What you pick and how to pick it?

If you’re diving into the world of statistics, whether as a high school student, a statistician, or a data scientist, then understanding sampling methods is a must. These methods form the foundation of surveys, experiments, and the reliability of machine learning projects. In this post, I’ll aim to demystify various sampling methods and explore when and why to use them.

Population vs. Sample

Before we dive into sampling methods, let’s clarify two key terms:

• Population: This is the entire group you want to study. For example, if you’re analyzing pizza preferences in your school, the population is all the students.
• Sample: A smaller group selected from the population to represent it. Instead of polling everyone, you might survey 50 students — that’s your sample.

Sampling saves time, effort, and resources while giving you insights about the whole population. The catch? Your sample must be chosen wisely!

Sample Size, Confidence Level, and Confidence Interval

Sample Size:

The larger your sample, the smaller the margin of error. However, bigger isn’t always better. It’s about finding a balance between accuracy and resources.

Confidence Level:

This indicates how sure you are that your sample reflects the population. A 95% confidence level means your method for creating samples will accurately reflect the population 95% of the time.

Confidence Interval:

This is the probability that the true value of something will fall between a particular range of values. Therefore, a confidence interval will have a lower bound and an upper bound. For example, if you have a confidence interval of 70%, this will be a range of values where you are 70% confident that the accurate value will be within this range.

Bias vs. Random Error

Bias (Systematic Error):

This occurs when your sample consistently skews in one direction. For instance, polling only your pepperoni-loving friends would overestimate pepperoni’s popularity.

Random Error:

This happens due to chance. Imagine surveying students, but accidentally choosing all the hungry ones after gym class. Random errors are unpredictable but should average out with larger samples.

Probability Sampling vs. Non-Probability Sampling

Sampling methods can be broadly divided into two categories:

Probability Sampling:

Here, everyone in the population has a non-zero chance of being selected, ensuring a fair and unbiased sample.

Non-Probability Sampling:

In this case, not everyone has a chance to be selected, often because the sample is chosen based on convenience or specific criteria. While this process is definitely faster and cheaper, it comes with a higher risk of bias.

Probability vs. Non-Probability Sampling

Probability Sampling is preferred when:

1. Generalisability is crucial: If you’re estimating the average income of a city’s population for policy-making, a sample that represents the demographics of the population is essential.
2. Hypothesis testing: Randomised experiments rely on probability sampling to ensure unbiased results. We won’t go into too much detail about hypothesis testing in this post, but do check out this article which gives a very quick summary.
3. Large-scale studies: For example, predicting election outcomes based on voter surveys.

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Non-probability sampling works best when:

1. A quick explorative insight is needed: Testing a new product feature with active users.
2. The population is hard to reach: Researching cryptocurrency traders using referral sampling.
3. Resources are limited: Startups analyzing customer feedback with a convenience sample.

Probability Sampling Methods

1. Simple Random Sampling:

This is the easiest and most desirable. Everyone in the population has an equal chance of being selected. For example, drawing names from a hat to pick survey participants.

2. Systematic Sampling:

Select every nth individual from a list. If your school has 1,000 students and you survey every 10th student, that’s systematic sampling.

3. Stratified Sampling:

Start by dividing the population into groups (strata) and then do simple random sampling to sample from each group. If you want to compare pizza preferences across grades, stratified sampling ensures all grades are represented.

4. Cluster Sampling:

Here we again divide the population into clusters (e.g., classrooms) and then sample entire clusters. This method is efficient when a sampling frame, which is a list of everyone in the population, isn’t available.

Non-Probability Sampling Methods

1. Convenience Sampling:

Here you choose whoever is easiest to reach. For example, surveying students in the cafeteria. It’s quick but often biased.

2. Voluntary Response Sampling:

This is when you let participants self-select. For instance, asking people to vote in an online poll. Beware: only the most passionate voices may respond and your results, therefore, have a very good chance of being biased.

3. Quota Sampling:

First, set quotas to ensure specific groups are represented and then sample according to the quotas. For example, survey an equal number of boys and girls about pizza preferences.

4. Referral Sampling (Snowball Sampling):

Ask participants to recruit others. This method works well for niche populations, such as cryptocurrency traders or rare disease patients.

Practical Example: Measuring Pizza Preferences

Let’s say you’re studying whether students prefer pizza or tacos. Here’s how different sampling methods might look:

• Simple Random Sampling: Randomly pick 50 students from the school student body.
• Systematic Sampling: Survey every 5th person in the lunch line.
• Stratified Sampling: Divide students by grade and sample proportionally from each grade.
• Cluster Sampling: Select two classrooms and survey everyone in them.
• Convenience Sampling: Ask whoever is hanging out in the cafeteria.
• Voluntary Response Sampling: Put up a sign, “Vote for Pizza or Tacos!” and let people come to you.

Final Thoughts

Sampling methods are the backbone of data collection and analysis. Choosing the right method — probability or non-probability — depends on your goals, resources, and the level of accuracy you need. Whether you’re polling pizza preferences or building a machine-learning model, understanding these methods will set you up for success. Sometimes, it’s worth noting that you may not have much of a choice in your method, but that’s outside of the scope of this post. If you end up with unbalanced data, then check out this post on what you can do.