Statistics By Jim

Making statistics intuitive

Basics

Percentiles: Interpretations and Calculations

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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 91st 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

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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: Comparing Groups

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Use boxplots and individual value plots when you have a categorical grouping variable and a continuous outcome variable. The levels of the categorical variables form the groups in your data, and the researchers measure the continuous variable. Both types of charts help you compare distributions of measurements between the groups. Boxplots are also known as box and whisker plots. [Read more…] about Boxplots vs. Individual Value Plots: Comparing Groups

Central Limit Theorem Explained

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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 vital in statistics. [Read more…] about Central Limit Theorem Explained

Assessing Normality: Histograms vs. Normal Probability Plots

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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. Normal probability plots are also known as quantile-quantile plots, or Q-Q Plots for short!
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Populations, Parameters, and Samples in Inferential Statistics

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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, learn the differences between population vs. sample, parameter vs. statistic, and how to obtain representative samples using random sampling.

Related post: Difference between Descriptive and Inferential Statistics
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Normal Distribution in Statistics

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The normal distribution, also known as the Gaussian distribution, is the most important probability distribution in statistics for independent, random variables. Most people recognize its familiar bell-shaped curve in statistical reports.

The normal distribution is a continuous probability distribution that is symmetrical around its mean, 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. While the normal distribution is symmetrical, not all symmetrical distributions are normal. For example, the Student’s t, Cauchy, and logistic distributions are symmetric.

As with any probability distribution, the normal distribution describes how the values of a variable are distributed. It is the most important probability distribution in statistics because it accurately describes the distribution of values for many natural phenomena. Characteristics that are the sum of many independent processes frequently follow normal distributions. For example, heights, blood pressure, measurement error, and IQ scores follow the normal distribution.

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

Probability Distribution: Definition & Calculations

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What is a Probability Distribution?

A probability distribution is a statistical function that describes the likelihood of obtaining all possible values that a random variable can take. In other words, the values of the variable vary based on the underlying probability distribution. Typically, analysts display probability distributions in graphs and tables. There are equations to calculate probability distributions.

Suppose you draw a random sample and measure the heights of the subjects. As you measure heights, you 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 Probability Distribution: Definition & Calculations

Interpreting Correlation Coefficients

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What are Correlation Coefficients?

Correlation coefficients measure the strength of the relationship between two variables. 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

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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

Mean, Median, and Mode: Measures of Central Tendency

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What is Central Tendency?

Measures of central tendency are summary statistics that represent the center point or typical value of a dataset. Examples of these measures include the mean, median, and mode. These statistics indicate where most values in a distribution fall and are also referred to as the central location of a distribution. You can think of central tendency as the propensity for data points to cluster around a middle value.

In statistics, the mean, median, and mode are the three most common measures of central tendency. Each one calculates 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 the mean, median, and mode as measures of central tendency, show you how to calculate them, and how to determine which one is best for your data.


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Difference between Descriptive and Inferential Statistics

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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

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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

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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 probability 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

Learn How Anecdotal Evidence Can Trick You!

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Anecdotal evidence is a story told by individuals. It comes in many forms that can range from product testimonials to word of mouth. It’s often testimony, or a short account, about the truth or effectiveness of a claim. Typically, anecdotal evidence focuses on individual results, is driven by emotion, and presented by individuals who are not subject area experts. [Read more…] about Learn How Anecdotal Evidence Can Trick You!

The Importance of Statistics

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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. [Read more…] about The Importance of Statistics