Inferential Statistics
Inferential statistics is a branch of statistics dedicated to making predictions or drawing conclusions about a population based on the analysis of a data sample.
Unlike descriptive statistics, which focuses on summarizing and describing the data collected from an entire population, inferential statistics seeks to make inferences or predictions about a broader population by studying a representative sample.
The key concepts in inferential statistics are the population and the sample:
- Population
The entire group of elements or individuals that you wish to study. - Sample
A subset of the population selected for analysis, chosen to accurately represent the whole population.
In simpler terms, inferential statistics enables us to make informed predictions and decisions based on a portion of the data, allowing us to analyze only part of the population while quantifying the associated uncertainty.
What is it used for? Inferential statistics is widely applied across various fields. For example, in scientific research, it is used to generalize the findings of experimental studies to a larger population. In economics, it is essential for making forecasts based on sample data.
A Practical Example
Imagine we want to estimate the average height of all students in a school with about 1,000 students.
Instead of measuring the height of every single student (the population), we could select a random sample of students (say, 100 students) and measure their heights.
Using inferential statistics, we can then estimate the average height of all students in the school and provide a confidence interval that reflects the precision of our estimate.
What is a confidence interval? It is a range of values, derived from the sample data, that is likely (according to a specified confidence level) to contain the true population parameter. Another important tool in inferential statistics is hypothesis testing, which helps determine whether the sample data provides sufficient evidence to accept or reject a specific hypothesis about the population.
Example 2
Let’s say I want to estimate how many people in Rome prefer Margherita pizza over Capricciosa pizza.
Obviously, I can't survey every single person in Rome—it would take forever...
Instead, I would select a sample that represents the population in terms of age distribution, income level, family status, and so on.
After collecting their pizza preferences through a survey, I can perform some calculations to estimate the overall preference.
Of course, there’s always a margin of error, but this approach is more time-efficient, cost-effective, and still yields a reliable result.
And so on.
