BASIC INTRODUCTION TO SYSTEMATIC RANDOM SAMPLING


Anwesha Nath

2048117

Systematic sampling definition:

Systematic sampling is defined as a probability sampling method where the researcher chooses elements from a target population by selecting a random starting point and selects sample members after a fixed ‘sampling interval.’

In a layman’s term Systematic sampling is when researchers select items from an ordered population using a skip or sampling interval.

For example: If researchers are interested in the population that attends a particular restaurant on a given day, they could set up shop at the restaurant and ask every tenth person to enter to be a part of their sample. 

When to Use Systematic Sampling?

Researchers should use systematic sampling instead of simple random sampling when a project is on a tight budget, or requires a short timeline, his especially happens when conducting a survey. Here are 4 other situations of when to use Systematic Sampling:   

1.       Budget restrictions: 

2.       Uncomplicated implementation

3.       Absence of data pattern

4.       Low risk of data manipulation in research

Systematic random sampling:

Systematic random sampling is a method to select samples at a particular pre-set interval. As a researcher, select a random starting point between 1 and the sampling interval. Sampling like this leaves the researcher no room for bias regarding choosing the sample. To understand how systematic sampling exactly works, take the above example. Below are the example steps to set up a systematic random sample:

·         First, calculate and fix the sampling interval. (The number of elements in the population divided by the number of elements needed for the sample.)

·         Choose a random starting point between 1 and the sampling interval.

·         Lastly, repeat the sampling interval to choose subsequent elements.

NOTE: The sampling starts by selecting an element from the list at random and then every kth element in the frame is selected, where k, is the sampling interval (sometimes known as the skip): this is calculated as: K=N/n

Some Important formulas related to this sampling method:

1.       Estimating the Population Mean

The population mean (μ) is the true average number of entities per sample unit and is estimated with the sample mean ( m-hat or y ) which has an unbiased estimator:

Where yi is the value from each unit in the sample and n is the number of units in the sample. 

2.       Estimating Population variance and Standard Error

The population variance (σ2 ) is estimated with the sample variance (s2 ) which has an unbiased estimator:

The standard error of the estimate is the square root of variance of the estimate, which as always is the standard deviation of the sampling distribution of the estimate.  Standard error is a useful gauge of how precisely a parameter has been estimated.   

The quantity (N-n)/N is the finite population correction factor which adjusts variance of the estimator (not variance of the population which does not change with n) to reflect the amount of information that is known about the population through the sample.  Practically, the correction factor reflects the proportion of the population that remains unknown.  Therefore, as the sample size n approaches the population size N, the finite population correction factor approaches zero, so the amount of variation associated with the estimate also approaches zero.

 When the sample size n is large relative to the population size N, the fraction of the population being sampled n/N is small, so the correction factor has little effect on the estimate of variance.

If the finite population correction factor is ignored, including those cases where N is unknown, FPC with N = 100 0 0.2 0.4 0.6 0.8 1 0 20 40 60 80 100 n FPC 5 the effect on the variance of the estimator is slight when N is large.  When N is small, however, the variance of the estimator can be overestimated appreciably. 

4.       Estimating the Population Total

Like the population mean, the total number of entities in the population is another attribute estimated commonly.  Unlike the population mean or proportion, estimating the population total requires that we know the number of sampling units in a population, N. 

Because the estimator tˆ is simply the number of sample units in the population N times the mean number of entities per sample unit, mˆ , the variance of the estimate tˆ reflects both the number of units in the sampling universe N and the variance associated with mˆ .  An unbiased estimate for the variance of the estimate tˆ is: 

Application and Example of Systematic Random Sampling:

 Systematic sampling is majorly used in surveys to save time and cost, and also to increase efficiency.  

I am going to talk about Multidimensional Poverty Survey.

The primary aim of the study was to generate information that would enable researcher to rank different areas (rural and urban) relative to each other in terms of overall, multidimensional impoverishment, and levels of deprivation in specific indicators.

The data was collected and the sampling technique used here was systematic random sampling.

About The Dataset


  • MPI Urban: Multi-dimensional poverty index for urban areas within the country
  • Headcount Ratio Urban: Poverty headcount ratio (% of population listed as poor) within urban areas within the country
  • Intensity of Deprivation Urban: Average distance below the poverty line of those listed as poor in urban areas
  • MPI Rural: Multi-dimensional poverty index for rural areas within the country
  • Headcount Ratio Rural: Poverty headcount ratio (% of population listed as poor) within rural areas within the country
  • Intensity of Deprivation Rural: Average distance below the poverty line of those listed as poor in rural areas




CONCLUSION

The estimated intensity of Deprivation in Rural areas is 3.37 which is the average distance below the poverty line of those listed as poor in rural areas or we can say that the mean deprivation felt by people in rural areas is 3.37 on an average.

Next one can compare the estimate with the intensity of deprivation in Urban Areas. And conclude its results


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