Student's t-test
Student's t-test
The Student's t-test is a statistical hypothesis test used to determine if there is a significant difference between the means of two groups. It is commonly used when the sample sizes are small, and the population standard deviations are unknown. The test was developed by William Sealy Gosset, who published under the pseudonym "Student."
Types of t-tests
There are several types of t-tests, each suited for different experimental designs and data structures:
- One-sample t-test: This test compares the mean of a single sample to a known value or population mean.
- Independent two-sample t-test: This test compares the means of two independent groups to determine if they are significantly different from each other.
- Paired sample t-test: This test compares the means of two related groups, such as measurements taken before and after a treatment on the same subjects.
Assumptions
The Student's t-test relies on several assumptions:
- The data are continuous.
- The data follow a normal distribution.
- The variances of the populations are equal (for the independent two-sample t-test).
- The samples are independent (for the independent two-sample t-test).
Calculation
The t-test statistic is calculated using the formula:
\[ t = \frac{\bar{X}_1 - \bar{X}_2}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}} \]
where:
- \(\bar{X}_1\) and \(\bar{X}_2\) are the sample means,
- \(s_1^2\) and \(s_2^2\) are the sample variances,
- \(n_1\) and \(n_2\) are the sample sizes.
The calculated t-value is then compared to the critical value from the t-distribution table, based on the desired level of significance (e.g., 0.05) and the degrees of freedom.
Applications
The Student's t-test is widely used in various fields, including:
- Medicine: To compare the effectiveness of treatments.
- Psychology: To test hypotheses about behavioral data.
- Education: To compare test scores between different teaching methods.
- Business: To compare the performance of different strategies or products.
History
The test was introduced by William Sealy Gosset in 1908 while he was working at the Guinness Brewery in Dublin. Due to the company's policy on publishing research, Gosset used the pseudonym "Student."
See also
- Analysis of variance
- Chi-squared test
- Hypothesis testing
- Normal distribution
- Statistical significance
References
External links
This article is a statistics-related stub. You can help WikiMD by expanding it!
Transform your life with W8MD's budget GLP-1 injections from $125.
W8MD offers a medical weight loss program to lose weight in Philadelphia. Our physician-supervised medical weight loss provides:
- Most insurances accepted or discounted self-pay rates. We will obtain insurance prior authorizations if needed.
- Generic GLP1 weight loss injections from $125 for the starting dose.
- Also offer prescription weight loss medications including Phentermine, Qsymia, Diethylpropion, Contrave etc.
NYC weight loss doctor appointments
Start your NYC weight loss journey today at our NYC medical weight loss and Philadelphia medical weight loss clinics.
- Call 718-946-5500 to lose weight in NYC or for medical weight loss in Philadelphia 215-676-2334.
- Tags:NYC medical weight loss, Philadelphia lose weight Zepbound NYC, Budget GLP1 weight loss injections, Wegovy Philadelphia, Wegovy NYC, Philadelphia medical weight loss, Brookly weight loss and Wegovy NYC
WikiMD's Wellness Encyclopedia |
Let Food Be Thy Medicine Medicine Thy Food - Hippocrates |
Medical Disclaimer: WikiMD is not a substitute for professional medical advice. The information on WikiMD is provided as an information resource only, may be incorrect, outdated or misleading, and is not to be used or relied on for any diagnostic or treatment purposes. Please consult your health care provider before making any healthcare decisions or for guidance about a specific medical condition. WikiMD expressly disclaims responsibility, and shall have no liability, for any damages, loss, injury, or liability whatsoever suffered as a result of your reliance on the information contained in this site. By visiting this site you agree to the foregoing terms and conditions, which may from time to time be changed or supplemented by WikiMD. If you do not agree to the foregoing terms and conditions, you should not enter or use this site. See full disclaimer.
Credits:Most images are courtesy of Wikimedia commons, and templates, categories Wikipedia, licensed under CC BY SA or similar.
Contributors: Prab R. Tumpati, MD