## Simple size -sampling decisions, Operation Research

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simple Size

When a survey  is undertaken and  it is not  possible  to cover  the entire population, the marketing  researcher has to  answer a basic  question  - how  large  should  the sample  be ? the  sample size  decision is related directly  to research cost,  and therefore must be  justified.

The  researcher while  deciding the appropriate size of the sample  compromises all the  factors  affecting  the sample  size. The  decision to decide the sample  size  must be  scientifically made  and should  not be  done arbitrarily because of the  risks  involved. The sample  size should  be neither too large  nor too  small.

Factors  Determining Sampling Size

Sample size  really  depends  on four  factors:

* The number of groups  and subgroups  within  the sample that will  be analyzed.

• the value of the information in the study in general and the accuracy required of the results in particular.
• The third factors is the cost of the sample. A cost benefit analysis must be considered. A larger sample size can be justified if sampling costs are low than if sampling costs are high.
• The final factors is the variability of the population. If tall members of the population have identical opinions on an issue a sample of one is satisfactory. As the variability within the population increases the sample size also will need to be large.

Determining  the Sample Size

There are two  basic approaches to the  problem to the  sample size:

a.  Ad hoc  or practical approach

b.Statistical approach

The  former  is widely  used in  marketing  research ,

Ad hoc  practical Methods: According  to this  approach, sample size  of less  than a few  hundred units  is not  chosen. This is  because when afield survey  is undertaken interviewers are appointed trained  and asked to  conduct field investigations. Since al this would cost substantially it  would  not be worth it for the marketing  researcher if only a small  sample is chosen. A survey confined to a relatively small number of unit would  mean a relatively high cost per interview. Another consideration in favour of  selecting  a reasonable size  of sample in that it enables the researcher to test   several hypotheses. This is especially true for sample in the  sub group. such  hypotheses can be  tested with  a high  degree of is statistical significance when  the sample  size is reasonably  large. Another practical  consideration in case  of a stratified sample  is that the  overall  sample size  is so  fixed  that the  sample  size  within  each  stratum is  not less than 30. A common  practice  in this regard  is to determine  the sample  size  of each  stratum  first  and then  add up  the samples  of all  the strata to obtain the overall  sample  size.

Few  common  ad hoc  methods  for determining  sample  size are:

1.Rules and Thumb : One  approach  is to  use come  rules  of thumb. Sudman  suggests that the  sample  should be  large enough  enough  so that  when it is divided into group  each  group  will have  a minimum  sample  size  of  100 or more.

Suppose that  the opinions of citizens  regarding  municipal  parks  are desired. In  particular  estimation  is to be  made  of the percentage who felt  that tennis courts are needed suppose further  that a  comparison i s desired among  those who (a)  use  parks frequently( c)  use parks  occasionally and (e) never use parks. Thus  the sample  size should  be such  that each  of these  groups  has at least  100peopl. If  the frequent park users  the smallest group, are thought to be  about  10 percent  of the population then  under  simple random sampling  size  of  1000 would  be needed  to generate a group  of 100 subjects.

In almost  every  study a comparison  between  group s provides  useful  information and is often the  motivating reason for  the study. It is therefore  necessary to consider the smallest group  and to  make sure  that it  is of  sufficient  size to  provide  the needed  reliability.

2.Budget Constraints : Often  there is  a strict  budget constraint. A museum  director  might  be able  to spare  only Rs. 50000 for a study  and no more. If  data  analysis will require Rs. 1000and  a respondent  interview is Rs. 50 ,then the  maximum affordable sample  size  is 80. The question then becomes  whether  a sample  size of 80 is worthwhile or if the  study  should  be changed or simply  not conducted.

3.Comparable Studies : Another  approach is to  find  similar studies  and use  sample  sizes as a  guide. The  studies  should be comparable in  terms  of the number of groups  into which  the sample is  divided for comparison purpose. They  also should have  achieved a satisfactory  level of reliability.

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