Topic - 3

Figure 7.1 Population, sample and individual cases

Population The entire group under study as defined by research objectives, sometimes called the “universe” Sampling frame a master list of the population from which the sample is drawn Population  Sample frame  Sample

Errors in sampling & How to eliminate or minimize them Sampling frame error? Random sample error? Non-response error?

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Deciding on a suitable sample size The greater the dispersion (variance) within the population, the larger the sample must be to provide estimation precision. The greater the desired precision of the estimate, the larger the sample must be. The higher the confidence level in the estimate, the larger the sample must be. The greater the number of subgroups within a sample, the greater the sample size must be, as each subgroup must meet minimum sample size requirements.

Deciding on a suitable sample size (Material, in this and the following slides is from Saunders et al. (2011) 1.Rule of thumb: a minimum number of 30 in each category within the overall sample. And where population in the category is less than 30, take all population in that category into the sample. 2.Where population is higher than 10000: To ensure 95% level of certainty (for population characteristics to be represented in sample), use the following formula: n = p% x q% x {z / (e%) } 2 where n = minimum sample size p% = proportion belonging to the specified category q% = proportion not belonging to the specified category z = z value (z = 1.96 for 95% level of certainty) e = margin of error (corresponding to z-value)

Deciding on a suitable sample size Worked example: Question: What should be the sample size where total population of community is 4000, and researcher is interested to study the performance of a salesperson? Solution: As per requirements of the formula given on previous slide, we need to know p (proportion belonging to the specified category) and q (proportion not belonging to the specified category). If we do not know, then we will have to carry out a pilot survey and try to know how many clients receive a visit by the salesperson per week. If such a pilot survey reveals that 12 out of 30 clients receive salesperson’s visit once a week, then this means 40 percent belong to this category, and 60 percent do not; so q = 40 and p = 60. And to ensure 95% level of certainty, z = 1.96 and e = 5. Applying the formula for sample size ‘n’: n = 40 x 60 x {1.96 / 5 } 2 = 2400 (0.392) 2 = 2400 (0.154) = (Say sample size = 370)

Deciding on a suitable sample size 3.Where population is less than 10000, an adjusted minimum sample size n’ is used, where n’ is: n’ = n / {1 + (n/N)} where n = minimum sample size (calculated earlier) n’ = adjusted minimum sample size N = Total population Worked example: If population is = 4000 n’ = / {1 + (369.6/4000)} = / {1 + (0.092)} = / = (Say sample size = 339)

Deciding on a suitable sample size 4.Incorporating for non-response: Common reasons for non-response: a. Refusal to respond b. Inability to respond c. Inability to locate respondent So, through a pilot/preliminary survey, it seems necessary to estimate the response rate. If the response rate estimates at 30 percent, the ‘actual sample size’ abbreviated as n a will be then: n a = (n/re) * 100 In our previous case, n = (for more than population) or n’ = (for less than population); then: n a = (369.60/30) * 100 = 1232 or n a = (338.46/30) * 100 =

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