Statistics 101: Two-way ANOVA with Replication, An Introduction 

What's so impressive about Brandon's videos is how slowly he works through the issues. What he spends 5 minutes talking about my university lecturers will go over in about 30 seconds. It really is a talent of Brandon to patiently teach this way. Thanks Brandon, this really helps me a lot...

Still the best video on two-way ANOVA w/o replication out there to this day (2024). I like it how you focus on just the "group" variable first. This way, it is much easier to understand that it is essentially a "paired" ONE-WAY ANOVA. Basically, an extension of the "paired" T-test to more than two groups, where the "blocking" variable can increase the power of the test (please correct me if I am wrong).

Brandon, you're a wizard brother. Thank you so much for such incredibly well explained, well visualized, and well prepared examples and lectures. You're getting me through Stats for business! Thank you thank you!!!

3:45 start, 7:55 two-factor model

You my hero. Thank you. You real scientist and teacher. I appreciate your work. Bless you

Absolutely FANTASTIC. The videos are GREAT. Best education video ever. Thank you so much for your efforts. God bless.

Couldn't thank you enough! You save my life since stat I and now stat II ❤️

Dear Brandon - Thanks so much for this 101 statistics series - so helpful and so easy to understand - keep doing this great job

Thank you so much for all you videos- I have read and read so many books but your explanations just make the penny drop!

Super happy to have found this channel. Thank you!!!

Thanks Brandon! you are excellent in teaching statistics. Your lesson, video and speech are very clarity

I really like your approach for your entire analysis of variance series.

Very helpful video and make me understand in detail about two way ANOVA. Thank you for sharing.

always struggled with anova until today, thank you brandon

A billion thanks! This was very helpful.

Hi brandon!! finally ive logged in to comment on your vids, because i loved them all!!!! I cant put into words how much you have saved my life, and I have used some of your vids to share with my students . Every year I learn more, is scary and challenging, but hey two years ago i came out of the blue. Is true what they say: if you torture the numbers they will confess to anything!. God Bless you, and if your not religious, doesnt matter, grateful to you for life! :=)

HELPFULLY AND EASY TO UNDERSTAND

HELPFUL AND EASY TO UNDERSTAND.

I really enjoy your explanations.. thank you

Excellent Brandon...!!:-) I wonder if those 9 who disliked can really elaborate....!!

I put all thumbs up onto your vids...........they are so great!!!!!!!! I wish I would see them years earlier!! OMG

Two Way = Two Factors = Two Categories. With Replication = Multiple samples per category = Each set of samples has its own mean

Thanks very much for this excellent video Brandon. It was really helpful..

Brilliant Brandon !!

Absolutely satisfied

Excellent lecture. helped immensely

Hi Wendy! This video was not in a playlist yet because I just uploaded it yesterday. :) It is now however. If you view my channel page by playlist, you will see that all videos are sorted by topic and then inside each topic by lesson. Let me know if you have any more questions! - B

Great, thank you so much.

I simply do not know what I would do without your help. Thank you very much! We are quite a few struggeling biochemistry students at the University of Århus here in Denmark that are relying heavily on your excellent video tutorials. You should be on the University payroll. You are a thousand times better at clearly illustrating statistical methods and their purposes. Thank you once again Mr. Foltz.

Awesome!

Thank you Sir.

LOVE IT!

Thank you!

very helpful thank you

very good work...

Your videos are a very good supplement to my learning :) Two questions: you mention variance, but you don’t really need variance in any of the calculations, correct? Also, could type CC food be considered an outlier? You can pretty much already tell from the difference in the means that there’s going to be an “interaction” & that you’re going to reject the null.

the best stat class of all

Thanks

Hello Brandon, My question is how the Sum of Squares is calculated for the Interaction (feedings vs plant food)? Also, I would like to verify whether significance value is the same as alpha and may you please explain how it is calculated ? Thank you,

Each cell has it's own mean and variance. [...it's... sic. its] Cheers. Just pointing it out for fun. I learn from your uploads!

Wonderful videos illustrating the concepts perfectly. I wonder if can ask for PPT slides.?

Questions for Brandon. I see that you don't have a video for Design of Experiment but I want to ask two questions related to this topic. (1.) Are each of the deltas analyzed as a 2 way ANOVA providing an Fo value for each factor (in the case of a two variable analysis the 3 factors A, B and interaction AB) in both the comparison of the averages Xbar as well as the standard deviations s) (2.) Is Multiple regression = ANOVA of the factors (as described above) inserted into the Taylor series approximation? The multiple regression is more accurate but the latter seems to be quite good and relatively easy to calculate.

hey brandon, how do we manually calculate interaction SS? thanks for the videos!

Thank you very much for your informative videos, can you add one for full factorial with blocking please?

I really want to congratulate with you .. Your videos are amazing!

Thanks for the great videos. it would be great if you could also make tutorials for FLOSS like Open/LibreOffice Calc. Not everyone has the luxury of having IBM's SPSS license.

Hello Brandon. Thank you for your video - are usefull. Are you thinking to do some videos also how to use statistical tests in R? Thank you for your answer.

Hi, thanks for the lecture. It always really helps me. BTW, you explain that SSB eats up SSE, but I've read in another paper that unlike regression, B does not serve as a control, which means C and B are independent and does not affect each other. Therefore, if interaction SS is not significant, two-way anova would be the same as multiple one-way anova. If this is true, is it correct to say that SSB eats up SSE? I'm so much confused now.

In general, if the P value is low (< 0.01) it is considered to be significant. But we do not want the Interaction terms to be significant right ? What does it say about our experiments and the data ? Should be rerun the experiments or find different factors ?

very informative..thank you!!can i download it for more studies about two-way anova?...

Hi Mr. Foltz, this video was really useful for me as I am finding my assignment very difficult. In my assignment though, there are different number of observations for each combination...like what if AA 1 feeding has 8 observations, but AA 2 feeding has 16 observations, BB 1 feeding has 10 observation....like that...can I use the sample mean for each to do the two-way anova?...If so, do I still use anova with replication?

Thanks.. :-)

My Question is regarding running the two-factor ANOVA. I have set up the labels and data exactly as you have shown in the video. I select input range with labels and data, 8 sample rows, and new worksheet, however when I try to run the program I get an message stating my input range contains non-numeric data. Do you have any advise regarding this message and how to fix the issue?

❤️‍🔥❤️‍🔥

During an experiment are the cotton foods randomly assigned to the plants just like the one in the 2 way ANOVA without replication design ?

when testing 8 plants, are we randomly picking up 8 plants after feeding in both 1st and 2nd feeding. Or the 8 plants are fixed over which we are testing our plant food.

How did you find the significance of the F value from the first example? Manually?

Hi,I am watching Statistics 101 two way anova marginal means graphs. You have suggested to look out for interaction effects in the spss output where you were mentioning on the significance level,I did not understand how to interpret the F and the significant value.Need your help

thanks a lottt. But you could have extended the video by interpreting other table values such as coefficients and R value and thier signficance

Hi! I hope you can help me. I'm trying to compare two types of sweeteners for antihyperglycemic ability. So my research has two independent variables: type of sweetener (2 types) and daily intake frequency (once, twice, and thrice a day), and one dependent variable. I also have a negative control. I'm kinda confused if I also have to apply the daily intake frequency with the control? Say, for each type of sweetener, 7 mice will be given the said sweetener once a day, another 7 will receive it twice a day, and another 7 given thrice a day. My question is, for the negative control group (which will only be given dH2O), is it okay if I just have 7 mice? Or do I also have to subdivide the control group into three subgroups each having 7 mice, such that subgroup 1: once a day, subgroup 2: twice a day, subgroup 3: thrice a day? Can you please give me advice on what to do with the negative control? Thank you so much in advance!

Brandon, you mentioned balanced design at the end of your video. What would be an unbalanced design? I've come across a scenario and I would like to know whether this scenario would fit into an unbalanced design. Scenario: A marketing advertisement conducted in a given month for 5 different markets (groups/columns) producing different number of responses measured by completed calls to a call-center, therefore one-way anova would be able to test for difference across the 5 different markets. But what if we have to find out whether viewer responses are significantly different on the weekends than weekdays? Would this characterize an unbalanced two-way anova with replication? Multiple groups (Markets), multiple blocks (weekday vs weekends), unbalanced (more responses for weekdays) with replication (multiple weekday and weekends responses in a given month).

how do you determine the number of replications that were used in a study? i need it for my final on Monday?

Hello ***** My question is how the Sum of Squares is calculated for the Interaction (feedings vs plant food)? Also, I would like to verify whether significance value is the same as alpha and may you please explain how it is calculated ? Thank you

Very nicely explained sir The output in this video seems to be of CRD what about RBD design two factor analysis with replication

+Brandon Foltz I was wondering if it is possible to do interaction test without any replicates ? that is using only one observation in each combination...

Great video. But is it possible to interpret the direction of the result for a 2-way ANOVA with replication?

at 6:45 you said that significance level is .331, but we are looking for significance level of .05 or lower, then how can you accept the null hypothesis if the significance level surpass the .05 level.

In the last vid the f value was lower than sig and we failed to reject the null hyp, here we have f value greater than sig and we still fail to reject the null hypo??

@Brandon, thank you very much for this great videos. I have a question, why is this called 'with replication'? Can you please clarify? Thanks in advance.

where can I get questions and answers about research like anova, t-test, chi square, because Im going to take licensure exam in physical therapy

The videos are great, but could you please rearrange the play list? Currently I have trouble sorting them, to follow up...Probably put different series...Thanks!

Can you explain how to calculate the sum of squares of the interaction? Like what is the exact formula?

Are the 8 plants or samples different for each cell? Do we pick up 8 different plants for each cell or are we testing the same 8 plants all over again?

excuse me, could you recommend me a book about Two-way ANOVA with Replication in order to study the mathematical model that coreesponds to this methodology?

Could please share a vedio on split/ split -split plot design?

Hi. I have a question. Wont you compare the results over time?

is there any way to buy your slides in this video? man

One important question. How can I address for writing a paper the result of it (df, y)=f, pvalue what is y?

can anyone tell me the difference between replication and repeated measures?

how do I calc ANOVA on 3 different group of banks (A,B and C) each rating 4 to 5 different factors on a scale of 1 to 4 (high to low) . with 1 group of banks having 14 responses other 15 and third 28.

in the first 1 minuet I heard the words I have waited 19 years to hear.

Hi, sorry, really basic question: This is with replication, so what is being measured for the second time? I thought replication meant taking a subject (plant) and measuring something (height), then performing the same measure on the same subject after a certain time. Surely in the example a plant can only grow once, so you can't repeat the measure on the exact same subject after treatment. I've come across a two-way ANOVA analysing memory training. Subjects are measured at the start, then they go away and perform various types of memory training, then those same subjects are measured again to test the effectiveness of the training types. The plant example does not seem analogous to this...

what if there is no interaction all of them?

17:00

I am sorry but I am already a bit confused on how this would practically look as a data table 3 categories of plant food..means three columns 8 types of plants - 8 rows. what about the 75 days? how does one factor that?

if it is given that two factors are independent, can we assume interaction SS is zero?

that wouldnt be a two-way anova with replication. its a normal two way anova since you don't have severeal messurement time points for the same entities (plants). Two-way anova messures effects within-subjects not between