Marketing Research Notes Chapter13

Students, today we shall be doing various issues in sampling . To understand it better it is necessary that we do certain related terms first. When we are doing certain investigation the interest lies in the assessment of the general magnitude and the study of variation with respect to one or more characteristics relating to individuals belonging to a group

Population This group of individuals is called population or universe.Thus we can define population as any entire collection of people, animals, plants or things on which we may collect data. It is the entire group of interest, which we wish to describe or about which we wish to draw conclusions. It is impractical for an investigator to completely enumerate the whole population for any statistical investigation. For example, if we want to have an idea about the average montly income of people residing in India, we will have to enumerate all the earning individuals in the country, which is rather a very difficult task. Also, when population is large infinite) or if units are destroyed during investigation it is not possible to enumerate or investigate whole population. But even if population is finite 100% inspection is not possible because of various factors like time, money and administrative convenience. Sampling Sampling is the selection of part of an aggregate or totality known as population, on the basis of which a decision concerning the population is made. Thus, we can say that a finite subset of statistical individuals in a population is called a sample and the number of individuals in a sample is called sample size. Sampling Unit

A unit is a person, animal, plant or thing which is actually studied by a researcher; the basic objects upon which the study or experiment is executed. For example, a person; a sample of soil; a pot of seedlings; a zip code area; a doctor’s practice. Activity Define population and sampling unit in each of the following problems 1. Popularity of family planning among families having more than two children _____________ 2. Election for a political office with adult franchise__________ 3. Measurement of the volume of timber available in a forest _______________________ 4. Annual yield of apple fruit in a hilly district.______ 5. Study of child mortality rate in a district

11.556

Parameter and Statistic A parameter is an unknown value, and therefore it has to be estimated.Parameters are used to represent a certain population characteristic. For example, the population mean m is a parameter that is often used to indicate the average value of a quantity. Within a population, a parameter is a fixed value that does not vary.Each sample drawn from the population has its own value of any statistic that is used to estimate this parameter. For example, the mean of the data in a sample is used to give information about the overall mean min the population from which that sample was drawn. A statistic is a quantity that is calculated from a sample of data.It is used to give information about unknown values in the corresponding population. For example, the average of the data in a sample is used to give information about the overall average in the population from which that sample was drawn. A statistic is a function of an observable random sample. It is therefore an observable random variable. Statistics are often assigned Roman letters (e.g. and s), whereas the equivalent unknown values in the population ( parameters ) are assigned Greek letters (e.g., µ, s). Variables A characteristic or phenomenon, which may take different values, such as weight, gender since they are different from individual to individual. Any object or event, which can vary in successive observations either in quantity or quality is called a “variable.”Variables are classified accordingly as quantitative or qualitative. A qualitative variable, does not vary in magnitude in successive observations. The values of quantitative called “Attributes”.A quantitative variable does vary in magnitude in successive observations. The values of quantitative are called “Variates” Variable Randomness

Randomness means unpredictability The fascinating fact about inferential statistics is that, although each random observation may not be predictable when taken alone, collectively they follow a predictable pattern called its distribution function. For example, it is a fact that the distribution of a sample average follows a normal distribution for sample size over 30. In other words, an extreme value of the sample mean is less likely than an extreme value of a few raw data. Desirable Characteristics of Sample Statistics 1. Unbiased:If the arithmetic mean of the statistic calculated for all possible samples of a given size n exactly equals its population parameter.

© Copy Right: Rai University

79

RESEARCH METHODOLOGY

LESSON 13: SAMPLING ISSUES IN RESEARCH

RESEARCH METHODOLOGY

2. Sufficient:Summarizes all relevant information about the parent population contained in the sample, while ignoring any samplespecific information. 3. Efficient:The more the statistic values for various samples cluster around the true parameter value, the lower the sampling error and the greater the efficiency. Consider an archer shooting at a target. The archer wants to be accurate, but also wants the arrows to cluster as closely to the centre of the target as possible. 4. Consistent:The larger the sample size, the closer the statistic should be to its parameter value.Every statistic in a sample might have a different sampling distribution

Example of the creation of a sampling distribution Six rocks were extracted from my team and each was weighed, labeled, and put in a bag. This forms the population from which I can draw samples. Suppose, I want to construct a sampling distribution of the mean weight of 3 rocks from the population of 6. To do this, I must enumerate all samples of size 3 which can be drawn from a population of size 6 (there are 20 in total) and compute the mean of each. The frequency distribution I can create from these 20 numbers is the sampling distribution I want. Below is the table I would use to create this distribution, and below that is the actual sampling distribution. Example Creation of a Sampling Distribution

Sampling Distribution The sampling distribution is a hypothetical device that figuratively represents the distribution of a statistic (some number you’ve obtained from your sample) across an infinite number of samples. You have to remember than your sample is just one of a potentially infinite number of samples that could have been drawn.While it’s very likely that any statistics you generate from your sample would be near the center of the sampling distribution, just by luck of the draw, the researcher normally wants to find out exactly where the center of this sampling distribution is. That’s because the center of the sampling distribution represents the best estimate of the population average, and the population is what you want to make inferences to. The average of the sampling distribution is the population parameter, and inference is all about making generalizations from statistics (sample) to parameters (population). You can use some of the information you’ve collected thus far to calculate the sampling distribution, or more accurately, the sampling error. In statistics, any standard deviation of a sampling distribution is referred to as the standard error (to keep it separate in our minds from standard deviation).In sampling, the standard error is referred to as sampling error. Definitions are as Follows • Standard deviation-the spread of scores around the average in

a single sample· Standard error- the spread of averages around the average of averages in a hypothetical sampling distribution.You never actually see the sampling distribution. All you have to work with is the standard deviation of your sample. The greater your standard deviation, the greater the standard error (and your sampling error). The standard error (this term was first used by Yule, 1897) is the standard deviation of a mean and is computed as: Standard Error= (s2/n)1/2,where ,s2 the sample size.

is the sample variance, n is

Let us illustration the sampling distribution, it will make the topic very clear. 80

Rock ID 1 2 Weight (g) 11.24 10.43 Sample Means

3 13.48

4 16.9

5 24.28

6 20.89

Sample 11 13.87

1

1

0

0

0

Sample 21 17.47

1

0

1

0

0

Sample 31 16.33

0

1

1

0

0

Sample 40 18.22

1

1

1

0

0

Sample 51 15.20

1

0

0

1

0

Sample 61 16.34

0

1

0

1

0

Sample 70 17.09

1

1

0

1

0

Sample 81 18.80

0

0

1

1

0

Sample 90 19.55

1

0

1

1

0

Sample 10 0 20.69

0

0

1

1

1

Sample 11 1 11.72

1

1

0

0

0

Sample 12 1 12.86

1

0

1

0

0

Sample 13 1 13.60

0

1

1

0

0

Sample 14 1 15.32

1

0

0

1

0

Sample 15 1 16.06

0

1

0

1

0

Sample 16 1 17.20

0

0

1

1

0

Sample 17 1 14.19

1

0

0

0

1

© Copy Right: Rai University

11.556

0

1

0

0

1

Sample 19 1 16.07

0

0

1

0

1

Sample 20 1 18.53

0

0

0

1

1

The Sampling Distribution Bin >11, <=13 >13, <=15 >17, <=19 >19, <=21

>15, <=17

Frequency

6

2

4

6

2

Relation between Standard Error and Sample Size Standard error is also related to sample size. The larger your sample, the smaller the standard error. You’re not reducing bias or anything by increasing sample size, only coming closer to the total number in the population. Validity and sampling error are somewhat similar. However, you can estimate population parameters from even small samples. Principles of Sample Survey The theory of sampling is based on the following important principles: 1. Principle of statistical regularity 2. Principle of validity 3. Principle of optimization 1. Principle of statistical regularity stresses the desirability and importance of selecting a sample at random so that each and every unit in the population has an equal chance of being selected in the sample.

Sampling Errors

These have the origin in sampling and arise out of the fact that only a part of the population is used to estimate the population parameters and draw inferences about the population. Therefore, sampling errors are absent in complete enumeration. The sampling errors are basically because of following reasons: a. Faulty selection of sample: If you use a defective technique for selecting a sample, e.g purposive or judgement sampling in which the investigator deliberately chooses the sample in order to deduce the desired results.This bias can be overcome by adhering to Simple Random Sampling. b.Substitution:If you substitute one unit for another if some difficulty arises in studying that particular unit (first one), this leads to some bias . This is because of the fact that the characteristics possessed by the substituted unit will usually be different from those possessed by the unit originally included in the sample. c . Faulty Demarcation of Sampling units It is significant in particularly areas surveys such as agricultural experiments in the field or in the crop cutting fields etc. d. Constant error due to improper choice of the statistics for estimating the population parameters: For example while estimating the standard deviation of population if we divide the sum of squares by “n” instead of “n-1”,we get an unbiased estimate of population standard deviation. Non-sampling Errors The non -sampling errors primarily arise at the stages of • Observation

We get an immediate derivation from this principle is the principle of Inertia of large numbers which states that

• Ascertainment

“Other things being equal as the sample size increases, the results tend to be more reliable and accurate.” For example , in a coin tossing experiment, the results will be approximately 50% heads and 50% tails provided we perform the experiment a fairly large number of times.

These are, therefore present in both complete enumeration and sample survey. Non-sampling errors can occur at every stage of planning or execution of census or sample survey.

2. Principle of validity means the sample design should enable us to obtain valid tests and estimates about the parameters of the population. The samples obtained by the technique of probability sampling satisfy this principle. 3. Principle of optimization impresses upon obtaining optimum results in terms of efficiency and cost of the design with the resources at disposal. The reciprocal of the sampling variance of an estimate provides a measure of its efficiency while a measure of cost of the design is provided by the total expenses incurred in terms of money and man hour. The principle of optimization consists in a. achieving a given level of efficiency at minimum cost b. obtaining maximum possible efficiency with given level of cost. Sampling and Non-sampling Error We can classify broadly the errors involved in the process of research into two heads: Sampling Errors and Non-Sampling Errors

11.556

• Processing of data

It is very difficult to prepare an exhaustive list of the sources of non-sampling errors. However some of the more important ones arise because of following factors: 1. Faulty planning or definition. 2. Response Errors 3. Non- Response bias 4. Errors in coverage 5. Compiling Errors 6. Publication Errors Now we will discuss them in detail 1. Faulty planning or Definition:As we all know the foremost step in research is explicitly stating the objectives of the study. These objectives are then translated into • A set of definitions of the characteristics for which data is to

be collected • Into a set of specificationsfor collection , processing and

publishing.

© Copy Right: Rai University

81

RESEARCH METHODOLOGY

Sample 18 1 14.93

RESEARCH METHODOLOGY

Here Non-Sampling Errors may Arise Due to

a. Data specification being inadequate and inconsistent with respect of the objectives of study b. Error due to location of the units and actual measurement of the characteristics, errors in recording the measurements, errors due to ill designed questionnaires.

it take less time, is less costly, and allows us to take more care in the data processing stage. 5. Destructive Tests: When a test involves the destruction of an item under study, sampling must be used. Statistical sampling determination can be used to find the optimal sample size within an acceptable cost.

There arise as a result of the responses furnished by the respondents because of following reasons

Limitations of Sampling The advantages of sampling over complete enumeration can be derived only if • The sampling units are drawn in a scientific manner,

• Response error may be accidental- e.g, the respondent may

• The appropriate sampling technique is used, and

c. Lack of trained and qualified investigators and 2.Response Errors

understand a particular question and accordingly furnish improper information un-intentionally. • Prestige Bias • Self-Interest

• The sample size is adequate

Sampling theory has its own limitations and problems which may be briefly outlined as 1. You have to take proper care in the planning and execution of the sample survey, otherwise the results obtained might be inaccurate and misleading

• Bias due to interviewer • Failure of respondent’s memory

3.Non- Response Bias

Non-Response biases occur if you do not obtain full information from all the sampling units. 4.Errors in Coverage If the objectives are not stated concisely in a clear cut manner it may lead to • Certain units which should not be included also gets

included

2. Until and unless sampling is done by trained and efficient personnel and sophisticated equipment for its planning, execution and analysis. In absence of these sampling is not trustworthy 3. If you want to have information of each and every unit of population you will have to go for complete enumeration only. In that case sampling will not be an appropriate method. Types of Sampling The type of enquiry and the nature of data fundamentally determines the technique or method of selecting a sample .

• Certain units which must be included gets excluded

5.Compiling Errors

Various operations of data processing such as editing and coding of the responses, punching of cards, tabulation and summarizing the origional observations made in study are the potential source of error.Compilation errors are subject to control through verification , consistency check, etc.

The procedure of selecting a sample may be broadly classified under the following three heads:

6.Publication Errors

• Mixed Sampling

The errors committed during presentation and printing of tabulated results are basically due to two sources: • Mechanics of publication-the proofing error and the like. • Failure of the survey organization to point out the

limitations of the statistics. Advantages of sampling over complete enumeration The following are the advantages and/or necessities for sampling in statistical decision-making: 1. Cost: Cost is one of the main arguments in favour of sampling, because often a sample can furnish data of sufficient accuracy and at much lower cost than a census. 2. Accuracy:Much better control over data collection errors is possible with sampling than with a census, because a sample is a smaller-scale undertaking. 3. Timeliness:Another advantage of a sample over a census is that the sample produces information faster. This is important for timely decision making. 4. Amount of Information: More detailed information can be obtained from a sample survey than from a census, because 82

• Non-Probability Sampling Methods: Subjective or

Judgement Sampling • Probability Sampling

These we will be studying in detail in the next lecture. Now, briefly tell me what concepts you have studied today? Yes, we studied various concepts like population, statistic, variablesqualitative and quantitative, variable randomness, characteristics of sample statistic, sampling distribution, standard error, principles of sample survey , sampling and non-sampling errors, merits and limitations of sampling.

References Aaker D A , Kumar V & Day G S - Marketing Research (John Wiley &Sons Inc, 6th ed.) Bell J- Doing your Research Project (OU Press, 1993) Donald R. Cooper-Business Research Methods, Tata McGraw-Hill Publication Kothari C R-Quantitative Techniques (Vikas Publishing House 3rd ed.) Levin R I & Rubin DS-Statistics for Management (Prentice Hall of India, 2002)

© Copy Right: Rai University

11.556