Making statistics intuitive
The lognormal distribution is a continuous probability distribution that models right-skewed data. The unimodal shape of the lognormal distribution is comparable to the Weibull and loglogistic distributions. [Read more…] about Lognormal Distribution: Uses, Parameters & Examples
In the United States, our Thanksgiving holiday is fast approaching. On this day, we give thanks for the good things in our lives.
For this post, I wanted to quantify how thankful we should be. Ideally, I’d quantify something truly meaningful, like happiness. Unfortunately, most countries are not like Bhutan, which measures the gross national happiness and incorporates it into their five-year development plans.
Instead, I’ll focus on something that is more concrete and regularly measured around the world—income. By examining income distributions, I’ll show that you have much to be thankful for, and so does most of the world! [Read more…] about A Statistical Thanksgiving: Global Income Distributions
Variance is a measure of variability in statistics. It assesses the average squared difference between data values and the mean. Unlike some other statistical measures of variability, it incorporates all data points in its calculations by contrasting each value to the mean. [Read more…] about Variance: Definition, Formulas & Calculations
Mean squared error (MSE) measures the amount of error in statistical models. It assesses the average squared difference between the observed and predicted values. When a model has no error, the MSE equals zero. As model error increases, its value increases. The mean squared error is also known as the mean squared deviation (MSD). [Read more…] about Mean Squared Error (MSE)
Natural numbers are the numbers you use for counting—for example, its definition includes all the positive integers from 1 to infinity. These numbers occur in nature and are the fundamental origins of the number system. Consequently, we see examples of natural numbers all around us in the world. [Read more…] about Natural Numbers: Definition & Examples
Validity in research, statistics, psychology, and testing evaluates how well test scores reflect what they’re supposed to measure. Does the instrument measure what it claims to measure? Do the measurements reflect the underlying reality? Or do they quantify something else? [Read more…] about Validity in Research and Psychology: Types & Examples
Internal and external validity relate to the findings of studies and experiments. [Read more…] about Internal and External Validity
The uniform distribution is a symmetric probability distribution where all outcomes have an equal likelihood of occurring. All values in the distribution have a constant probability, making them uniformly distributed. This distribution is also known as the rectangular distribution because of its shape in probability distribution plots, as I’ll show you below. [Read more…] about Uniform Distribution: Definition & Examples
Discrete vs continuous data are two broad categories of numeric variables. Numeric variables represent characteristics that you can express as numbers rather than descriptive language. These are quantitative data.
When you have a numeric variable, you need to determine whether it is discrete or continuous.
In broad strokes, the critical factor is the following:
[Read more…] about Discrete vs. Continuous Data: Differences & Examples
The geometric mean is a measure of central tendency that averages a set of products. Its formula takes the nth root of the product of n numbers.
Like the arithmetic mean, the geometric mean finds the center of a dataset. While the arithmetic mean finds the center by summing the values and dividing by the number of observations, the geometric mean finds the center by multiplying and then taking a root of the product. Meanwhile, the harmonic mean is best for averaging rates and ratios. [Read more…] about Geometric Mean: Definition, Formula & Finding
I’m very much an empirical, data, statistics, and science type of guy. So, it might be a surprise to learn that I’ve gone ghost hunting a number of times. Now, I’m not a paranormal enthusiast. I’m definitely a skeptic. However, in my view, being skeptical about something does not preclude collecting data about it. I also have friends I trust completely who are sure they’ve experienced paranormal activity. Plus, I don’t need much of an excuse to try something new and unusual! [Read more…] about Ghost Hunting with a Statistics Mindset
Use a paired t-test when each subject has a pair of measurements, such as a before and after score. A paired t-test determines whether the mean change for these pairs is significantly different from zero. This test is an inferential statistics procedure because it uses samples to draw conclusions about populations.
Paired t tests are also known as a paired sample t-test or a dependent samples t test. These names reflect the fact that the two samples are paired or dependent because they contain the same subjects. Conversely, an independent samples t test contains different subjects in the two samples. [Read more…] about Paired T Test: Definition & When to Use It
Use an independent samples t test when you want to compare the means of precisely two groups—no more and no less! Typically, you perform this test to determine whether two population means are different. This procedure is an inferential statistical hypothesis test, meaning it uses samples to draw conclusions about populations. The independent samples t test is also known as the two-sample t-test. [Read more…] about Independent Samples T Test: Definition, Using & Interpreting
A frequency table lists a set of values and how often each one appears. Frequency is the number of times a specific data value occurs in your dataset. These tables help you understand which data values are common and which are rare. These tables organize your data and are an effective way to present the results to others. Frequency tables are also known as frequency distributions because they allow you to understand the distribution of values in your dataset. [Read more…] about Frequency Table: How to Make & Examples
The mean absolute deviation (MAD) is a measure of variability that indicates the average distance between observations and their mean. MAD uses the original units of the data, which simplifies interpretation. Larger values signify that the data points spread out further from the average. Conversely, lower values correspond to data points bunching closer to it. The mean absolute deviation is also known as the mean deviation and average absolute deviation. [Read more…] about Mean Absolute Deviation: Definition, Finding & Formula
Stem and leaf plots display the shape and spread of a continuous data distribution. These graphs are similar to histograms, but instead of using bars, they show digits. It’s a particularly valuable tool during exploratory data analysis. They can help you identify the central tendency, variability, skewness of your distribution, and outliers. Stem and leaf plots are also known as stemplots. [Read more…] about Stem and Leaf Plot: Making, Reading & Examples
A conditional probability is the likelihood of an event occurring given that another event has already happened. Conditional probabilities allow you to evaluate how prior information affects probabilities. For example, what is the probability of A given B has occurred? When you incorporate existing facts into the calculations, it can change the likelihood of an outcome. [Read more…] about Conditional Probability: Definition, Formula & Examples
Cluster sampling is a method of obtaining a representative sample from a population that researchers have divided into groups. An individual cluster is a subgroup that mirrors the diversity of the whole population while the set of clusters are similar to each other. Typically, researchers use this approach when studying large, geographically dispersed populations because it is a cost-controlling measure. This technique is a probability sampling method. [Read more…] about Cluster Sampling: Definition, Advantages & Examples
Stratified sampling is a method of obtaining a representative sample from a population that researchers have divided into relatively similar subpopulations (strata). Researchers use stratified sampling to ensure specific subgroups are present in their sample. It also helps them obtain precise estimates of each group’s characteristics. Many surveys use this method to understand differences between subpopulations better. This technique is a probability sampling method, and it is also known as stratified random sampling. [Read more…] about Stratified Sampling: Definition, Advantages & Examples
A skewed distribution occurs when one tail is longer than the other. Skewness defines the asymmetry of a distribution. Unlike the familiar normal distribution with its bell-shaped curve, these distributions are asymmetric. The two halves of the distribution are not mirror images because the data are not distributed equally on both sides of the distribution’s peak. [Read more…] about Skewed Distribution: Definition & Examples