I’m thrilled to release my new ebook! *Introduction to Statistics: An Intuitive Guide for Analyzing Data and Unlocking Discoveries*. [Read more…] about New eBook Release! Introduction to Statistics: An Intuitive Guide

# Basics

## Causation versus Correlation in Statistics

Causation indicates that an event affects an outcome. Do fatty diets cause heart problems? If you study for a test, does it cause you to get a higher score?

In statistics, causation is a bit tricky. As you’ve no doubt heard, correlation doesn’t necessarily imply causation. An association or correlation between variables simply indicates that the values vary together. It does not necessarily suggest that changes in one variable cause changes in the other variable. Proving causality can be difficult.

If correlation does not prove causation, what statistical test do you use to assess causality? That’s a trick question because no statistical analysis can make that determination. In this post, learn about why you want to determine causation and how to do that. [Read more…] about Causation versus Correlation in Statistics

## Observational Studies Explained

Observational studies use samples to draw conclusions about a population when the researchers do not control the treatment, or independent variable, that relates to the primary research question.

In my previous post, I show how random assignment reduces systematic differences between experimental groups at the beginning of the study, which increases your confidence that the treatments caused any differences between groups you observe at the end of the study.

Unfortunately, using random assignment is not always possible. For these cases, you can conduct an observational study. In this post, learn about observational studies, why these studies must account for confounding variables, and how to do so. I’ll close this post by reviewing a published observational study about vitamin supplement usage. [Read more…] about Observational Studies Explained

## Random Assignment in Experiments

Random assignment uses chance to assign subjects to the control and treatment groups in an experiment. This process helps ensure that the groups are equivalent at the beginning of the study, which makes it safer to assume the treatments caused any differences between groups that the experimenters observe at the end of the study. [Read more…] about Random Assignment in Experiments

## 5 Steps for Conducting Scientific Studies with Statistical Analyses

The scientific method is a proven procedure for expanding knowledge through experimentation and analysis. It is a process that uses careful planning, rigorous methodology, and thorough assessment. Statistical analysis plays an essential role in this process.

In an experiment that includes statistical analysis, the analysis is at the end of a long series of events. To obtain valid results, it’s crucial that you carefully plan and conduct a scientific study for all steps up to and including the analysis. In this blog post, I map out five steps for scientific studies that include statistical analyses. [Read more…] about 5 Steps for Conducting Scientific Studies with Statistical Analyses

## Percentiles: Interpretations and Calculations

Percentiles indicate the percentage of scores that fall below a particular value. They tell you where a score stands relative to other scores. For example, a person with an IQ of 120 is at the 91^{st }percentile, which indicates that their IQ is higher than 91 percent of other scores.

Percentiles are a great tool to use when you need to know the relative standing of a value. Where does a value fall within a distribution of values? While the concept behind percentiles is straight forward, there are different mathematical methods for calculating them. In this post, learn about percentiles, special percentiles and their surprisingly flexible uses, and the various procedures for calculating them. [Read more…] about Percentiles: Interpretations and Calculations

## Using Histograms to Understand Your Data

Histograms are graphs that display the distribution of your continuous data. They are fantastic exploratory tools because they reveal properties about your sample data in ways that summary statistics cannot. For instance, while the mean and standard deviation can numerically summarize your data, histograms bring your sample data to life.

In this blog post, I’ll show you how histograms reveal the shape of the distribution, its central tendency, and the spread of values in your sample data. You’ll also learn how to identify outliers, how histograms relate to probability distribution functions, and why you might need to use hypothesis tests with them.

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## Boxplots vs. Individual Value Plots: Graphing Continuous Data by Groups

Graphing your data before performing statistical analysis is a crucial step. Graphs bring your data to life in a way that statistical measures do not because they display the relationships and patterns. In this blog post, you’ll learn about using boxplots and individual value plots to compare distributions of continuous measurements between groups. You’ll also learn why you need to pair these plots with hypothesis tests when you want to make inferences about a population. [Read more…] about Boxplots vs. Individual Value Plots: Graphing Continuous Data by Groups

## Central Limit Theorem Explained

The central limit theorem in statistics states that, given a sufficiently large sample size, the sampling distribution of the mean for a variable will approximate a normal distribution regardless of that variable’s distribution in the population.

Unpacking the meaning from that complex definition can be difficult. That’s the topic for this post! I’ll walk you through the various aspects of the central limit theorem (CLT) definition, and show you why it is so important in the field of statistics. [Read more…] about Central Limit Theorem Explained

## Assessing Normality: Histograms vs. Normal Probability Plots

Because histograms display the shape and spread of distributions, you might think they’re the best type of graph for determining whether your data are normally distributed. However, I’ll show you how histograms can trick you! Normal probability plots are a better choice for this task and they are easy to use.

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## Sample Statistics Are Always Wrong (to Some Extent)!

Here’s some shocking information for you—sample statistics are *always* wrong! When you use samples to estimate the properties of populations, you never obtain the correct values exactly. Don’t worry. I’ll help you navigate this issue using a simple statistical tool! [Read more…] about Sample Statistics Are Always Wrong (to Some Extent)!

## Populations, Parameters, and Samples in Inferential Statistics

Inferential statistics lets you draw conclusions about populations by using small samples. Consequently, inferential statistics provide enormous benefits because typically you can’t measure an entire population.

However, to gain these benefits, you must understand the relationship between populations, subpopulations, population parameters, samples, and sample statistics.

In this blog post, I discuss these concepts, and how to obtain representative samples using random sampling.

**Related post**: Difference between Descriptive and Inferential Statistics

[Read more…] about Populations, Parameters, and Samples in Inferential Statistics

## Normal Distribution in Statistics

The normal distribution is the most important probability distribution in statistics because it fits many natural phenomena. For example, heights, blood pressure, measurement error, and IQ scores follow the normal distribution. It is also known as the Gaussian distribution and the bell curve.

The normal distribution is a probability function that describes how the values of a variable are distributed. It is a symmetric distribution where most of the observations cluster around the central peak and the probabilities for values further away from the mean taper off equally in both directions. Extreme values in both tails of the distribution are similarly unlikely.

In this blog post, you’ll learn how to use the normal distribution, its parameters, and how to calculate Z-scores to standardize your data and find probabilities. [Read more…] about Normal Distribution in Statistics

## Understanding Probability Distributions

A probability distribution is a function that describes the likelihood of obtaining the possible values that a random variable can assume. In other words, the values of the variable vary based on the underlying probability distribution.

Suppose you draw a random sample and measure the heights of the subjects. As you measure heights, you can create a distribution of heights. This type of distribution is useful when you need to know which outcomes are most likely, the spread of potential values, and the likelihood of different results.

In this blog post, you’ll learn about probability distributions for both discrete and continuous variables. I’ll show you how they work and examples of how to use them. [Read more…] about Understanding Probability Distributions

## Interpreting Correlation Coefficients

A correlation between variables indicates that as one variable changes in value, the other variable tends to change in a specific direction. Understanding that relationship is useful because we can use the value of one variable to predict the value of the other variable. For example, height and weight are correlated—as height increases, weight also tends to increase. Consequently, if we observe an individual who is unusually tall, we can predict that his weight is also above the average. [Read more…] about Interpreting Correlation Coefficients

## Measures of Variability: Range, Interquartile Range, Variance, and Standard Deviation

A measure of variability is a summary statistic that represents the amount of dispersion in a dataset. How spread out are the values? While a measure of central tendency describes the typical value, measures of variability define how far away the data points tend to fall from the center. We talk about variability in the context of a distribution of values. A low dispersion indicates that the data points tend to be clustered tightly around the center. High dispersion signifies that they tend to fall further away.

In statistics, variability, dispersion, and spread are synonyms that denote the width of the distribution. Just as there are multiple measures of central tendency, there are several measures of variability. In this blog post, you’ll learn why understanding the variability of your data is critical. Then, I explore the most common measures of variability—the range, interquartile range, variance, and standard deviation. I’ll help you determine which one is best for your data. [Read more…] about Measures of Variability: Range, Interquartile Range, Variance, and Standard Deviation

## Measures of Central Tendency: Mean, Median, and Mode

A measure of central tendency is a summary statistic that represents the center point or typical value of a dataset. These measures indicate where most values in a distribution fall and are also referred to as the central location of a distribution. You can think of it as the tendency of data to cluster around a middle value. In statistics, the three most common measures of central tendency are the mean, median, and mode. Each of these measures calculates the location of the central point using a different method.

Choosing the best measure of central tendency depends on the type of data you have. In this post, I explore these measures of central tendency, show you how to calculate them, and how to determine which one is best for your data. [Read more…] about Measures of Central Tendency: Mean, Median, and Mode

## Difference between Descriptive and Inferential Statistics

Descriptive and inferential statistics are two broad categories in the field of statistics. In this blog post, I show you how both types of statistics are important for different purposes. Interestingly, some of the statistical measures are similar, but the goals and methodologies are very different. [Read more…] about Difference between Descriptive and Inferential Statistics

## Guide to Data Types and How to Graph Them in Statistics

In the field of statistics, data are vital. Data are the information that you collect to learn, draw conclusions, and test hypotheses. After all, statistics is the science of learning from data. However, there are different types of variables, and they record various kinds of information. Crucially, the type of information determines what you can learn from it, and, importantly, what you cannot learn from it. Consequently, it’s essential that you understand the different types of data. [Read more…] about Guide to Data Types and How to Graph Them in Statistics

## Maximize the Value of Your Binary Data with the Binomial and Other Probability Distributions

Binary data occur when you can place an observation into only two categories. It tells you that an event occurred or that an item has a particular characteristic. For instance, an inspection process produces binary pass/fail results. Or, when a customer enters a store, there are two possible outcomes—sale or no sale. In this post, I show you how to use the binomial, geometric, negative binomial, and the hypergeometric distributions to glean more information from your binary data. [Read more…] about Maximize the Value of Your Binary Data with the Binomial and Other Probability Distributions