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

[@petemurphy7164]

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...

[@BrandonFoltz]

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

[@somiaafzal6807]

Great work. Can you please add some videos about chi sequare

[@jdsterne]

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!!!

[@muniu911]

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

[@guthrie_the_wizard]

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

[@jessamhan]

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

[@gsaint78]

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

[@SK-rj1ti]

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).

[@alis5893]

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

[@kansineesanguanwong6546]

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

[@avinoamporat4763]

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

[@pampamy]

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! :=)

[@gregorydashnaw2522]

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.

[@BrandonFoltz]

Thank you Gregory! It is a pleasure to help such wonderful students in Denmark. You have no idea how bad I want to visit Copenhagen before I die! The best way to thank me is to "pay it forward" and teach someone something new each day. All the best to you, your classmates, and everyone at the University of Århus! Best, B.

[@gregorydashnaw2522]

Just come in the summer months since it is otherwise very cold and rainy most of the time.

[@jaffsoran]

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

[@davidxu646]

always struggled with anova until today, thank you brandon

[@malvis8737]

I really enjoy your explanations.. thank you

[@vuphamtuanpro]

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

[@acharapornseeherunwong7728]

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

[@LonglongFeng]

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

[@abubakarsaddiqumar9854]

HELPFULLY AND EASY TO UNDERSTAND

[@abubakarsaddiqumar9854]

HELPFUL AND EASY TO UNDERSTAND.

[@grahamfulton1566]

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!

[@karannchew2534]

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

[@arsu90011]

A billion thanks! This was very helpful.

[@ebaihans2024]

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

[@BrandonFoltz]

Ebai Hans You are so very welcome. Glad you find it helpful!

[@eshitab9667]

Hi! Thanks for the amazing video. In your plant food research example, if I want to test whether there is a significant difference for each plant, can I do a repeated measures ANOVA separately for each plant on the data from 75 days (i.e 75 data points in each conditions)?

[@wendyxie3632]

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!

[@gauravpadalia7983]

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.

[@vakkalamanohar]

Gaurav Padalia, if significance level is lower than .05 (alpha), we reject the null hypothesis Or If F-stat greater than F-critical, we reject null hypothesis The only thing, I curious is how the significant level is calculated (in output table)

[@rrmm122]

The significance level is the p-value corresponding to the F-stat and can be computed in excel as F.DIST.RT(F-stat,2,21)

[@orlandowan5847]

We FAIL TO REJECT the Null Hypothesis when P of the tail (here called Fsig) >= the alpha of 0.05. This is indeed the case where 0.331 > 0.05.

[@sharonchetia54]

P values are the cumulative AREA enclosed by the F values. Now in case of chi,f and t distributions, the cumulative area is calculated from right to left unlike in Z distributions. This gives rise to all this confusion. Anything to the right of the F critical is the rejection area. Now if F statistic> F critical it means it falls in rejection area. But at the same time since area is calculated from the right, F critical will actually end up having more AREA enclosed than F statistic. Thus P statisticF critical. Excel takes this into account. In r by default it always calculates from left to right, so you have to make necessary changes to give the same results as given by excel...This was quite long but hope it was helpful

[@neo-qn1vs]

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

[@dhavaldwivedi]

Excellent lecture. helped immensely

[@adityasangore5323]

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

[@orlandowan5847]

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.

[@nasrmhm]

Brilliant Brandon !!

[@polytheneprentiss1534]

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.

[@davidxu646]

the best stat class of all

[@saraths9044]

Thank you Sir.

[@dr.naimrashid4284]

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

[@himanshuthakur7742]

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

[@edoardoalimandi110]

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

[@sherefgawish9621]

very good work...

[@SinatSumAgri-tech]

Absolutely satisfied

[@barwaryb465]

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

[@luoruicd86]

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

[@empaulstube6947]

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?

[@john.dry.]

Awesome!

[@paulofreitas1600]

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).

[@cococnk388]

Hello, did you finally answer your question...what was it?

[@mustafa6455]

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

[@musicofmaja]

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.

[@riaddarawish9563]

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,

[@ΜιχαελαπΜπαλκουδη]

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?

[@YesHerself]

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

[@sonalux]

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?

[@cococnk388]

Same question ? ....I understand the concept.... but if the observations are not even between the columns which type of ANOVA do I use?

[@jeedthirlwall5070]

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!

[@cococnk388]

What did you finally do? For me I think you have to the same for the control group have the same blocks as that of the treatment group I will be glad to know what you finally did.

[@dineshv8761]

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 ?

[@jonathansantos9330]

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

[@ayatakshee9276]

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

[@matsholstaandahl4615]

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

[@gauravpadalia7983]

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.

[@inkyukang2358]

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.

[@ZaraOver]

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

[@bckeeney1]

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?

[@riyadhalkhafaji202]

Great, thank you so much.

[@foadsf]

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.

[@riaddarawish9563]

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

[@jacobgebhardt3401]

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

[@shsh-ip3xd]

+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...

[@BrandonFoltz]

Hello! Good question and a common one. Evaluating an interaction requires more than one observation per cell. - Brandon

[@cactikaty]

very helpful thank you

[@sosweet12345678]

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

[@napier995]

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...

[@BrandonFoltz]

HI Gary! I agree the terminology can be confusing. What you are referring to is a Repeated Measures ANOVA which is different than a 2-way with Replication. The difference is in their dependence. In a 2-way with replication there is more than one measurement per cell and each set of measurements are independent (random sample). In a repeated measures ANOVA, the measurements are dependent (often times they are the same person or thing) and look for individual differences over time or under different conditions. Hope that helps!

[@napier995]

***** Ah... The old terminology trips me up again... Cheers mate, and keep up the good work. Your videos are quality.

[@BrandonFoltz]

Another way to think about it is this. There is 2-way with Replication and 2-way without replication. Under 2-way without replication there are two types: Randomized Block and Repeated Measures. In Repeated measures, we ignore the subject main effect because each person serves as his/her own control.

[@Zh9254]

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

[@TheAl1221]

LOVE IT!

[@anuragchoubey]

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??

[@srinu88]

@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.

[@woodchuk1]

Srinivas Godavarthi What "with replication" means in this context is that there is more than one data point for each combination of the two factors of interest.

[@mmax7770]

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

[@kinjalvora3352]

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?

[@LonglongFeng]

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

[@musliminontong2611]

what if there is no interaction all of them?

[@usersandu]

Thank you!

[@countrysideview]

Thanks

[@extramiles3831]

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

[@BrandonFoltz]

+VIVEK SINGH In a proof sense that would seem to be correct but I cannot say for sure. In practice though it will rarely occur that an interaction SS is completely zero.

[@extramiles3831]

thanks for the fast reply:)

[@shivanidikshit1932]

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.

[@BrandonFoltz]

shivani dikshit Hello! Are there multiple measurements (scale of 1 to 4) for each bank / factor combination or just one measurement? Either way really, this would have to be done via computer (Minitab, SPSS,, etc). Doing it by hand is just not feasible for many reasons.

[@malenaramirez5333]

❤️‍🔥❤️‍🔥

[@ThePhilipp96]

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

[@Bennett_Mcfresh]

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

[@dafni5674]

17:00

[@shanuagrawal8197]

Thanks.. :-)