Hotelling's T-square - explained with a simple example

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In this video, we will discuss the Hotelling's T-square test. We will start by comparing it to ANOVA, MANOVA and the t-test. Then (03:15) we will see how we can calculate the test statistic, F-ratio and p-value based on a simple example. I recommend that you first watch the video about the Euclidean distance and Mahalanobis distance because the Hotelling's T-square test statistic involves the calculation of the Mahalanobis distance.

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3 окт 2024

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Комментарии : 35

Год назад

This whole playlist is excellent, thank You very much for creating these videos!

@catherinewanjiru2402 3 года назад

You literally simplified my 3 hours lecture thanks

@tilestats 3 года назад

Thank you!

@CalzOmon 4 месяца назад

Amazing! Thanks so much

@Japan-explore Год назад

You made my day Thank you so much

@guidenote771 3 года назад

Great Lecture! Thank you very much!

@tilestats 3 года назад

Thank you!

@silviatalaveramarcos4754 3 года назад

Thank you for your videos, they are very clear

@tilestats 3 года назад

Thank you!

@alexandrelemos4990 2 года назад

Thank you very much for this video, very good!

@tilestats 2 года назад

Thank you!

@陳宏丞-c8v 2 года назад

Thank you! so appreciate your sharing!

@tilestats 2 года назад

Thank you!

@reitertamas11 2 года назад

Thank you! Does it make sense to have hundreds of samples in one group and only one sample in the other group so new observations or samples can be monitored over time (outlier detection). Let us say if we assume the first sample group as baseline.thx

@sophielerouge8835 2 года назад

Thank you, sir. I would apply this method to my data. The problem is that the number of samples is unequal.I use the formula: np.dot(n1-1,cov_0)+np.dot(n2-1,cov_1))/n1+n2-2. and there is a problem with broadcasting. Is there any alternative, please? Thank you.

@paulinaramirezwulff2736 Год назад

Thank you so much for this video. Is it possible to conduct the Hotelling t2 test if the data is from the same sample? every person filled out the same tests at two different days (within-subjects).

@tilestats Год назад

Yes, you can also use the test on paired data.

@paulinaramirezwulff2736 Год назад

@@tilestats thanks for your fast reply. Im cunfised tho on how to do it in SPSS, where do I choose the option?

@tilestats Год назад

Maybe this can help you statistics.laerd.com/spss-tutorials/one-way-repeated-measures-manova-using-spss-statistics.php

@borjacanobarredo3451 3 года назад

Hello, Is it possible to apply T2 hotteling for only one variable? Like in this example only for tumor size? I know its not the purpose of T2 H to be used for an univariate case. But could have sense to compare two treatments in a time series so its not affected by inflated error due to multiple testing like t-test.

@tilestats 3 года назад

Hi If you have only one DV it is simply just an ANOVA. Since you have two factors (treatment and time) you can use a two-way ANOVA or regression. If time is based on repeated measurements, use a mixed two-way ANOVA or linear/non-linear mixed-effect regression model.

@borjacanobarredo3451 3 года назад

@@tilestats Thanks! We think about doing RM ANOVA for this. But also need a pairwise comparison between each group and a control and t-test would have a lot of error for a time series like this.

@tilestats 3 года назад

@@borjacanobarredo3451 Yes, a mixed 2-way ANOVA can then be used, which is a mixture of RM ANOVA (for time) and a one-way ANOVA (for treatment). If you are going to compare for each time point, I would recommend a post-hoc test like Holm's test.

@borjacanobarredo3451 3 года назад

@@tilestats thanks again. Do you know a tutorial about how 2way mixed ANOVA works?. Its very hard to find information. There are a lot of info and videos about how to perform the tests using different software like excel, spss, graphpad, etc but not about how it works inside. Thanks!

@tilestats 3 года назад

@@borjacanobarredo3451 It is on my to-do list to make a video about 2-way ANOVA. If you contact me through the form at my home page (see above) I can send you some material that I use in one of my courses.

@joycelaw7182 2 года назад

Please help me !! How to calculate the cov of virus? How do the four numbers (188, -21, -21, 4) come from ?

@tilestats 2 года назад

Calculate the covariance matrix based on the CRP and Temp for only the virus group. If you like to know how to calculate a covariance matrix, I have a video on that at: www.tilestats.com

@chenp6_1117 4 месяца назад

I had the same question just then. And I found that it might mean [cov(crp,crp) cov(crp,temp) cov(crp,temp) cov(temp,temp)]

@sherlocksilver9392 3 года назад

Nice video! I take you could have many dependent variables in this test, not just two? e.g. CRP + body temp + weight

@tilestats 3 года назад

Yes, that is correct.

@toniiicarbonelll287 3 года назад

You're god

@tilestats 3 года назад

Thank you!

@younique9710 2 месяца назад

Thank you for the good video! One question I have is, how to draw the ellipse shown in 2:40? As far as I know, we usually use 95% of a confidence ellipse (p = 0.05). Is it obtained by the value of the Hotelling's T-square test statistic? or F-statistic?

@tilestats 2 месяца назад

It can be based on the T2 value in combination with the eigenvalues and eigenvectors of the covariance matrix, similar to how an ellipse is drawn based on the Mahalanobis distance. ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-xXhLvheEF7o.html

@younique9710 2 месяца назад

@@tilestats Thank you for your answer!