Systematic Sampling in Pandas

Systematic sampling is a probability-based method for selecting a subset of observations from a larger dataset. In this technique, we select every nth observation from the dataset, where n is a predefined number. This method is particularly useful when we want to ensure that the sample is representative of the population and that the data points are evenly distributed.

Alternative approaches to sampling include simple random sampling and stratified sampling. Simple random sampling involves selecting observations randomly, without any regard to their position in the dataset. Stratified sampling, on the other hand, involves dividing the dataset into distinct strata or groups and then selecting a random sample from each stratum. Each of these methods has its advantages and disadvantages, and the choice of sampling technique depends on the research question and the characteristics of the dataset.

Mathematically, the systematic sampling formula can be represented as:

$N = \text{total number of observations in the dataset}\ n = \text{sampling interval}\n i = \text{starting index}\ X_i = X_{i+nk} \text{for } k = 1, 2, ..., \frac{N}{n}$

Here, N represents the total number of observations in the dataset, $n$ is the sampling interval, and i is the starting index. The systematic sample consists of the observations $X\_i, X\_{i+n}, X\_{i+2n}$ , and so on, up to the last observation $X\_{i+\frac{N}{n}}$ .

Let’s see how to perform systematic sampling using the Pandas library in Python. First, we need to load our dataset into a Pandas DataFrame.

import pandas as pd

# Load dataset into a Pandas DataFrame
df = pd.read_csv('data.csv')

Next, we define the sampling interval and the starting index. In this example, we will select every 5th observation, starting from the first observation.

# Define sampling interval and starting index
n = 5
i = 0

We can then use the index property of the DataFrame to select every nth observation using slicing.

# Perform systematic sampling
sample = df.iloc[i:len(df):n]

Finally, we can print the resulting systematic sample to verify that every nth observation has been selected.

# Print systematic sample
print(sample)

For more information on sampling techniques and statistical analysis using Pandas, refer to the following resources:

On Statistics

Systematic Sampling in Pandas

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