Statistical Inference

Overview

Questions

• What does statistical inference mean?
• What other mathematical concepts are needed to understand statistical inference better?

Objectives

• Understand the mathematical concept of statistical inference.
• Understand the difference between descriptive and inferential statistics, correlation and causation.
• Understand the meaning of regression.

This episode demonstrates that data visualization is about more than just storytelling. A common misconception is that humanities researchers and scholars find it difficult to grasp statistical concepts and, therefore, the mathematics behind machine learning and AI. In this episode, you’ll explore the concept of statistical inference, with data visualization serving as a helpful learning tool as you will see in the next episode. This episode will show you how, besides describing your research data, you can also use visualization for predicting missing values and coming up with hypotheses for further research.

Question

Have you ever heard of statistical inference? What does this concept mean in statistics?

Answer

Inferential statistics, along with descriptive ststistics, are two major methods of statistical analysis.

• Descriptive statistics summarizes and explains the data we already have, without making generalizations about a larger population.
• In contrast, inferential statistics allows us to draw conclusions about an entire population or predict future trends through hypotheses. These hypotheses are formed based on observations and analysis of a sample from the population. The next step is to test whether the hypothesis is true and applicable to the broader population, or whether our observations were simply due to chance, making the hypothesis false.

Statistical inference according to The online Encyclopedia of Mathematics

“At the heart of statistics lie the ideas of statistical inference. Methods of statistical inference enable the investigator to argue from the particular observations in a sample to the general case. In contrast to logical deductions made from the general case to the specific case, a statistical inference can sometimes be incorrect. Nevertheless, one of the great intellectual advances of the twentieth century is the realization that strong scientific evidence can be developed on the basis of many, highly variable, observations.

The subject of statistical inference extends well beyond statistics’ historical purposes of describing and displaying data. It deals with collecting informative data, interpreting these data, and drawing conclusions. Statistical inference includes all processes of acquiring knowledge that involve fact finding through the collection and examination of data. These processes are as diverse as opinion polls, agricultural field trials, clinical trials of new medicines, and the studying of properties of exotic new materials. As a consequence, statistical inference has permeated all fields of human endeavor in which the evaluation of information must be grounded in data-based evidence.

A few characteristics are common to all studies involving fact finding through the collection and interpretation of data. First, in order to acquire new knowledge, relevant data must be collected. Second, some variability is unavoidable even when observations are made under the same or very similar conditions. The third, which sets the stage for statistical inference, is that access to a complete set of data is either not feasible from a practical standpoint or is physically impossible to obtain.” (Encyclopedia of Mathematics)

When using methods of statistical inference, we work with samples of data because we don’t have access to the entire population. We observe and measure patterns and categories within these samples to form a hypothesis. Proving or rejecting the hypothesis requires mathematical methods that go beyond the scope of this lesson. If you’re interested in learning more about hypothesis testing, you can watch the YouTube video on this topic by DATAtab.

3.1. Correlation and Regression in Inferential Statistics

---

To perform inferential statistical analysis, it’s important to identify correlations between features in the data. If two numerical features are correlated, an increase or decrease in one tends to coincide with an increase or decrease in the other. For example, if we have data on the lifestyle habits of a group of people and their age at death, we can look for lifestyle factors (such as the frequency of physical exercise or eating habits) that may correlate with longevity and a higher age at death.

If such a correlation is observed and measured, we can use it to predict the lifespan of individuals whose data is not part of the sample. To make this prediction, we first need to establish a mathematical or numerical relationship between lifespan and the other features in the dataset that may correlate with it. In this case, lifespan is considered the dependent variable, as its value depends on the other features. The other features, in turn, are considered independent variables, as their values do not depend on lifespan. This process of numerically relating a dependent variable to independent variables is called regression.

Note

Correlation is not causation! In the example above, even if a correlation is found between lifestyle and lifespan, scientists must seek clinical evidence to determine whether there is also a causal relationship between these two factors. Tyler Vigen, author of the book Spurious Correlations, created a website where he shares humorous correlations between unrelated trends to emphasize this important point: correlation does not imply causation.

However, correlations can still be useful for predicting future trends through regression methods, even if they don’t explain the underlying reasons for these trends.

Key Points

• The concept of statistical inference.
• The difference between descriptive and inferential statistics.
• The concepts of correlation, regression and causation.