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# Stratified Sampling

Go to solution Solved by Shashikant Adlakha,

Stratified Sampling is a sampling method where the population (or sampling frame) is divided into sub-populations or strata, according to some common characteristic. A simple random sample is selected from each strata for sampling

An application-oriented question on the topic along with responses can be seen below. The best answer was provided by Shashikant Adlakha on 18th February 2020.

Applause for all the respondents - Shashikant Adlakha, Rahul Choudhary, Kiran Kumar, Shaily Chhabra

Also review the answer provided by Mr Venugopal R, Benchmark Six Sigma's in-house expert.

## Question

Q 236. The “Trial of the Pyx” seems to be the longest continuing practice of stratified sampling. Provide some other very common and effective uses of stratified sampling.

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• Solution

Stratified sampling is a  popular statistical method to allocate the population into strata/subgroups.  The stratum should essentially be a representative of a subpopulation of the entire population. Each member of the stratum should be mutually exclusive, should not be included in more than one stratum. After allocating the population into different strata,  simple random or systemic sampling is applied. The purpose of doing stratified sampling is to reduce the sampling error. The weighed mean obtained is much less variable than the arithmetic mean of simple random sample.

Stratified sampling strategies :

1.     Proportionate allocation:  The sampling fraction in each of the stratum  is proportional to that of  proportion of stratum in total population. This kind of sampling is commonly used. Suppose there are three  groups/strata- A,B,C with size of 50, 70, 80 respectively-Total 200 and we have only resources  to study a total  of  60 individuals, so we will have samples- with group A-(50/200)*60- 15 samples, group B- (70/200)*60-21 samples and group C- (80/200)*60-24 samples

2.     Optimum allocation/disproportionate allocation: The sampling  fraction is not proportional to the fraction/size of the stratum in the entire population. Rather  it is proportional to the standard deviation of the distribution of the variable in the stratum. So, largest sample are taken from the stratum with greatest standard deviation or  the variability to obtain the the least possible total sampling variance. The best example is - economical surveys, which fails to form homogenous strata. So optimum allocation is preferred.

-    Stratification leads to  more precision and smaller error in estimation, if measurements in strata have lower standard deviation.

-  By stratified sampling, we get estimates of population parameter of different groups.

-       Analyzing entire  population and allocating  into subgroups may be quite exhaustive and may  not be feasible.

-       Overlapping commonly occurs in few of the characteristics. It may be difficult to place a sample strictly into a subgroup.

Common Uses of Stratified Sampling:-

1.     Trial of the Pyx: It involves selecting, analyzing and certifying that  minted coins conform to the required standards, in United Kingdom. This procedure has been conducted from twelfth century till date, usually once per calendar year. Coins to be tested are selected  from the regular production of the Royal Mint.  Selection of the coins are done randomly and in a fixed proportion in different groups - example-  for every 5,000 bimetallic coins issued, one is selected , whereas for silver ones, one out of every 150 is chosen. The criteria for assessment  includes:- diameter, chemical composition and weight for each class of coin.

2.     Stratified random sampling can be used,  to assess the student’s grade point averages(GPA) across the nation, taking into the account major and minor subjects opted by the students.

3.   People that  work overtime in profession, taking into account the different types of jobs, males and female subgroups etc.

4.   Life expectancy  across the world , taking into account regional characteristics, demographic population data including age, sex, ethnicity , lifestyle etc.

5.     Political Surveys.  In political surveys, diversity of population has to be taken into account. Various minority groups of different races, religion are chosen and  number of samples from each group is taken, based on the proportionality to total population.

6.  Stratified sampling is  used as a method of variance reduction in computational statistics, when Monte Carlo methods are used  in estimating population statistics from a known population.

7.     Water use estimation across the population in a city or town.

8.  Resident travel information in urban cities, for planning of urban transportation

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Benchmark Six Sigma Expert View by Venugopal R

When there is reason to believe that a population has heterogeneity based on certain characteristics, a ‘stratified sampling’ method may be adopted rather than going for a simple random sampling. Such sub-grouping of the population is based on defined characteristics and the groups are referred to as ‘strata’.

Below are a few assorted situations where the stratified sampling would be useful:

1. An opinion poll for a government decision on a population where the strata could be done based on gender, age group and location.
2. Quality characteristic evaluation of a chemical in powder form, where the stratification may be done based on the location of the powder in the container – eg. top right, top left, bottom right, middle left and so on..
3. To study the productivity levels of processing of invoice data, the sampling strata could be based on grouping types of invoices – say, from different industry domains like Retail, Pharmacy, Manufacturing, Restaurant etc.
4. For measuring the diameter of holes on a component, using multiple drilling bits, holes created by each drill bit may be taken as separate strata.
5. For studying transit related damages for a consumer durable, the products may be stratified based on their location on the truck during transportation.
6. While assessing the air quality in a city, it makes sense to identify different locations based on factors such as intensity of traffic and draw samples from each location.
7. Assessing quality of a product by stratifying based on – starting of shift, middle of shift and end of shift.
8. For analyzing reasons for overdue on Loan repayment, samples of defaulters may be taken by stratifying them based on Age, Income, type of employment, Gender, Location, Loan amount etc.

The variation within each strata is expected to be smaller compared to the variation across strata. By adopting the method of stratified sampling, the overall sample size will reduce as well as more accurate conclusions can be obtained. The interpretation from the sampling results may also be used to identify whether the interested outcome has dependency on any of the strata characteristics.

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Stratified Sample provides great precision, in service industry most of the accounts has various process with different tolerance and way of working.

Stratified sampling is most commonly used for quality check processes, below mentioned are a few key advantages:

1. Assures representation of all groups/queue in sample population selected.

2. Characteristics of each layer can be estimated and comparisons can be driven for the same.

3. Reduces Variability from systematic approach

Thanks

Rahul Choudhary.

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In the OCEAN of Data scenario of today, Stratified Sampling can stand tall in relevance. Reasoning :

1) Data availability on anything & everything has increased Multifold Eg : how many times one visited the Metro to How many times one spent on a mobile(with finer classification of the activity one indulged in).

2) Processing ALL data/Information continues to be a BAD/Unviable option for all businesses. And, unnecessary act too !!

Few Hospitality Examples : Restaurant presence within a Hotel Chain : Let's assume it's a 50+ Hotels chain covering 15 cities. The expected occupancy of a Breakfast/Lunch/Dinner venues across could be estimated with help from  Stratified Sampling. The stratification can be based on : Room Category mix / Guest nationality Mix / Gender Mix  of occupancy / Purpose of Visit mix & lot many more meaningful/insightful buckets.

A Local SuperMarket : The product mix & space usage (Veggies/ Groceries / Eat in / sub retailing etc) can evolve over years in tandem with the study of Stratified sampling of population mix in the 10-15 km radius(including the Home Delivery Opportunity). The criteria of stratification could be : By Education / By Family size / By density of population distribution / Gender Mix / By competition presence/ By Traffic volume etc...

The Best way forward would always be : Identifying the Best set of Stratification Criteria & validating the criteria at regular intervals(like once in 2 years or whatever is appropriate). Name any Statistical Analysis, "Stratified Sampling" qualifies to be one of the Best/Robust/ Cost effective Sampling methodology.

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Stratified sampling is a common sampling methodology where the data is divided into strata so as to draw eligible conclusions from the different sub-groups or strata. Ideally the sub groups should be different and should not overlap. The researcher should use simple probability sampling while using stratified sampling. The various sun groups the data can be divided into are:-age, gender, nationality, job profile, educational qualifications etc. The idea here is to understand the relationship between two different sub-groups.

There are 2 different types of stratified sampling techniques:- Proportionate stratified random sampling and disproportionate stratified random sampling . The only difference between the two is the sampling fraction in the disproportionate stratified random sampling. Also, its often seen that if the researchers lie too much emphasis on one subgroup it can lead to skewed results.

Some of the common and effective uses of stratified sampling are:-

-Population size:-This method allows the researchers to obtain a sample population that best represent the overall population size by dividing the overall data into homogeneous group called strata for example determining the GPA of the college students across the US and along with it can also look at the Demographics of college students

With the above the researchers would have a proportionate stratified random sample of college students which better represents students college majors in US. This can help the researchers in highlighting various studies of US college graduates and observe the various grade point averages.

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The winner for this question is Shashikant Adlakha as he has provided a good number of examples along with advantages and disadvantages of stratified sampling.

Please go through the response by Mr Venugopal as well.

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