Page 82 - DMGT404 RESEARCH_METHODOLOGY

Research Methodology

Notes 4. The greater the number of sub-groups of interest within the sample, the greater its size
must be.
5. Cost is a factor that determines the size of the sample.

6. The issue of response rate: The issue to be considered in deciding the necessary sample
size is the actual number of questionnaires that must be sent out. Calculation-wise, we
may send questionnaires to the required number of people, but we may not receive the
response. For example, we may like to obtain the family income level from a mail survey,
but the researcher may not receive response from everyone. If the researcher feels the
response rate is 40%, then he needs to despatch that many extra questionnaires. A low
percentage of response can cause serious problems to the researcher. This is known as the
non-response error.
Non-response error may be due to (1) failure to locate, (2) flat refusal.

Failure to locate: People move to new destinations. However, if the sample frames used are of
recent origin, this problem can be overcome.
Flat refusal: We do not know if those who did not respond hold different views or opinions
from those who responded.
This implies that those who don't respond should be motivated. It can be done in any one of the
following ways:
1. An advance letter informing the respondents that they will receive a questionnaire and
requesting their cooperation. This will generally increase the rate of response.

2. Monetary incentive or gift given to respondents will yield a larger response rate.
3. Proper follow up is necessary after the potential respondent received the questionnaire.

Example: Determine the sample size if standard deviation of the population is 3.9, population
mean is 36 and sample mean is 33 and the desired degree of precision is 99%.
Solution:

Given,  = 3.9,  = 36, x and z = 1% (99% precision implies 1% level of significance)
i.e. z = 2.576 (at 1% l.o.s) (Table value)

We know that sample size n can be obtained using the relation

2
 z  

n =   where d    X
 d 
2

 2.576 3.9 

n =    11.21 11

 36 33 
Example: Determine the sample size if the standard deviation of population is 12 and the
standard error (standard deviation of the sampling distribution) is 3.69.
Solution:
Given the standard deviation of population
 = 12

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