# Archive | Statistics

## A Gentle Introduction to the Chi-Squared Test for Machine Learning

A common problem in applied machine learning is determining whether input features are relevant to the outcome to be predicted. This is the problem of feature selection. In the case of classification problems where input variables are also categorical, we can use statistical tests to determine whether the output variable is dependent or independent of […]

## How to Calculate the 5-Number Summary for Your Data in Python

Data summarization provides a convenient way to describe all of the values in a data sample with just a few statistical values. The mean and standard deviation are used to summarize data with a Gaussian distribution, but may not be meaningful, or could even be misleading, if your data sample has a non-Gaussian distribution. In […]

## A Gentle Introduction to Statistical Sampling and Resampling

Data is the currency of applied machine learning. Therefore, it is important that it is both collected and used effectively. Data sampling refers to statistical methods for selecting observations from the domain with the objective of estimating a population parameter. Whereas data resampling refers to methods for economically using a collected dataset to improve the […]

## How to Calculate Critical Values for Statistical Hypothesis Testing with Python

In is common, if not standard, to interpret the results of statistical hypothesis tests using a p-value. Not all implementations of statistical tests return p-values. In some cases, you must use alternatives, such as critical values. In addition, critical values are used when estimating the expected intervals for observations from a population, such as in […]

## A Gentle Introduction to Statistical Data Distributions

A sample of data will form a distribution, and by far the most well-known distribution is the Gaussian distribution, often called the Normal distribution. The distribution provides a parameterized mathematical function that can be used to calculate the probability for any individual observation from the sample space. This distribution describes the grouping or the density […]

## A Gentle Introduction to Data Visualization Methods in Python

Sometimes data does not make sense until you can look at in a visual form, such as with charts and plots. Being able to quickly visualize your data samples for yourself and others is an important skill both in applied statistics and in applied machine learning. In this tutorial, you will discover the five types […]

## A Gentle Introduction to Estimation Statistics for Machine Learning

Statistical hypothesis tests can be used to indicate whether the difference between two samples is due to random chance, but cannot comment on the size of the difference. A group of methods referred to as “new statistics” are seeing increased use instead of or in addition to p-values in order to quantify the magnitude of […]

## A Gentle Introduction to Statistical Tolerance Intervals in Machine Learning

It can be useful to have an upper and lower limit on data. These bounds can be used to help identify anomalies and set expectations for what to expect. A bound on observations from a population is called a tolerance interval. A tolerance interval comes from the field of estimation statistics. A tolerance interval is […]

## Prediction Intervals for Machine Learning

A prediction from a machine learning perspective is a single point that hides the uncertainty of that prediction. Prediction intervals provide a way to quantify and communicate the uncertainty in a prediction. They are different from confidence intervals that instead seek to quantify the uncertainty in a population parameter such as a mean or standard […]

## Confidence Intervals for Machine Learning

Much of machine learning involves estimating the performance of a machine learning algorithm on unseen data. Confidence intervals are a way of quantifying the uncertainty of an estimate. They can be used to add a bounds or likelihood on a population parameter, such as a mean, estimated from a sample of independent observations from the […]