Statistics 101: Two-way ANOVA with Replication, Marginal Means Graphs 

Best Educational Statistics Videos in RU-vid. Hands down!!

I cannot express in words how valuable these videos have been to me and how grateful I am with you. Thank you very very much.

Dear Brandon, I would like to congratulate you for your outstanding work with these tutorial lectures. They are clear and surely will help who is interested in this wonderful and hard issue that is statistics. Please, keep on with your work! Here, in Brazil, it will be always appreciated!

Happy new year, Brandon. I wish you all the best. You've helped me a lot figuring out how statistics really works. Thank you!

Thanks for the great explanations of concepts and all of your examples! I'm refreshing (and building) some of these skills prior to starting a full time research program this fall and I already feel my confidence boosted because of what I've been able to learn from you! Thanks again for setting an example as a patient and kind teacher!

Thank you so much Mr Brandon, your hardwork uploading videos on biostatistics few years ago really do help us on understanding and applying it in our lives now!! 👍🏻👍🏻👍🏻👍🏻👍🏻 wish you all the best

thank you for such a great explanation. perfect to brush up or learn the basics. thank you again.

Thank you Brandon for very clear explanations. You are GREAT.

Thank you soo much for making these videos. I would've given up otherwise if it wasn't for you. I wish you a wonderful life and success in all of your endeavors !

You're a genius. This video is simply AMAZING!

you are a true teacher, very nice I like all your lectures

thank you Brandon for these tutorials! They have helped me immensely esp in preparation for my exams .I wish you a blessed Christmas and successful 2014!

Thank you very much and Happy new year Brandon!

Fantastic! Please continue your wonderful job. I'm waiting for more advanced topics like multiple regression and factor analysis. Great Job! THANKS.

Thank you very much. this video is very helpful.

Thank you very much for your lecture. I got many knowledge from you. :)

Thank you Brandon for this wonderful video

Thanks a lot for making these videos !

Thank you so much!

These videos are amazing!

I may have mentioned it before, but I'd love to see some videos on mixed methods (GLMMs). In the meantime thanks for what you have done it is making a difference to this autistic student of statistics.

Thank you Brandon...Anova is Crystal clear to me now ...great effort by you..can you please make video for Cluster Analysis

Great presentation

Hi, Brandon! First, I'm really appreciate these valuable and helpful videos. I have learned a lot about statistics through your videos. Thanks! These days I have tried to lean about anova and t-test. And I have met some questions when analyzing my sample data. I have tried to search for help on Internet, but I have not found answers yet. Maybe I don't know how to correctly describe my problems, and thus the search results are not perfect. So I want to search for help from you. Thanks for your time and help first! 1. I have learned to use one-way anova and two-way anova through the videos. And for two-way anova, the interactions between factors can be investigated. My sample data have five factors with five levels each (The data was obtained through Orthogonal experiment), and I have used two-way anova to analyze my data. The analysis results indicated that the interactions between factors are significant. As you have said, I cannot tell whether these factors are significant when the interactions between factors are significant. However, the one-way anova can avoid (or escape) this phenomenon because there is only one factor. And I really want to know whether these factors are significant. So I have tried to use one-way anova to analyze these data(5 times for these 5 factors). But I don't know that can I use one-way anova method to analyze the problems with two or more factors. 2. My data have 5 factors and each factor has 5 levels, and there is only one result. Through the one-sample t-test, I have tried to obtain the 95% confidence intervals for each factor level. And I have plotted the change of confidence intervals with the factor level. The reason that I calculated these confidence intervals is that I want to know the result intervals when one factor remains at one level. However, I don't know that can I apply one-sample t-test to these data. Because when one factor remains at the same level, the sample results are also influenced by other factors. It seems not to be a general one-sample t-test problem. And because I am short of the theory of statistics, I don't know whether I have correctly used these analysis method. At present, I have used one-way anova to solve a two-way anova problems in order to escape the interaction phenomenon. And I have used one-sample t-test to a "special" data. There are other 4 factors influencing the sample results in this one-sample. It seems that I can control the analysis result because I can change the other 4 factors. These are the problems I have met and cannot figure it out. Sorry about my shortage about statistics. And I hope you can help me! Thanks again for your time and help! Appreciate! Shusen Guo

Hello brandon...!! Is there a video to understand post hoc tukey hsd test..!?

thank u sooooo much

Thank you so much Brandon, can you make a video on constrained optimisation and exponential function, please

Hi Brandon. I conclude I can comment on the treatments that are involved in the interaction if I limit this to a comparison of variability between columns and rows. But is it OK to cite the the p-values and test statistic when doing so? I presume it is.

Brandon, Can't thank you enough for the videos. It has been a long time since college stats class. Have you or would you provide a table of contents, etc. to watch the videos in a logical learning progression? Thanks again

Hello Brandon, Thanks a lot for the video. I am a big fan of you teaching. It is helping me a lot. I have doubt and need your help. At 20:25 in the video "Two-way ANOVA with Replication (Part 2B), Marginal Means Graphs"...for the interaction we have a F value of 3.315 and Sig value of 0.16. So you said that the Interaction is significant. How did you conclude that the Interaction is significant? I want to know the logic. Thank again...from India :)

Wow, wonderful class! Brandon. After this video, I just did marginal means graph at all the exercises in my stats book, and I found some cases (GMAT famous exercise) where there are crossing lines, but no significant interaction. Can we still evaluate factors or column and row effects? Best regards from Mexico, sincerely Humberto.

Dear Mr. Foltz, I am more than grateful and thankful for what you have done in the past years; your videos are undoubtedly the best contents I have ever found about statistics. BTW, I have 2 questions; 1st; If we had significant interaction in a Two-way ANOVA with Replication, can we remove its effect by ANCOVA? and second, in such a case, can we still compare two cells with each other, using t or LSD? Thanks a lot In advance and best wishes

Thank you for the wonderful videos! I have one question if you can answer that....:) What is the advantage of replication in 2 Factor experiment? Does it increase the precision of the results....and if that iss the only advantage? Looking forward to your reply

Dear Brandon, do you have some videos on Correlation analysis?

Thank you Brandon, any chance you could do some video's using Jamovi?

How do I see the Marginal Medias crossing if I have different types of units in the vertical axis? I have 4 conditions (columns) and 14 participants of an experiment where they were measured, performance, heart rate, pupil size, and electroencephalogram during each of the conditions. Is the 2 way anova the best way to analyse this data? I Z-scored all of the independent medias of each case and Log10, but everything becomes 1 (as it should be) so I am stucked.

Brandon Foltz wrote: +Carlos Chaveznava ANOVA is a test about whether or not there are differences among groups for the same hypothesized population. Therefore all the data in ANOVA must be of the same characteristic measurement. The columns cannot be different measurements. What exactly is your research question / idea?

Hi Brandon, at 20:43 sig is 0.16 which is greater than 0.05 alpha. So why is it significant?

I really wish you were my professor...

Confused. ANOVA is to evaluate whether the factors (eg. plant types, number of feeding) are significant. 26:49 If interaction exists between the factors, then ANOVA analysis cannot be used. Then what? Does it mean the significance exist but not quantifiable? What alternative methods can be used?