From Sample to Population: Basics of Sampling in Statistics
🎯 What’s the Difference Between a Population and a Sample?
In statistics:
- The population refers to the entire group we want to study or draw conclusions about.
- A sample is a subset of that population, selected to represent it.
Why? Because studying the whole population is often too expensive or impractical. That’s where sampling comes in.
📚 This post is part of the "Intro to Statistics" series
🔙 Previously: Understanding Binomial Distribution
🔜 Next: Understanding the Sampling Distribution of the Sample Mean and the Central Limit Theorem
🔍 Parameters vs. Statistics
When we study data:
- The characteristics of a population are called parameters — written using Greek letters (e.g., \( \mu \), \( \sigma \)).
- The characteristics of a sample are called statistics — written using Roman letters (e.g., \( \bar{x} \), \( s \)).
We use inferential statistics to predict population parameters from sample statistics.
🧪 The Importance of Simple Random Sampling
To make sure our sample fairly represents the population, we often use a Simple Random Sample (SRS).
In SRS:
- Every member of the population has an equal chance of being selected.
- This helps reduce bias and increases the accuracy of our predictions.
🧭 How to Take a Simple Random Sample
- Define your population.
- Create a sampling frame — a complete list of all cases.
- Use random methods (like a random number generator) to select your sample.
- Contact the selected respondents using:
- Face-to-face interviews
- Phone calls
- Online or paper questionnaires (easiest but less accurate)
⚠️ Common Sampling Errors and Biases
Even with careful planning, things can go wrong:
- Undercoverage Bias: Not all classes or groups are included in the sampling frame.
- Sampling Bias: For example, choosing a convenient sample (only nearby people).
- Non-response Bias: Selected individuals don’t respond.
- Response Bias: People give inaccurate answers (on purpose or by mistake).
🎯 Making a truly random sample is not easy, especially with real-world constraints.
🧰 Other Sampling Techniques
When Simple Random Sampling is too difficult, we use other methods:
1. Stratified Random Sampling
- The population is divided into groups (strata).
- A random sample is taken from each stratum.
- Works best when strata are clearly defined and understood.
2. Multistage Cluster Sampling
- Useful when there is no complete sampling frame.
- Select groups (clusters) randomly, then sample within them.
✅ In both techniques, knowing the population structure (strata or clusters) is key.
📏 Bigger Is Better… But Randomness Matters
- A larger sample reduces random error.
- But if it’s not random, the results can still be misleading.
🎯 Randomness beats size if you must choose.
🧠 Level Up: Real-World Sampling Challenges
- Sampling frames may be outdated or incomplete — especially in population surveys.
- People may opt out of participation, especially in phone or online surveys.
- Oversampling certain strata is a valid strategy when some groups are small but important.
- Weighting responses after collection can help adjust for biases — but requires expertise.
📌 Try It Yourself: Sampling Basics
Q1: Which of the following best describes a parameter?
💡 Show Answer
- A) A value from a sample
- B) A value that describes a population ✓
- C) A sampling technique
- D) A hypothesis result
Q2: What is the main reason for using a sample?
💡 Show Answer
- A) To save cost and effort ✓
- B) To test a theory
- C) To get biased results
- D) To increase variation
Q3: What makes Simple Random Sampling "random"?
💡 Show Answer
- A) Choosing only volunteers
- B) Every individual has an equal chance ✓
- C) Picking based on opinion
- D) Using clusters
Q4: Which bias happens when certain groups are not in the sampling frame?
💡 Show Answer
- A) Response bias
- B) Sampling bias
- C) Undercoverage bias ✓
- D) Convenience bias
Q5: Which sampling method works best when strata are known?
💡 Show Answer
- A) Convenience sampling
- B) Stratified random sampling ✓
- C) Cluster sampling
- D) Quota sampling
✅ Summary
| Concept | Description |
|---|---|
| Population | The entire group you’re interested in |
| Sample | A subset selected from the population |
| Parameters | Characteristics of population (\( \mu, \sigma \)) |
| Statistics | Characteristics of sample (\( \bar{x}, s \)) |
| SRS | Simple Random Sample: equal chance selection |
| Bias Types | Undercoverage, Sampling, Non-response, Response |
| Other Techniques | Stratified, Cluster sampling |
🔜 Up Next
In the next post, we’ll explore the Sampling Distribution of the Sample Mean — how sample averages behave, the Central Limit Theorem, and why these concepts form the foundation of many statistical procedures
Stay curious! 📊