Introduction to Statistics: An Intuitive Guide for Analyzing Data and Unlocking Discoveries

Book Preface

Statistics are everywhere today. You’ll run across them in your everyday life. Four of day life. Four of five dentists prefer this toothpa five dentists prefer this toothpaste! On the news. ste! On the news. This scientific poll used random sampling and has a margin of error of 3%. In school. Your grades were averages of scores. Perhaps you were graded on a curve? Then, graded on a curve? Then, you took the SAT, ACT, or you took the SAT, ACT, or GRE and received GRE and received your results with percentiles. You’ll find statistics in almost every aspect of life: Nielsen TV ratings, surveys, political polls, insurance rates, and so on. And then, of course, there are the ubiquitous sports statistics, batting averages, third-down conversions, and countless more! Politicians and policy wonks use statistics to make their cases. Companies use statistics to use data to make decisions and increase their profits.

The field of statistics is crucial for expanding scientific knowledge. Statistical analyses are present in virtually every scientific study. Indeed, these analyses determine whether the results of the study are significant and worthy of being published. It’s powerful stuff. But what is the field of statistics exactly

The field of statistics is the science of learning from data. Statistical knowledge helps you use the proper methods to collect the data, employ the correct analyses, and effectively present the results. Statistics is a crucial process behind how we make discoveries in science, make decisions based on data, and make predictions. Statistics allows you to understand a subject much more deeply. Surprisingly, the field isn’t only about numeric results. It only about numeric results. It also involves a wide also involves a wide range of practic range of practices, decisions, and methodologies for both collecting data and analyzing them in a manner that produces valid findings and sound conclusions.

Let’s start by covering two main reasons why studying the field of statistics is crucial in modern society. First, statisticians are guides for learnin learning from data a g from data and navigating common problems that can nd navigating common problems that can lead you lead you to incorrect conclusions. Second, given the growing importance of decisions and opinions based on data, it’s crucial that you can critically assess the quality of analyses that others present to you. In my view, statistics is an exciting field about the thrill of discovery,
learning, and challenging your assumptions. Statistics facilitates the creation of new knowledge. Bit by bit, we push back the frontier of what is known.

Draw Valid Conclusions
Statistics are not just numbers and facts. You know, things like 4 out of 5 dentists prefer a specific toothpaste. Instead, it’s an array of knowledge and procedures that allow you t knowledge and procedures that allow you to learn from data reliably. from data reliably. Statist Statistics enable you to evaluate claims based on q ics enable you to evaluate claims based on quantita uantitative evidence tive evidenceand help you differentiate between reasonable and dubious conclusions. That aspect is particularly vital these days because data are so plentiful along with interpretations presented by people with an agenda.

Statisticians offer critical guidance in producing trustworthy analyses and predictions. Along the way, statisticians can help investigators avoid a wide variety of analytical traps

When analysts use statistical procedures correctly, they tend to produce accurate results. In fact, statistical analyses account for uncertainty and error in the results. Statisticians ensure that all aspects of a study follow the appropriate methods to produce reliable results.

These methods include:
• Collecting reliable data.
• Analyzing the data appropriately.
• Drawing reasonable conclusions.
Avoid Common Pitfalls

Please notice that statistical practices begin before the analysis phase!
Using statistical analyses to produce findings for a study is the culmination of a long process. This process includes constructing the study design, selecting and measuring the variables, devising the sampling technique and sample size, cleaning the data, and determining the analysis methodology among numerous other issues. The overall quality of the results depends on the entire chain of events. A single weak link might produce unreliable results. The following list provides a small taste of potential problems and analytical errors that can affect a study.

Biased samples: An incorrectly drawn sample can bias the conclusions from the start. For example, if a study uses human subjects, the subjects might be different than non-subjects in a way that affects the results.

Overgeneralization: Findings from one populat Findings from one population migh ion might not appl t not apply to another population. Statistical inferences are always limited, and you must understand the limitations.
Causality: How do you determine when X causes a change in Y? Statisticians need tight standards to assume causality, whereas others accept causal relationships more easily. When A precedes B, and correlates with B, many mistakenly believe it is a causal connection!
However, you’ll need to use an experimental design that includes random assignment to assume confidently that the results represent cau sality.

Incorrect analysis: Are you analyzing a multivariate study area with only one variable? Or, using an inadequate set of variables? Perhaps you’re assessing the mean when the median might be better? You can use a wide range of analytical tools, but not all of them are correct for a specific situation.

Violating the assumptions for an analysis: Most statistical analyses have assumptions. These assumptions often involve properties of the
sample, variables, data, and the model. Adding to the complexity, you can waive some assumptions under specific conditions—sometimes
thanks to the central limit theorem. When you violate an essential assumption, you risk producing misleading results. Data mining: Even when analysts do everything else correctly, they can produce falsely significant results by investigating a dataset for too long. When analysts conduct many tests, some will be statistically statistically significant due to chance patterns in the data. Fastidious statisticians track the number of tests performed during a study and place the results in the proper context. Numerous considerations must be correct to produce trustworthy conclusions. Unfortunately conclusions. Unfortunately, there , there are many ways to are many ways to mess up mess up analyses analyses and produce misleading results. Statisticians can guide others through this swamp! We’ll cover everything, and more, on that list above.