Sample size determination

Research Methodology:Sample Size Determination

1. Sample size Determination Pritish Biswal Utsho Chowdhary Anurag Guha Gopal Kumar

2. General Idea Sample size is usually determined by the primary objective of trial. Sample size calculation should be explicitly mentioned in the protocol.

3. Determining sample size The estimate of the population standard deviation The acceptable level of sampling error The desired confidence level

4. Methods Unaided Judgment All You can Afford Average Size for samples for similar studies Required Size per cell Use of a Traditional Statistical Model Use of a Bayesian Model

5. Sampling Distribution To help understand the concept of a sampling distribution of the mean by drawing samples from a population of 1250 sales invoices. We use simple random sample of size n=50 from this population for the illustration. A sampling distribution of the mean is the relative frequency distribution of the means of all possible samples of size n taken from a population of size N should be taken, and the mean of each sample be calculated and plotted in a relative frequency distribution.

6. sampling distribution of the mean Frequency of Sample Means Relative frequency of sample means 38-39.99 1 1/500=.002 40-41.99 2 2/500=.004 42-43.99 17 17/500=.034 44-45.99 39 39/500=.078 46-47.99 52 52/500=.104 48-49.99 85 85/500=.170 50-51.99 110 110/500=.220 52-53.99 77 77/500=.154 54-55.99 64 64/500=.128 56-57.99 37 37/500=.074 58-59.99 10 10/500=.020 60-61.99 4 4/500=.008 62-63.99 2 2/500=.004 Total 500 1.000

7. Facts A sampling distribution of the mean for simple random samples that are large(30 or more) has A normal distribution A mean equal to the population(M) A standard deviation called the standard error of the mean,i.e equal to the population standard deviation divided by the square root of the sample size  

8. Statistical Estimation & the sampling distribution of the Mean We want to estimate a population mean that we do not know from a sample mean. Two kinds of estimates of a population mean Point-An estimate involving only a single value. If a random sample is taken, the sample mean is the best estimate that can be made from the sample data. Interval-An estimate concerning an interval, or range of values. A statement of probability that the interval will enclose the true value of the mean is also given. It is called confidence coefficient and the interval is called a confidence interval.

9. Sampling distribution of the proportion A sampling distribution of the proportion is the relative frequency distribution of the proportion(p) of all possible samples of size n taken from a population of size N.A sampling distribution of a proportion for a simple random sample has A normal distribution A mean equal to the population proportion(p) A standard error  

10. Traditional statistical methods of determining sample size What information is needed before a calculation of the sample size can be made? Specification of error that can be allowed-how close must the estimate be? Specification of confidence coefficient-what level of confidence is required that the actual sampling error does not exceed that specified? Estimate of the population standard deviation-what is the s.d of the population?

11. Estimating variances for rating scales used in marketing research On a 5 point scale responses can't be <1 or >5. This constraint leads to a relationship between mean & variance. If a sample mean is 4.6 on a 5 point scale,then there must be a large proportion of responses of 5. If the mean is near 3,the variance can be potentially much greater. The nature of the relationship between the mean and the variance depends on the number of scale points and on the shape of the distribution of responses.

12. Specification required for estimation problems involving proportions The specification must be made to determine the sample size for an estimation problem involving a proportion are very similar to those for the mean Specification of error that can be allowed-how close must the estimate be? Specification of confidence coefficient-what level of confidence is required that the actual sampling error does not exceed that specified? Estimate of population proportion using prior information-what is the approximate or estimated population proportion?

13. Sample size, Incidence & Nonresponse Incidence-is the percentage of individuals who have the traits necessary to be included in a survey. Nonresponse-refers to the percentage of respondents who refuse to participate in a survey or can’t be contacted. Initial sample size=required response÷(incidence× response rate)

14. Thank You