking at the bottom.

4. Picked the required number of sample units from the lottery drum.

SYSTEMATIC SAMPLING• Select a random starting point using

chits,etc. and then select every kth subject in the population• Simple to use so it is used often

 

where n is the sample size, and N is the population size

Example:

Choosing a sample of size 84 from 500.k = N/nwhere N = 500 and n = 84

k = 500/84k = 5.95k 6

STRATIFIED SAMPLING

• The population is divided into two or more groups called strata, according to some criterion, such as geographic location, grade level, age, or income, and subsamples are randomly selected from each strata.

CLUSTER SAMPLINGDivide the population into groups (called clusters), randomly select some of the groups, and then collect data from ALL members of the selected groups

Used extensively by government and private research organizations

Examples: Exit Polls

Snowball Sampling

Convenience Sampling

Nonprobability Sampling

Judgment Sampling

Quota Sampling

CONVENIENCE SAMPLING

It attempts to obtain a sample of convenient elements. Often, respondents are selected because they happen to be in the right place at the right time. Examples:

Using family members or students in a classroom

Mall shoppers

JUDGMENT/PURPOSIVE SAMPLINGIt is a form of convenience samplingin which the population elements are selected based on the Judgment of the researcher.

Examples:Test markets, engineers selectedin industrial marketing research,expert witnesses used in court,etc.

QUOTA SAMPLINGQuota sampling may be viewed as two-stage restricted judgmental sampling: • The first stage consists of developing

control categories, or quotas, of population elements.

• In the second stage, sample elements are selected based on convenience or judgment.

SNOWBALL SAMPLING• In snowball sampling, an initial group of respondents is selected, usually at random.

• After being interviewed, these respondents are asked to identify others who belong to the target population of interest.

• Subsequent respondents are selected based on the referrals.

SAMPLING PROCESS

1. DEFINE POPULATION TO BE SAMPLED...

Identify the group of interest and its characteristics to which the findings of the study will be generalized.

Note: Mostly the “accessible” or “available” population must be used.

2. DETERMINE THE SAMPLE SIZE• The size of the sample influences both the

representativeness of the sample and the statistical analysis of the data

Note: 1.Larger samples are more likely to detect a

difference between different groups.2.Smaller samples are more likely not to be

representative.

RULES OF THUMB FOR DETERMINING THE SAMPLE SIZE• The larger the population size, the smaller the

percentage of the population required to get a representative sample

• For smaller samples (N ‹ 100), there is little point in sampling. Survey the entire population.

• If the population size is around 500, 50% should be sampled.

• If the population size is around 1500, 20% should be sampled.

• Beyond a certain point (N = 5000), the population size is almost irrelevant and a sample size of 400 may be adequate.

3. CONTROL FOR SAMPLING BIAS AND ERROR

• Be aware of the sources of sampling bias and identify how to avoid it.

• Decide whether the bias is so severe that the results of the study will be seriously affected in the final report, document awareness of bias, rationale for proceeding, and potential effects

4. SELECT THE SAMPLE...

• A process by which the researcher attempts to ensure that the sample is representative of the population from which it is to be selected.

Note: Requires identifying the sampling method that will be used.

TYPES OF ERRORS

• In general, there are two types of errors: 1) non-sampling errors 2)sampling errors

SAMPLING ERROR• These are errors that arise because data has been

collected from a part, rather than the whole of the population.

• Because of the above, sampling errors are restricted to sample surveys only unlike non-sampling errors that can occur in both sample surveys and censuses data.

• There are no sampling errors in a census because the calculations are based on the entire population.

• They are measurable from the sample data in the case of probability sampling.

FACTORS AFFECTING SAMPLING ERRORIt is affected by a number of factors including:Sample Size• In general, larger sample sizes decrease the

sampling error, however this decrease is not directly proportional.

• As a rough rule of the thumb, you need to increase the sample size.

The Sampling Fraction• This is of lesser influence but as the sample size

increases as a fraction of the population, the sampling error should decrease.

CONTINUED…The Variability Within The Population. • More variable populations give rise to larger errors

as the samples or the estimates calculated from different samples are more likely to have greater variation.

• The effect of variability within the population can be reduced by the use of stratification.

Sample Design • An efficient sampling design will help in reducing

sampling error.

NON-SAMPLING ERROR

• Nonsampling errors are more serious and are due to mistakes made in the acquisition of data or due to the sample observations being selected improperly.

• These are errors that arise during the course of all data collection activities.

• In summary, they have the following characteristics: 1) exist in both sample surveys and censuses data. 2) difficult to measure .

SOURCES OF NON-SAMPLING ERRORS

Non-sampling errors arise from:• defects in the sampling frame.• failure to identify the target population. • non response.• responses given by respondents.

REDUCING NON-SAMPLING ERRORSCan be minimised by adopting any of the following approaches:• using an up-to-date and accurate sampling

frame. • careful selection of the time the survey is

conducted.• careful questionnaire design.• providing thorough training and periodic

retraining of interviewers and processing staff.

WHAT IS A SURVEY ?

• A “survey” is a systematic method of gathering information from a sample.

• A survey usually originates when an individual or institution is confronted with an information need and the existing data are insufficient

MAIL / PHONE / INTERNET SURVEYS

• Literacy issues• Consider accessibility

reliability of postal service turn-around time

• Consider bias What population segment has telephone

access? Internet access?

ADVANTAGES AND CHALLENGES OF SURVEYS

Advantages

Best when you want to know what people think, believe, or perceive, only they can tell you that.

Challenges People may not accurately recall their behavior or may be reluctant to reveal their behavior if it is illegal. What people think they do or say they do is not always the same as what they actually do.

SURVEY TIPS

• Keep them short (under 5 minutes)• Avoid huge long checklists• Allow for text comments• Allow for categorical identifications --

school, job function, grade, etc.

BASIC SURVEY TYPES

• Surveys can be administered in a number of ways:

• Face to face• Telephone• Self-administered

RESPONSE CATEGORIES• Survey questions can either be open or closed:• Open questions: These questions ask

respondents to construct answers using their own words. Open questions can generate rich and candid data, but it can be data that is difficult to code and analyse

• Closed questions: These questions force respondents to choose from a range of predetermined responses, and are generally easy to code and statistically analyse .