This article describes the paired t-test formula, which is used to compare the means of two related groups or samples. The paired t-test formula is also referred as:
- dependent t test formula,
- paired sample t test formula,
- paired samples t test formula,
- formula for paired t test,
- paired t test equation and
- dependent t test equation
The procedure of the paired t-test analysis is as follow:
- Calculate the difference (\(d\)) between each pair of value
- Compute the mean (\(m\)) and the standard deviation (\(s\)) of \(d\)
- Compare the average difference to 0. If there is any significant difference between the two pairs of samples, then the mean of d (\(m\)) is expected to be far from 0.
Contents:
Related Book
Practical Statistics in R II - Comparing Groups: Numerical VariablesFormula
The paired t-test statistics value can be calculated using the following formula:
\[
t = \frac{m}{s/\sqrt{n}}
\]
where,
mis the mean differencesnis the sample size (i.e., size of d).sis the standard deviation of d
We can compute the p-value corresponding to the absolute value of the t-test statistics (|t|) for the degrees of freedom (df): \(df = n - 1\).
If the p-value is inferior or equal to 0.05, we can conclude that the difference between the two paired samples are significantly different.
Recommended for you
This section contains best data science and self-development resources to help you on your path.
Coursera - Online Courses and Specialization
Data science
- Course: Machine Learning: Master the Fundamentals by Stanford
- Specialization: Data Science by Johns Hopkins University
- Specialization: Python for Everybody by University of Michigan
- Courses: Build Skills for a Top Job in any Industry by Coursera
- Specialization: Master Machine Learning Fundamentals by University of Washington
- Specialization: Statistics with R by Duke University
- Specialization: Software Development in R by Johns Hopkins University
- Specialization: Genomic Data Science by Johns Hopkins University
Popular Courses Launched in 2020
- Google IT Automation with Python by Google
- AI for Medicine by deeplearning.ai
- Epidemiology in Public Health Practice by Johns Hopkins University
- AWS Fundamentals by Amazon Web Services
Trending Courses
- The Science of Well-Being by Yale University
- Google IT Support Professional by Google
- Python for Everybody by University of Michigan
- IBM Data Science Professional Certificate by IBM
- Business Foundations by University of Pennsylvania
- Introduction to Psychology by Yale University
- Excel Skills for Business by Macquarie University
- Psychological First Aid by Johns Hopkins University
- Graphic Design by Cal Arts
Amazon FBA
Amazing Selling Machine
Books - Data Science
Our Books
- Practical Guide to Cluster Analysis in R by A. Kassambara (Datanovia)
- Practical Guide To Principal Component Methods in R by A. Kassambara (Datanovia)
- Machine Learning Essentials: Practical Guide in R by A. Kassambara (Datanovia)
- R Graphics Essentials for Great Data Visualization by A. Kassambara (Datanovia)
- GGPlot2 Essentials for Great Data Visualization in R by A. Kassambara (Datanovia)
- Network Analysis and Visualization in R by A. Kassambara (Datanovia)
- Practical Statistics in R for Comparing Groups: Numerical Variables by A. Kassambara (Datanovia)
- Inter-Rater Reliability Essentials: Practical Guide in R by A. Kassambara (Datanovia)
Others
- R for Data Science: Import, Tidy, Transform, Visualize, and Model Data by Hadley Wickham & Garrett Grolemund
- Hands-On Machine Learning with Scikit-Learn, Keras, and TensorFlow: Concepts, Tools, and Techniques to Build Intelligent Systems by Aurelien Géron
- Practical Statistics for Data Scientists: 50 Essential Concepts by Peter Bruce & Andrew Bruce
- Hands-On Programming with R: Write Your Own Functions And Simulations by Garrett Grolemund & Hadley Wickham
- An Introduction to Statistical Learning: with Applications in R by Gareth James et al.
- Deep Learning with R by François Chollet & J.J. Allaire
- Deep Learning with Python by François Chollet
Version:
Français
No Comments