Adventures in Machine Learning

Stratified Sampling: An Essential Tool for Accurate Data Analysis

Stratified Sampling: An Overview

When it comes to data analysis, sampling is a fundamental part of the process. Although collecting data from an entire population can be ideal, it is not always feasible due to time, cost, and convenience constraints.

Sampling methods, therefore, provide a way to accurately represent a population without having to survey every individual. Stratified sampling is one of the most popular sampling methods used in statistics and research.

This method involves dividing a population into subgroups or strata and then selecting samples from each stratum to create a final sample. The aim of this method is to ensure that the subgroups are well-represented in the final sample.

In this article, we will look at some of the stratified sampling approaches and provide examples of how this method can be used.

Stratified Random Sampling

Stratified random sampling is a commonly used and highly accurate form of stratified sampling. In this method, subgroups or strata are created based on a specific variable that characterizes the population, such as age, gender, income, or education level.

Once the subgroups have been identified, the researcher selects a random sample from each one. The advantage of using stratified random sampling is that it improves the accuracy and precision of the sample by ensuring that it is representative of the entire population.

By dividing the population into subgroups, the researcher can capture the diversity and variability within the population and reduce any potential bias that could arise from a random selection. Example 1: Stratified Sampling Using Counts

To illustrate how stratified random sampling works, let us consider an example of a basketball team consisting of 50 players.

Suppose we want to select a sample of 10 players from this team for a research study on player performance. We can use a pandas DataFrame to organize the data, with columns representing player names, team, position, assists, and rebounds.

In this case, we can use position as the stratifying variable. The positions in the team are point guard (PG), shooting guard (SG), small forward (SF), power forward (PF), and center (C).

The number of players in each position is as follows:

PG – 8

SG – 14

SF – 10

PF – 11

C – 7

To create a representative sample, we need to select players from each position proportional to the number of players in that position in the population. Therefore, we would need to select 10/50 = 20% of players from each position.

That is, we would select 2 PGs, 3 SGs, 2 SFs, 2 PFs, and 1 C.

Proportional Sampling

Another stratified sampling approach is proportional sampling. In this method, the size of each subgroup is proportional to its size in the population.

Proportional sampling is particularly useful when the researcher wants to ensure equal representation of each stratum in the final sample. The advantage of using proportional sampling is that it simplifies the sampling process and reduces the potential bias that can arise from sample selection.

However, this method may not always be suitable when the strata are significantly different in size. Example 2:

Proportional Sampling of Players

Using our basketball example, let us consider proportional sampling.

In this method, we would select players in each position based on their proportionate representation in the population. That is, we would calculate the percentage of players in each position and then select the corresponding percentage of players from each position.

To illustrate, suppose we want to select a sample of 15 players from the basketball team using proportional sampling. The percentage of players in each position can be calculated as follows:

PG – 16%

SG – 28%

SF – 20%

PF – 22%

C – 14%

Using proportional sampling, we would select 16% of players from the PG position, 28% from SG, 20% from SF, 22% from PF, and 14% from C, giving us 2.56, 3.92, 3, 3.3, and 2.1 players, respectively.

Since we cannot select fractional players, we would round up or down to the nearest whole number, giving us 3, 4, 3, 3, and 2 players, respectively.

Conclusion

In conclusion, stratified sampling is a powerful tool in statistical analysis and research. The method enables researchers to collect accurate and representative data from a population without surveying every individual.

By dividing the population into subgroups or strata, stratified sampling takes into account the diversity and variability of the population and reduces the potential bias that can arise from random selection. Stratified random sampling and proportional sampling are two common stratified sampling approaches.

Both methods have their advantages and disadvantages, and the choice of method depends on the research question and the characteristics of the population. Overall, stratified sampling is a robust and powerful sampling method that can improve the accuracy and precision of research findings.

Understanding the principles and guidelines of stratified sampling is crucial for any researcher who wants to collect valid and reliable data from a population.

Implementation in Python

Stratified sampling can be implemented in Python using a number of libraries, including Pandas, NumPy, and Scikit-learn. This section will cover how to select a random sample using grouping and lambda functions in Pandas, as well as two examples of stratified sampling applications.

Sample Selection

To select a random sample using stratified sampling, we can use grouping and lambda functions in Pythons Pandas library. Grouping by a specific column allows us to create subgroups, and the lambda function enables us to calculate the size or proportion of each subgroup.

For example, suppose we have a dataset of students from three different schools, and we want to select a random sample of ten students from each school. We can use the following code:

import pandas as pd

import numpy as np

# Create a Pandas DataFrame

data = {‘Name’: [‘John’, ‘Jane’, ‘Mark’, ‘Sarah’, ‘David’, ‘Adam’, ‘Emily’,

‘Matthew’, ‘Kevin’, ‘Sophie’, ‘Olivia’, ‘Daniel’, ‘Jessica’,

‘Thomas’, ‘Lucy’, ‘Iris’, ‘Peter’, ‘George’, ‘Maria’, ‘Cathy’],

‘School’: [‘A’, ‘B’, ‘C’, ‘A’, ‘B’, ‘C’, ‘A’, ‘B’, ‘C’, ‘A’,

‘B’, ‘C’, ‘A’, ‘B’, ‘C’, ‘A’, ‘B’, ‘C’, ‘A’, ‘B’],

‘Grade’: [70, 65, 80, 75, 85, 90, 85, 80, 70, 75, 90, 85, 80, 75, 70, 90, 85, 80, 75, 70]}

df = pd.DataFrame(data)

# Group by School and select a random sample of 10 students from each school

sample = df.groupby(‘School’).apply(lambda x: x.sample(n=10, random_state=1)).reset_index(drop=True)

In this code, we create a Pandas DataFrame with columns for student names, school, and grade. We then group the data by school and use a lambda function to select a random sample of ten students from each school.

The random_state parameter ensures that the sample selection is consistent every time the code is run.

Example 1 Application

To demonstrate the application of stratified random sampling in Python, let us consider an example of selecting a random sample of basketball players from a league. Suppose there are ten teams in the league, and each team has 15 players.

We want to create a sample of 10% of players from each team, which totals 15 players for the entire sample. We can use the following code:

import pandas as pd

import numpy as np

# Create a Pandas DataFrame

data = {‘Team’: [‘A’, ‘A’, ‘A’, ‘A’, ‘A’, ‘A’, ‘A’, ‘A’, ‘A’, ‘A’,

‘B’, ‘B’, ‘B’, ‘B’, ‘B’, ‘B’, ‘B’, ‘B’, ‘B’, ‘B’,

‘C’, ‘C’, ‘C’, ‘C’, ‘C’, ‘C’, ‘C’, ‘C’, ‘C’, ‘C’,

‘D’, ‘D’, ‘D’, ‘D’, ‘D’, ‘D’, ‘D’, ‘D’, ‘D’, ‘D’,

‘E’, ‘E’, ‘E’, ‘E’, ‘E’, ‘E’, ‘E’, ‘E’, ‘E’, ‘E’,

‘F’, ‘F’, ‘F’, ‘F’, ‘F’, ‘F’, ‘F’, ‘F’, ‘F’, ‘F’,

‘G’, ‘G’, ‘G’, ‘G’, ‘G’, ‘G’, ‘G’, ‘G’, ‘G’, ‘G’,

‘H’, ‘H’, ‘H’, ‘H’, ‘H’, ‘H’, ‘H’, ‘H’, ‘H’, ‘H’,

‘I’, ‘I’, ‘I’, ‘I’, ‘I’, ‘I’, ‘I’, ‘I’, ‘I’, ‘I’,

‘J’, ‘J’, ‘J’, ‘J’, ‘J’, ‘J’, ‘J’, ‘J’, ‘J’, ‘J’],

‘Player’: [‘A1’, ‘A2’, ‘A3’, ‘A4’, ‘A5’, ‘A6’, ‘A7’, ‘A8’, ‘A9’, ‘A10’,

‘B1’, ‘B2’, ‘B3’, ‘B4’, ‘B5’, ‘B6’, ‘B7’, ‘B8’, ‘B9’, ‘B10’,

‘C1’, ‘C2’, ‘C3’, ‘C4’, ‘C5’, ‘C6’, ‘C7’, ‘C8’, ‘C9’, ‘C10’,

‘D1’, ‘D2’, ‘D3’, ‘D4’, ‘D5’, ‘D6’, ‘D7’, ‘D8’, ‘D9’, ‘D10’,

‘E1’, ‘E2’, ‘E3’, ‘E4’, ‘E5’, ‘E6’, ‘E7’, ‘E8’, ‘E9’, ‘E10’,

‘F1’, ‘F2’, ‘F3’, ‘F4’, ‘F5’, ‘F6’, ‘F7’, ‘F8’, ‘F9’, ‘F10’,

‘G1’, ‘G2’, ‘G3’, ‘G4’, ‘G5’, ‘G6’, ‘G7’, ‘G8’, ‘G9’, ‘G10’,

‘H1’, ‘H2’, ‘H3’, ‘H4’, ‘H5’, ‘H6’, ‘H7’, ‘H8’, ‘H9’, ‘H10’,

‘I1’, ‘I2’, ‘I3’, ‘I4’, ‘I5’, ‘I6’, ‘I7’, ‘I8’, ‘I9’, ‘I10’,

‘J1’, ‘J2’, ‘J3’, ‘J4’, ‘J5’, ‘J6’, ‘J7’, ‘J8’, ‘J9’, ‘J10’]}

df = pd.DataFrame(data)

# Group by Team and select a random sample of 10% players from each team

sample = df.groupby(‘Team’).apply(lambda x: x.sample(n=2, random_state=1)).reset_index(drop=True)

This code creates a DataFrame with columns for team name and player name. We then use grouping and lambda functions to select a random sample of 10% players (2 players) from each team, resulting in a sample of 20 players.

Example 2 Application

To illustrate the use of proportional sampling in Python, let us consider an example of selecting a sample of employees from a company. Suppose the company has 200 employees, and we want to select a sample of 50 employees that is proportional to the size of each department.

We can use the following code:

import pandas as pd

import numpy as np

# Create a Pandas DataFrame

data = {‘EmployeeID’: range(1, 201),

‘Department’: [‘Finance’, ‘IT’, ‘HR’, ‘Marketing’, ‘Sales’]*40}

df = pd.DataFrame(data)

# Calculate the proportion of employees in each department

proportions = df[‘Department’].value_counts(normalize=True)

# Calculate the size of the sample for each department

sample_sizes = (proportions * 50).round().astype(int)

# Select a random sample of employees from each department

sample = df.groupby(‘Department’).apply(lambda x: x.sample(n=sample_sizes[x.name], random_state=1)).reset_index(drop=True)

In this code, we create a DataFrame with columns for employee ID and department. We first calculate the proportion of employees in each department using the value_counts() and normalize() functions.

We then use the proportions and multiply by the target sample size (50) to determine the sample size for each department. Finally, we use grouping and lambda functions to select a random sample of employees from each department based on the sample size.

Conclusion

Stratified sampling is a powerful and useful tool in data analysis and research. By dividing a population into subgroups or strata, stratified sampling provides a more accurate representation of the population and reduces any potential bias that could arise from random sampling.

Pythons Pandas library offers various functions that enable easy and efficient implementation of stratified sampling. With grouping and lambda functions, we can easily create subgroups and calculate the size or proportion of each subgroup.

In this article, we covered how to select a random sample using grouping and lambda functions in Pandas and provided two examples of stratified sampling applications. By understanding stratified sampling principles and implementing these in Python, researchers and data analysts can accurately and efficiently obtain a valuable sample of a population of interest.

Stratified sampling is a valuable and widely used tool in data analysis and research, enabling researchers to collect accurate and representative data from a population without surveying every individual. This method involves dividing the population into subgroups or strata and then selecting samples from each to ensure that subgroups are well-represented in the final sample.

Proportional sampling and stratified random sampling are two popular stratified sampling approaches in Python. By implementing stratified sampling in Python using Pandas libraries and understanding its principles, data analysts can achieve a valuable, more accurate, and more representative sample of a population.