Research Methodology

Lecture No :16( Sampling / Non Probability, Confidence and Precision, Sample size)

Recap Lecture

• Systematic ,stratified sampling, cluster, area and double sampling are the common types of complex sampling.

• Convenience, judgment, quota and snowball sampling are the common types of non probability sampling.

Lecture Objectives

• Non Probability Based sampling (Quota/snow ball)

• Discuss about the precision and the confidence.

• Precision and Confidence

• Factors to be taken into consideration for determining sample size.

• Managerial implications of sampling.

Non-Probability Sampling

Quota Sampling:

This is a sampling technique in which the business researcher ensures that certain characteristics of a population are represented in the sample to an extent which is he or she desires.

Non-Probability Sampling

Quota SamplingExample: A business researcher wants to determine through interview, the demand for Product X in a district which is very diverse in terms of its ethnic composition.

If the sample size is to consist of 100 units, the number of individuals from each ethnic group interviewed should correspond to the group’s percentage composition of the total population of that district.

Quota Sampling

Example: Quotas have been set for gender only. Under the circumstances, it’s no surprise that the sample is representative of the population only in terms of gender, not in terms of race. Interviewers are only human;.

Non-Probability Sampling

Snowball Sampling :

•This is a sampling technique in which individuals or organizations are selected first by probability methods, and then additional respondents are identified based on information provided by the first group of respondents

Non-Probability Sampling

Snowball Sampling•The advantage of snowball sampling is that smaller sample sizes and costs are necessary; a major disadvantage is that the second group of respondents suggested by the first group may be very similar and not representative of the population with that characteristic.

Example: Through a sample of 500 individuals, 20 antique car enthusiasts are identified which, in turn, identify a number of other antique car enthuiasts

More Snowball Sampling…

More systematic versions of snowball sampling can reduce the potential for bias. For example, “respondent-driven sampling” gives financial incentives to respondents to recruit peers.

Issues in Sample Design and Selection

• Availability of Information – Often information on potential sample participants in the form of lists, directories etc. is unavailable (especially in developing countries) which makes some sampling techniques (e.g. systematic sampling) impossible to undertake.

• Resources – Time, money and individual or institutional capacity are very important considerations due to the limitation on them. Often, these resources must be “traded” against accuracy.

Issues in Sample Design and Selection

• Geographical Considerations – The number and dispersion of population elements may determine the sampling technique used (e.g. cluster sampling).

• Statistical Analysis – This should be performed only on samples which have been created through probability sampling (i.e. not probability sampling).

• Accuracy – Samples should be representative of the target population (less accuracy is required for exploratory research than for conclusive research projects).

Issues of precision and confidence in determining sample size

Precision•Precision is how close our estimate is to the true population characteristic.•Precision is the function of the range of variability in the sampling distribution of the sample mean.

Population and Sample distinctiveness

• Sample Statistics( Mean, Std Deviation, Variance) and Population parameters ( Mean, Std Deviation, Variance)

• Compare the Sample estimates and population characteristic. Where the estimates should be the representative of the population charactertics

• Sample statistics (mean, sd, ..) should be representative of the population parameters(mean, sd …)

Issues of precision and confidence in determining sample size

Precision:•How close are the estimates to the population.

•While expecting that the population mean would it fall between (+,- )10 points or (+,-) 5 points based on the sample estimates is precision.

•The narrower the more precise our statement is

•E.g: The average age of the a particular class based on the sample is between 20 and 25•Or it between 18 and 28.

•How close are the estimates to the population.

Confidence•Confidence denotes how certain we are that our estimate will hold true for the population.•The level of confidence can range from 0 to 100%. However 95% confidence is the conventionally accepted for most business research.

• The more we want to be precise the less confident we become that our statement is going to be true.

• So at one level we want to be accurate in our statement but on the other we taking a higher risk of proved incorrect.

• In order to maintain the precision and increase the confidence or increase the precision and the confidence we need to have a larger sample.

Determining sample size

Roscoe (1975) proposes the following rules of thumb for determining sample size.

•Sample sizes larger than 30 and less than 500 are appropriate for most research

•Where sample sizes are broken into subsamples (males/females, juniors/seniors etc.), a minimum sample size of 30 for each category is necessary.

Determining sample size

• In multivariate research (including multiple regression analysis), the sample size should be several times (preferably ten times or more) as large as the number of variables in the study.

• For simple experimental research with tight experimental controls (matched pairs, etc.), successful research is possible with samples as small as 10 to 20 in size.

• Tools and mathematical equations are available to establish the right size of the sample.

• Refer to the book for the sample size calculation equation.

• Standard Tables are available

• Use a software like RAO calculator available on the internet.

Types of Sampling Designs

Sampling Designs

Non-probability Probability

Convenience Judgmental Quota Snowball

Systematic Stratified Cluster Other SamplingTechniques

Simple Random

Managerial Implications

• Awareness of sampling designs and sample size helps managers to understand why a particular of sampling is used by researchers.

• It also facilitates understanding of the cost implications of different designs, and the trade off between precision and confidence vis-à-vis the costs.

Managerial Implications

• This enables managers to understand the risk they take in implementing changes based on the results of the research study.

• By reading journal articles, this knowledge also helps managers to assess the generazibility of the findings and analyze the implications of trying out the recommendations made therein in their own system.

Recap

• Non Probability based sampling ( • Precision we estimate the population parameter to fall

within a range, based on sample estimate.• Confidence is the certainty that our estimate will hold

true for the population.• Roscoe (1975) rules of thumb for determining sample

size.• Some sampling designs are more efficient than the

others.• The knowledge about sampling is used for different

managerial implications.