Research Methods in MIS: Sampling Design Dr. Deepak Khazanchi

Definitions Sampling: Population: Sample: The process of selecting subgroups from a population of elements such as people, objects or events. Population: All members of a defined category of elements such as people, objects or events. Sample: A portion of a larger category of elements called the population.

Definitions (cont’d) Population (Sampling) Frame A sampling unit is The sampling frame is a listing of all the elements in the population from which the sample is drawn. A sampling unit is the element or object to be sampled or a larger unit containing objects. Subject A subject is a single member of the sample, just as an element is a single member of the population.

Definitions (cont’d) Parameter: Statistic: A population characteristic or value such as mean, variance, proportion, etc. For example, the average gross sales might be the population characteristic of interest (ratio data). Statistic: A numerical index of a population characteristic (e.g., mean, variance, proportion, etc.) computed from sample data, usually to estimate the corresponding population characteristic.

What is a Good Sample? Accurate Accuracy is the degree to which bias is absent from the sample. Any sample will have some sample elements underestimate the population and others overestimate them. An accurate sample is one in which the understimators and the overestimators are balanced among the members of the sample. I.e., There is no systematic variance in an accurate sample.

What is a Good Sample? (cont’d) Precise estimate: sampling error No sample will fully represent its population in all respects. The numerical descriptors that describe samples may be expected to differ from those that describe populations because of random fluctuations inherent in the sampling process. This is called sampling error and reflects the influences of chance in the drawing of random numbers. Precision is measured by the standard error of estimate, a type of standard deviation measurement; the smaller the standard error of estimate, the higher the precision of the sample.

Types of Commonly Used Sampling Methods Random or Probability Sampling Simple Random Stratified Random Proportional Constant Nonrandom or Nonprobability Sampling Methods Systematic Convenience Purposive Quota Representation: The members of a sample are selected either on a probability basis or by other means. Probability sampling is based on the concept of random selection- a controlled procedure that assures that each population element is given a known nonzero chance of selection. In contrast, nonprobability sampling is arbitrary (nonrandom) and subjective. Each member does not have a nonzero chance of being included.

Selecting the Sampling Method Selected Sampling Method Bias Free Method Major Advantage Major Disadvantage RANDOM METHODS: Simple Random YES High probability of sample representing population Requires sizable numbers of Ss Stratified Random Controls for Stratification Variables Often more time and cost than for SRS NONRANDOM METHODS: Systematic NO Cheaper, Easier and Faster with Large Population Potentially Biased Method Convenience Quicker and Cheaper Than Other Methods Purposive Ss Possess Characteristics Desired by Researchers Quota Sample is Proportional to Population in the Selected Characteristics

Steps in Sampling Design What is the relevant population? What is the sampling unit? What are the parameters of interest? What is the population (sampling frame)? What is the type of sample (sampling method)? What size sample is needed? How much will it cost?

Normality of Distributions Features of the Normal Curve: The normal probability curve is symmetric around the mean. The toral area under the curve is equal to 100% The curve appears to hit the x-axis but it never does. The chance of events very far above and below the mean or expected value is, however, very small. A z-score tells you how many standard deviations the value of the random variable is above or below the mean. Attributes or characteristics in the population are generally normally distributed.

Concepts to help understand Probability Sampling Point Estimate: A sample statistic such as a mean or proportion used to estimate the corresponding population parameter. Confidence interval: A range of values which have a specified probability of including the parameter estimated and are computed from values gathered from a sample of the population. Confidence Limits: The upper and lower boundaries of the confidence interval. Confidence Level: The specified probability that the confidence interval will include the true value of the parameter estimated. In order to compute a confidence interval, the researcher must decide what the level of confidence should be. =The most commonly used confidence levels are the 95% and 99% levels which represent the area under the NORMAL CURVE expressed as 2.58 or 1.96 times the standard error.

Concepts to help understand Probability (cont’d) Standard error: The standard deviation of a sampling distribution which is computed for sample statistics such as a mean or proportion. It is based on the concept that the sampling errors of a series of samples from the same population will form a normal distribution. A standard deviation of this distribution of errors (standard error) could then be computed. Generally estimated in practice using a single sample. Standard Error of a Mean = /SQRT(n). Central limit theorem: According to CLT, for sufficiently large samples (n=3), the sample means will be distributed around the population mean approximately in a normal distribution. If the researcher draws repeated samples and plotted the sample in a histogram. It will be approximate to a normal curve shape. Sampling Error: The difference between parameter and the sample estimate of the parameter value which occurs when sampling a population.

Probability Sampling Designs Simple Random Sampling (SRS) Use random numbers to chose sample elements. Stratified Random Sampling Elements are randomly selected from each designated subpopulation (stratum) of a population. Proportionate: Select elements from each stratum in a predetermined proportion equal to that size in the population Disproportionate (Constant): Select the same number of elements from each stratum regardless of size in the population

Nonprobability Sampling Reasons to use Procedure satisfactorily meets the sampling objectives Lower Cost Limited Time Not as much human error as selecting a completely random sample Total list population not available

Nonprobability Sampling Systematic Sampling: Every nth element is chosen from a list of numbered elements. Convenience Sampling: Some convenient group or individuals is used as the sample. Also called: grab sampling, accidental sampling, incidental sampling Purposive Sampling: Sample is arbitrarily (by JUDGMENT or QUOTA) selected because characteristics which they possess are deemed important for the research.