The Student’s t Distribution and the corresponding t-tests play an important role in hypothesis testing of the mean. We review the key properties of the t distribution and how to perform the various t-tests in Excel, along with how to handle situations where some of the sample data is missing.
Topics
- Basic Concepts
- One sample t-test
- Two independent samples t-test
- Paired sample t-test
- Problems with the data (when t-test assumptions are not met)
- Noncentral t Distribution
- Statistical Power
- Sample Size Requirements
- Confidence Intervals for Effect Size and Power
- Sample Size for t-test based on the Confidence Interval
- Studentized Range Distribution
- Non-standardized t Distribution
- Cauchy Distribution
- Confidence Interval for Coefficient of Variation
- Testing the Coefficient of Variation
- Identifying Outliers using t Distribution (Grubbs’ Test)
- Equivalence Testing (TOST)
Reference
Howell, D. C. (2010) Statistical methods for psychology (7th ed.). Wadsworth, Cengage Learning.
https://labs.la.utexas.edu/gilden/files/2016/05/Statistics-Text.pdf
Zar. J. H. (2010) Biostatistical analysis 5th Ed. Pearson
https://bayesmath.com/wp-content/uploads/2021/05/Jerrold-H.-Zar-Biostatistical-Analysis-5th-Edition-Prentice-Hall-2009.pdf
Dear Dr, welcome a greeting.
Dr I apologize, I was looking at the significance wrong, I beg your pardon
Thank you very much
Dear Dr, welcome a greeting.
Dr. I think he has an error with the estimation of the value of the student’s T since a manual test of the data:
X: 600 650 530 800 750 700 750
Y: 500 450 800 650 500 500 450 400
They do not show significant difference and using Real Statistics, reports that if there is.
Could you please check it?
Thank you very much
Sir, i need guidance for conducting t test for the following situation. please guide me.
I want to use t test for my work. three different samples are taken to compare.
question 1: do I work on the raw data or standardize them before t- test?
question 2: is this test only for non-parametric?
With 3 samples you would need to conduct multiple t tests. This increases experimentwise error.
Q1. generally it is sufficient to work with the raw data.
Q2. the test is a parametric test.
Charles
thank you!
I have understood that I have to rather do ANOVA.
plz tell me about the history test statistic distribution of t test and also the derivation and all the things which are included in topic i will be very thank full to you.
Sorry Anum, but I don’t have the time to explain the history of the t distribution. I have included some proofs, but again I have other priorities and don’t have time to provide the proofs of all the properties of the t tdistribution.
Charles
I have an unanswered question from nearly 15 years ago regarding student-T distribution for sample population vs. Normal distribution for population. My concern is the “double” bias since we already correct for variance of population with the Sq Rt of the variance being divided (n-1). This compares to Normal distribution whereby the Sq T of the variance is divided by n. MY confusion, therefore, is I thought that already makes the distribution confidence interval correction for smaller population. Why then would we double penalize with the T-distribution
Sorry, but I don’t see where there is a double penalty. If changing n to n-1 is one penalty, what is the other? The mathematical theory explains why you divide by n-1 instead of n.
Charles
hi sir do your have power point presentations for these different topics?
Sorry, but I don’t have a Powerpoint presentation for each topic. I expect to publish a book which includes this subject.
Charles
thank you mr charles. hopefully we can have a copy of your book. its very useful on my part.
I hope to release the book later this month.
Charles
Charles, thank you for the very useful statistics toolbox. I am hoping that you can help me solve a problem I have when running the ttest and non-parametric equivalents option. When I click that option from the menu I get a “run-time error 424”. I am using the add-in on MS Excel for Mac 2011 (Version 14.3.2). Any suggestions are much appreciated. Thank you. -Kathleen
Kathleen,
Unfortunately I don’t have a Mac and so I need to borrow someone elese’s Mac to investigate these sort of issues. I plan to do so next week, at which time I will try to understand what is causing this problem. I will also get the Mac version of the software up to the current release level. Stay tuned.
Charles
Dear Charles:
There´s still an unfixed bug in Real Statistics 2.14.1 (I downloaded it on June 3th):
When I use t Test, the add-in uses TDIST Excel formula (compatible for Excel 2007 version) for obtaining the p-value in the case of equal variances, and TTEST Excel formula (compatible for Excel 2007 version) for obtaining the p-value in the case of unequal variances. That difference produces a mistake in the p-value calculation for the case of unequal variances: the correct formula must be TDIST.
I recognize that error when using the Data Analysis Add in of Excel 2010 (t-Test: Two Sample Assuming Equal Variances; and t-Test: Two Sample Assuming Unequal Variances) and Minitab, to prove if the results are the same.
I hope this comment will be useful.
regards.
William Agurto.
Dear Charles:
I forgot to mention that the error presented when using the t-Test in Real Statistics 2.14.1 occurs with the option: T Test: Two Independent Samples, and when the results are showed in a new worksheet. In that case, the table showing the T Test results for Unequal Variances in Real Statistics 2.14.1 uses the TTEST Excel formula to calculate the p-values, but with a wrong reference: arrays used by TTEST formula must be in the original worksheet (where is all the source data), not in the new worksheet that is showing the results. That’s the origin of the problem. Because of that, is better to use TDIST formula to calculate p-values (that formula doesn’t depend on arrays located in other sheets), or to correct the array source in the TTEST formula.
Regards.
William Agurto.
Dear William,
Thanks again for finding this error. I will include a correction in the next release of the software (2.15), which should be ready in the next few days.
I decided to use the TTEST function instead of TDIST since it doesn’t round off the degrees of freedom to the nearest integer.
Charles