The Basics of Statistical Inference

In the last chapter, we learned how to explore data using different graphs and extract information from the data. We discovered relationships between different variables in our datasets, but how do we decide whether these relationships are real or just by coincidence? How do we decide whether we can make a generalization about the dataset or not? This is where inferential statistics comes in.

Inferential statistics

Before we see what inferential statistics is all about, we need to understand the concept of a population and a sample.

A population includes all the elements from a set of data that we are studying. For example, if we are interested in finding out how grades of students in a school are affected by alcohol consumption, all the students in that school form a population. A measurable characteristic of the population, such as a mean or standard deviation, is known as a parameter.

A sample is a subset of the population. In our school example, if we randomly choose a single grade and analyze students in that grade, then those chosen students form a sample. A measurable characteristic of a sample is known as a statistic.

Inferential statistics is the branch of statistics that helps us make inferences about the general population from a sample. It aims at gaining insights about the population from which the data was collected, based on the collected samples. There are two main areas of inferential statistics:

• Estimation: This involves taking a statistic of a sample and using that to say something about a population parameter.

• Hypothesis testing: This involves answering some research questions about a population using a sample of that population.

Point estimates

Point estimates are estimates of population parameters based on sample data. Let’s say we want to measure the average salary of all data ...