Tags: #◇CSMODEL #◇Data Collection #◇Computer Science #◇Data Science #◇Statistical Modeling #◇Python #◇Machine Learning

Module 2: Data Collection and Sampling

◇1. Introduction to Data Collection in Statistics

In statistical modelling, data collection is the process of selecting a subset of individuals (a sample) from a larger group (a population) to estimate characteristics of the whole population. Because examining an entire population is usually impractical or impossible, proper sampling techniques are essential to ensure the sample is representative.

◇2. Populations and Samples Population: The entire group of individuals or instances about whom we hope to learn. Sample: A smaller, representative group drawn from the population used for actual analysis. Parameter: A numerical summary of the population (e.g., population mean, $\mu$). Statistic: A numerical summary of a sample (e.g., sample mean, $\bar{x}$).

◇3. Sampling Strategies (Techniques)

To avoid biased data, statistical sampling methods must involve randomization: Simple Random Sampling (SRS): Every individual in the population has an equal chance of being selected. Stratified Sampling: The population is divided into distinct, non-overlapping groups (strata) based on a specific characteristic (e.g., gender, age group). A simple random sample is then drawn from each stratum. Cluster Sampling: The population is divided into clusters (usually geographically). A random sample of clusters is chosen, and all individuals within the chosen clusters are sampled. Systematic Sampling: Selecting every $k^{th}$ individual from a population list. Convenience Sampling (Non-Probability): Sampling individuals who are easily accessible. This often leads to severe bias and should generally be avoided.

◇4. Types of Studies Observational Study: Researchers observe individuals and measure variables of interest but do not intervene or manipulate the environment. It can show association, but not causation. Experimental Study (Experiment): Researchers deliberately impose some treatment on individuals to measure their responses. Well-designed experiments can prove causation.

Principles of Experimental Design

1. Control: Control for lurking variables by comparing treatment groups to control groups.
2. Randomization: Randomly assign subjects to treatments to eliminate bias.
3. Replication: Ensure an adequate number of subjects in each group to measure variability.
4. Blocking: If there are variables known to affect the outcome, group similar individuals into blocks and randomize treatments within those blocks.

◇5. Sampling in Python

While collecting data manually happens in the real world, we often simulate sampling or create data partitions (like train/test splits) in Python using pandas.

import pandas as pd
import numpy as np

# Create a dummy population dataset
np.random.seed(42)
population = pd.DataFrame({
    'ID': range(1, 101),
    'Age': np.random.randint(18, 65, size=100),
    'Category': np.random.choice(['A', 'B', 'C'], size=100)
})

# 1. Simple Random Sampling
# Sample 10 random rows without replacement
srs_sample = population.sample(n=10, replace=False, random_state=1)
print("Simple Random Sample:\n", srs_sample.head(3))

# 2. Stratified Sampling
# Sample 2 items from each category (stratum)
stratified_sample = population.groupby('Category', group_keys=False).apply(lambda x: x.sample(n=2, random_state=1))
print("\nStratified Sample:\n", stratified_sample)

◇6. Sampling Biases Selection Bias: Occurs when the sample is not representative of the population (e.g., using convenience sampling). Non-response Bias: Occurs when individuals chosen for the sample cannot be contacted or refuse to participate, and these individuals differ from those who do participate. Response Bias: Occurs when respondents give inaccurate answers (e.g., due to poorly worded questions or lying about sensitive topics).

◇Practice Questions

Q1. A researcher divides a city into 50 distinct neighborhoods, randomly selects 5 of these neighborhoods, and surveys every household in those 5 neighborhoods. What sampling method is this?
A) Simple Random Sampling
B) Stratified Sampling
C) Cluster Sampling
D) Systematic Sampling

Q2. Which of the following study designs is best suited for establishing a cause-and-effect relationship between two variables?
A) A retrospective observational study
B) A randomized controlled experiment
C) A voluntary response survey
D) A cross-sectional study

Q3. A polling agency conducts a phone survey during working hours. People who work full-time are less likely to answer. What type of bias does this primarily introduce?
A) Response bias
B) Non-response bias
C) Measurement bias
D) Confounding bias

◇References & Navigation

• Previous Topic: ◇Introduction to Data
• Next Topic: ◇Data Cleaning
• Related Notes: ◇Data Cleaning, ◇Data Preprocessing