MANOVA - explained with a simple example 

May I ask if the example data is bivariate?

Thank you! You can run an ANOVA after a significant MANOVA, and then use some method for multiple comparison, as I have several videos on.

Thank you!

This is a one-way MANOVA because we only have one factor, the type of infection. Suppose that we would also include sex as an independent variable, then we will have a two-way MANOVA because we will then have two factors.

The F-stat requires a lot of calculations and is different for the four different statistics. That is why I did not include it in the video. I would recommend this page for calculating the F-stat by hand: ncss-wpengine.netdna-ssl.com/wp-content/themes/ncss/pdf/Procedures/NCSS/Multivariate_Analysis_of_Variance-MANOVA.pdf Also, if you have only two groups, you can instead use the Hotelling's T-square test, which has simpler math, explained in this video: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-RmktDvMrhGw.html

I do not have any material for that at the moment. I'm planning to do factorial ANOVA first. I hope to do this in the future.

@@tilestats sounds good! Love your channel by the way :)

Great!

That is calculated by the numerator in the equation for the covariance. Watch this video, starting at around 6 min, to see how this is calculated: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-2bcmklvrXTQ.html

@@tilestats thank you.

No, if you, for example, would have a third DV, you will instead get 3-by-3 matrices and thus 3 eigenvalues and 3 eigenvectors, and so forth.

The number of DV = number of eigenvalues. The number of groups does not effect how many eigenvalues we will compute. It seems like you have 3 DV -> 3 eigenvalues.

@@tilestats Awesome thanks! Here is another question for you :) Using the regress procedure, a researcher tests the interaction between a binary variable condition (0=control, 1=experimental) and a numeric variable, age. She enters condition using the indicator coding i. She enters age as centred around the mean. She finds that the simple slope of age in the control condition is 1.0, and the coefficient for the interaction is -.5 What will the simple slope of age be in the experimental condition?

I have a video on multiple linear regression with interaction (second example) that might help you: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-AP_K7SaKkIE.html

See my answer to one of the comments below for how to calculate the F-statistics. Once you have the F-statistics, you can use an F-distribution to compute the p-value.

I have no book for my examples. It is based on my own research.

​@@tilestatsoh okay, can I ask some of your references of research? MANOVA is my report in statistics and I am basing my explanation off of your explanation since you executed it easily and clearly

Thank you!

Yes, since the data set consists of two variables.

If you violate the assumptions of MANOVA (or have ordinal data), the rankMANOVA might be an alternative since it is a non-parametric test based on ranks.