Statistics By Jim

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Median Absolute Deviation: Definition, Finding & Formula

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What is the Median Absolute Deviation?

The median absolute deviation is a measure of variability that indicates the typical distance between observations and the median. Unlike the mean absolute deviation, which uses the average, this method centers on the median, making it more resistant to outliers. The result uses the same units as the data, which helps with interpretation. Larger values signify that the data points spread further from the median, while lower values mean they cluster more tightly around it. Statisticians frequently abbreviate it as MAD, but sometimes use MADM to avoid confusion with the mean absolute deviation. [Read more…] about Median Absolute Deviation: Definition, Finding & Formula

Weighted Least Squares (WLS) Explained

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What is Weighted Least Squares (WLS)?

Weighted least squares (WLS) is a type of linear regression that assigns different weights to each data point when fitting the model. Instead of minimizing the simple residual sum of squares as ordinary least squares (OLS) does, WLS minimizes the weighted (wi) sum of squared residuals as the summation symbol below indicates:

Weighted least squares formula for minimizing the sum of the weighted residuals.

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Marginal Probability: Definition, Formula & Examples

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What Is Marginal Probability?

Marginal probability is the chance that an event will happen without considering other variables. Statisticians write this as p(A), denoting the probability of event A. You can think of it as an unconditional probability. It tells you how likely something will happen on its own, independently of other variables. [Read more…] about Marginal Probability: Definition, Formula & Examples

Covariance vs Correlation: Understanding the Differences

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Covariance vs correlation both evaluate the linear relationship between two continuous variables. While this description makes them sound similar, there are stark differences in how to interpret them.

Although these statistics are closely related, they are distinct concepts. How are they different?

In this post, learn about the differences between covariance vs correlation and what you can learn from each. [Read more…] about Covariance vs Correlation: Understanding the Differences

One Sample T Test: Definition, Using & Example

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What is a One Sample T Test?

Use a one sample t test to evaluate a population mean using a single sample. Usually, you conduct this hypothesis test to determine whether a population mean differs from a hypothesized value you specify. The hypothesized value can be theoretically important in the study area, a reference value, or a target. [Read more…] about One Sample T Test: Definition, Using & Example

T Test Overview: How to Use & Examples

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What is a T Test?

A t test is a statistical hypothesis test that assesses sample means to draw conclusions about population means. Frequently, analysts use a t test to determine whether the population means for two groups are different. For example, it can determine whether the difference between the treatment and control group means is statistically significant. [Read more…] about T Test Overview: How to Use & Examples

Kruskal Wallis Test Explained

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What is the Kruskal Wallis Test?

The Kruskal Wallis test is a nonparametric hypothesis test that compares three or more independent groups. Statisticians also refer to it as one-way ANOVA on ranks. This analysis extends the Mann Whitney U nonparametric test that can compare only two groups. [Read more…] about Kruskal Wallis Test Explained

Mann Whitney U Test Explained

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What is the Mann Whitney U Test?

The Mann Whitney U test is a nonparametric hypothesis test that compares two independent groups. Statisticians also refer to it as the Wilcoxon rank sum test. The Kruskal Wallis test extends this analysis so that can compare more than two groups. [Read more…] about Mann Whitney U Test Explained

Box Plot Explained with Examples

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What is a Box Plot?

A box plot, sometimes called a box and whisker plot, provides a snapshot of your continuous variable’s distribution. They particularly excel at comparing the distributions of groups within your dataset. A box plot displays a ton of information in a simplified format. Analysts frequently use them during exploratory data analysis because they display your dataset’s central tendency, skewness, and spread, as well as highlighting outliers. [Read more…] about Box Plot Explained with Examples

Joint Probability: Definition, Formula & Examples

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What is Joint Probability?

Joint probability is the likelihood that two or more events will coincide. Knowing how to calculate them allows you to solve problems such as the following. What is the probability of:

  • Getting two heads in two coin tosses?
  • Consecutively drawing two aces from a deck of cards?
  • The next customer being a woman who buys a Mac computer?
  • A bike rental customer getting both a flat front tire and a flat rear tire?

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Principal Component Analysis Guide & Example

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What is Principal Component Analysis?

Principal Component Analysis (PCA) takes a large data set with many variables per observation and reduces them to a smaller set of summary indices. These indices retain most of the information in the original set of variables. Analysts refer to these new values as principal components. [Read more…] about Principal Component Analysis Guide & Example

Fisher’s Exact Test: Using & Interpreting

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Fisher’s exact test determines whether a statistically significant association exists between two categorical variables. You can also use it for a 2-sample proportion test when you have a small sample size.

For example, does a relationship exist between gender (Male/Female) and voting Yes or No on a referendum? [Read more…] about Fisher’s Exact Test: Using & Interpreting

Paired T Test: Definition & When to Use It

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What is a Paired T Test?

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

Independent Samples T Test: Definition, Using & Interpreting

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What is an Independent Samples T Test?

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

Mean Absolute Deviation: Definition, Finding & Formula

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What is the Mean Absolute Deviation?

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 Plot: Making, Reading & Examples

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What is a Stem and Leaf Plot?

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

Pareto Chart: Making, Reading & Examples

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What is a Pareto Chart?

A Pareto chart is a specialized bar chart that displays categories in descending order and a line chart representing the cumulative amount. The chart effectively communicates the categories that contribute the most to the total. Frequently, quality analysts use Pareto charts to identify the most common types of defects or other problems.

Learn how to use and read Pareto charts and understand the Pareto principle and the 80/20 rule that are behind it. I’ll also show you how to create them using Excel. [Read more…] about Pareto Chart: Making, Reading & Examples