Population Parameters vs Sample Statistics

In the data science and analytics community, it’s a privilege to analyze all available and relevant (or irrelevant) data. Instead, we infer about the whole from a portion of it. This is what inferential stats are all about, and the crux of it comes down to Population Parameters vs. Sample Statistics.

This requires understanding the different patterns, so that models are fitted and hypotheses tested correctly and conclusions are not biased.

What is a Population?

A population is a full set of the thing you want to draw conclusions from. For instance, if you were trying to get an sense of the average height of people in New York City, the "population" is every adult person who lives in that city.

What is a Sample?

A sample is some specific group from which you gather data. It is only a portion of the population. Because measuring everyone in NYC is often either not feasible, or too expensive, you might measure 1,000 people. These 1,000 are your sample.

Key Differences & Symbols.

To differentiate between the two is by the use of different symbols. Population parameters are usually denoted by Greek letters while the same sample statistics use Latin letters otherwise known as the English letters.

Why This Distinction Matters

Estimating the Truth

The purpose of statistics is to use the Sample Statistic (we know) to estimate the Population Parameter (typically unknown). For example, we take the sample mean (𝑥̄) to represent the actual population mean (μ).

Standard Error and Bias

Since a sample is part of the population, it can never be completely accurate. This discrepancy is known as the sampling error. Data scientists use these symbols to keep track of whether they’re talking about the “true” value or an “estimated” one.

Degrees of Freedom

When computing the variance on a sample, you typically divide by n-1 instead of n (Bessel's correction). This guarantees that our sample statistic will be an unbiased estimator of the population variance (σ)

Summary

"The big picture" population(pricing)(μ,σ,β)

Sample: The “Snapshot” Statistics(𝑥̄, s, r)

The deeper understanding and use you have for these symbols and concepts, the more you will be a machine learning or statistical modeling pro. When you are doing A/B tests or fitting predictive models, always ask the yourself the question: "Am I looking at the parameter or the statistic?"

Frequently Asked Questions (FAQS):

Q1. What are population parameters?

Population parameters are characteristics of the population that can be defined using some numerical values describing either the whole population or groups of individuals in that population, for example a mean value (μ) and standard deviation (σ). They are constant values, however, often unknown since is usually impossible to study the whole population.

Q2. What are sample statistics?

Statistics of the sample. Statistics calculated on a subset (the “sample”) rather than on the entire population, for example the sample mean (x̄), or sample standard deviation (s). These estimates are then used to calculate the equivalent population parameters.

Q3. What are the differences between population parameters and sample statistics?

Population parameters refer to the entire population and are stable, versus sample statistics that change from sample to sample. Sample statistics are estimates and might be different on the selected sample.

Q4. Why do we use sample statistics in place of population parameters?

It can be expensive, time-consuming, or impossible to undertake a survey of an entire population. Sample statistics are a convenient mechanism to infer population parameters.

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Author:- 

Prasad Deshmukh