ANOVA (Analysis of Variance) Analysis - FULLY EXPLAINED!!!

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  • Опубликовано: 2 фев 2025

Комментарии • 249

  • @Jogadora_109
    @Jogadora_109 11 месяцев назад +87

    You clarified in 30 minutes what my professor confused me about for three months. Thank you -- you're an excellent teacher.

    • @greenbeltacademy
      @greenbeltacademy  11 месяцев назад +3

      Wow, thank you! I appreciate that, and I"m happy to help!

    • @mahendradhungel8011
      @mahendradhungel8011 9 месяцев назад +3

      @@greenbeltacademy same here, if i found this video, I would rather pay you!

    • @greenbeltacademy
      @greenbeltacademy  9 месяцев назад

      @@mahendradhungel8011 thanks for the awesome feedback, I'm happy to help!

    • @belkismedina678
      @belkismedina678 2 месяца назад

      AMAZING!!!!

  • @sidtamang4728
    @sidtamang4728 10 месяцев назад +10

    Thanks for condensing the entire ANOVA concept and your hours and hours of effort into 30 minutes and explaining it so succinctly. Thanks!!

  • @Newreelshare
    @Newreelshare Год назад +26

    This is the best video on ANOVA ever made

  • @ismaelkinoti962
    @ismaelkinoti962 9 месяцев назад +4

    You have made Perfect and simple-to-follow explanations regarding ANOVA... Saved me a lot of time and energy.
    Thank you so much!

  • @yousefyousefi8617
    @yousefyousefi8617 Месяц назад +3

    what a beautiful explanation! 3 hours of reading an academic book on design experiments had resulted in more confusion and this 30-minute video would enlighten me!

    • @greenbeltacademy
      @greenbeltacademy  Месяц назад

      Thank you so much, I'm glad that video was so helpful!

  • @SamBahadurManekshaw
    @SamBahadurManekshaw 9 месяцев назад +4

    Thank you so much! You have done what so many books and so many youtube videos couldn't do: which is to make me understand ANOVA. You are a hero .... God bless

    • @CQEAcademy
      @CQEAcademy 9 месяцев назад

      You're absolutely welcome, I'm happy to help!!

    • @greenbeltacademy
      @greenbeltacademy  9 месяцев назад +1

      hahaha, thank you!! I appreciate that!

  • @reagan360
    @reagan360 3 месяца назад +1

    ANOVA explained perfectly in 30 minutes!!! Feeling so ready for my quiz tomorrow!

  • @bryanchen4703
    @bryanchen4703 Год назад +15

    Fully, well expalined! Much better than our profs lol

  • @baharcetinsoy1194
    @baharcetinsoy1194 10 месяцев назад +1

    The Anova Test couldn't have been explained better! Thank you for this video!

  • @JaneOchuka-l3c
    @JaneOchuka-l3c Год назад +7

    Finally, ANOVA makes sense to me! Very well explained! Thanks Andy. I have subscribed to the channel for more useful videos as such

  • @shuyiyu4113
    @shuyiyu4113 8 месяцев назад

    Best ANOVA explanation in YT!!! Love how you repeated key concept again and again, now its completely clarified from the confusion i got before watching.

  • @arishmahmood8581
    @arishmahmood8581 7 месяцев назад +2

    One of the best teacher in my life. He made complicated thing like a cake

  • @Kira-vs4np
    @Kira-vs4np 9 месяцев назад +10

    Hands down the best explanation of ANOVA on yt

  • @CADable
    @CADable Год назад +3

    An Excellent Overview of ANOVA. Highly Recommended!

  • @alman3mmm
    @alman3mmm 6 месяцев назад +1

    I love the way you explained it and the example you used. Very much appreciated Andy!

  • @katlawliss9496
    @katlawliss9496 Год назад +2

    Thank you so much. I've spent weeks looking for a video like this one.

  • @adebayoolufemi2074
    @adebayoolufemi2074 Год назад +1

    The best I have seen so far.
    The example alone does wonders ❤

  • @robertgernat2236
    @robertgernat2236 8 месяцев назад +2

    You really changed my prospect toward biostatistics ( MD. by the way ), getting my Masters in Clinical Research. I really enjoyed it , believe me. Thank you. Really!!

  • @NickDall
    @NickDall 5 месяцев назад +1

    Thank you for this video! Trying to teach myself statistics for my advanced degree and you've clarified a lot of confusion.

  • @cyrus_mbui
    @cyrus_mbui Год назад +2

    Fantastic explanation.
    Loved how you delivered it. Cheers Andy.

    • @greenbeltacademy
      @greenbeltacademy  Год назад

      You're absolutely welcome, and thanks for the comment!!

  • @indrebeaty8309
    @indrebeaty8309 10 месяцев назад +1

    Excellent video !!! Super explanation ! Thank you so much !

    • @greenbeltacademy
      @greenbeltacademy  10 месяцев назад

      You're absolutely welcome, and thank you so much for the kind comment!

  • @MerieyeM
    @MerieyeM Год назад +1

    Thanks a lot for the extremly well explained ANOVA video.I have been struggeling with this subject in stats. Until i came accros your video!
    Greetings from Holland!

  • @SarahLiu-k6l
    @SarahLiu-k6l Год назад +3

    This is an incredible video, thank you so much for making it, very helpful to me as a college student!

  • @jawadhafeez901
    @jawadhafeez901 Год назад +1

    Thanks Andy...it was great video! one checked towards the preparation of final exam!!!!

  • @danieltesfay6690
    @danieltesfay6690 Год назад +5

    Thanks Andy for sharing this great video!!!

  • @apophoenyx
    @apophoenyx 7 месяцев назад +2

    Best explanation so far, really great job!!

  • @mohamedbelazreg9949
    @mohamedbelazreg9949 Год назад +4

    WAW ! what a useful video Thank's for this wonderful explanation

  • @theplayers6460
    @theplayers6460 4 месяца назад +1

    yup I plus one that...really the best video i have ever seen so far

  • @hariharayedas2925
    @hariharayedas2925 10 месяцев назад +1

    best brother today is my exam of data science and this video help me the way out appreciate a lot may god bless you

    • @greenbeltacademy
      @greenbeltacademy  10 месяцев назад +1

      You're absolutely welcome, I'm glad I was able to help you out!

  • @rayped2771
    @rayped2771 Год назад +1

    MY GUY!!! Thank you, super well explained video. Thank you so so much :)

  • @Sawdust6666
    @Sawdust6666 7 месяцев назад +2

    Thank you that was superbly done. Massive help for my assessment

    • @CQEAcademy
      @CQEAcademy 7 месяцев назад

      You're absolutely welcome!

    • @greenbeltacademy
      @greenbeltacademy  5 месяцев назад

      Thanks for the positive comment and you’re welcome!

  • @Error_Mode1219
    @Error_Mode1219 8 месяцев назад +1

    hands down fantastic video 👏👏👏please don't stop making awesome videos like this sir

  • @alfaproximacentauri5335
    @alfaproximacentauri5335 Год назад +1

    Great video, super explanations, elegant English (that even I can well understand)!

  • @chenfan3515
    @chenfan3515 8 месяцев назад +2

    very clear explanation!!! I now know what is ANOVA 🥰 (learned it several times but unclear about its core meaning 😮‍💨

  • @honggle1874
    @honggle1874 Год назад +1

    Thank you so so much...I finally understood ANOVA!!!!

  • @revisionandthewritingproce846
    @revisionandthewritingproce846 9 месяцев назад +1

    BEST Anova video EVER!

  • @uthirapathi4453
    @uthirapathi4453 9 месяцев назад +1

    Very nice explanations. This lecture got me to understand well.

  • @karegaral
    @karegaral Год назад +3

    Best explanation so far! thank you!

  • @ghettosupastar7226
    @ghettosupastar7226 9 месяцев назад +1

    Incredibly clear explanation 5/5 stars !!!!!

  • @nelsona.s.7017
    @nelsona.s.7017 Год назад +2

    Wow, you are so good. This was well explained.

  • @jai.jai.jaishree
    @jai.jai.jaishree 7 месяцев назад +1

    Very well explained especially the null hypothesis :-) THank you

  • @abhishek8686
    @abhishek8686 9 месяцев назад +1

    Crystal clear explanation, thanks!

  • @michaeljhonramos4823
    @michaeljhonramos4823 8 месяцев назад +1

    Thank you so much!!!! This is very helpful I hope you will discuss more in statistics like One way to two way anova, chi square and etc.

  • @TheYoungBillionaire17
    @TheYoungBillionaire17 Год назад +3

    Well explained, thank you so much 🎉

  • @msnageshrao
    @msnageshrao 6 месяцев назад +2

    Very good explanation, thank you

    • @greenbeltacademy
      @greenbeltacademy  6 месяцев назад

      You're welcome, and thanks for the great feedback

  • @marcellabernardo1
    @marcellabernardo1 11 месяцев назад +1

    Great explanation! Thank you so much!

  • @belgischial59
    @belgischial59 Год назад +2

    Very good explanation....congratulation...!!!!

    • @CQEAcademy
      @CQEAcademy Год назад

      Thanks, and you're welcome!!

  • @TochukwuVictor-qe4xd
    @TochukwuVictor-qe4xd Год назад +3

    Thanks for your time and effort sir. Great video

  • @quanghuyluu9464
    @quanghuyluu9464 Год назад +1

    Thank u for sharing! It's very easy to understand for me despite English is my second language. Great video

  • @mnmusher1
    @mnmusher1 10 месяцев назад +1

    Great Presentation!

  • @MohammedAlbattashi-x5w
    @MohammedAlbattashi-x5w Год назад +2

    That incredible, well explanation

  • @ideejikepatrick3002
    @ideejikepatrick3002 Год назад +1

    Thank you very much for this your detailed explanation of ANOVA, I can comfortably use ANOVA in analysis. How i wish i can see, excel and sql video like this. Thank you Sir.

  • @KiranLata-x8w
    @KiranLata-x8w 5 месяцев назад +1

    Very well explained.Thank you

  • @AnnMarieCarrier
    @AnnMarieCarrier 9 месяцев назад +1

    Thank you. Very Helpful conceptual model!

  • @jim2218
    @jim2218 11 месяцев назад +1

    Great presentation!

  • @ChickenBoo32
    @ChickenBoo32 5 месяцев назад +1

    This man is doing God’s work

  • @moosemoss2645
    @moosemoss2645 8 месяцев назад +3

    There’s something to be said for seeing it all broken down. It’s my pet peeve when someone treats a stats tool like a black box then ties their colours to the mast without appreciation of all the out falls and inner workings. Great video, I’ve often wondered how to cross validate duplicate tool performance correctly and now I know.

  • @Olibuckets
    @Olibuckets 2 месяца назад

    Well explained! Thank you sooooo much for fixing my statistics lectures that I can’t keep up with😂

    • @greenbeltacademy
      @greenbeltacademy  2 месяца назад

      You're absolutely welcome, I'm glad you found it helpful!

  • @TaySwift332
    @TaySwift332 9 месяцев назад +2

    Thank you!!!!

    • @CQEAcademy
      @CQEAcademy 9 месяцев назад

      You're welcome!

  • @somayehgholami1334
    @somayehgholami1334 Год назад +1

    Thank you very much. It is really Great video👏👏👏

  • @leonardofreitas9877
    @leonardofreitas9877 5 месяцев назад +1

    Great video!🙏

  • @mmathaborantsieng7586
    @mmathaborantsieng7586 Год назад +2

    Thank you so much this was really helpful! 💕💕💕

  • @ermang9565
    @ermang9565 10 месяцев назад +1

    Great explanation, much appreciated. The only thing i am confused about, why do we need to write the total line for anova table? Before we need to calculate the F value, why do we need to determine total line at all? It has nothing to do for calculation of F neither the F table, right? Which point i am missing?

    • @CQEAcademy
      @CQEAcademy 10 месяцев назад

      Great question! Okay, so remember that ANOVA tables and ANOVA calculations were historically performed by hand, and the total row allow for the calculations to be "reconciled" and confirmed to be accurate when the total row adds up.

    • @jilliangilchrest9
      @jilliangilchrest9 9 месяцев назад

      The f value will determine your critical region! This will allow you to make the decision whether or not you are rejecting or failing to reject the null hypothesis

  • @muhaiminulrahi513
    @muhaiminulrahi513 6 месяцев назад +1

    It was very helpful.

  • @ferenebyu8911
    @ferenebyu8911 Год назад +1

    Simple and clear explanation 👌 tnx

  • @explorewithshahriar7114
    @explorewithshahriar7114 Месяц назад

    please upload some videos on different types of distributions in statistics
    your way of delivering the lecture will truly benefit the students
    and why not a statistics playlist !!

    • @greenbeltacademy
      @greenbeltacademy  Месяц назад

      Thanks for that suggestion!
      I do plan on creating more content in 2025.

  • @sibongakonkemathunjwa2902
    @sibongakonkemathunjwa2902 11 месяцев назад +1

    This is an excellent video

  • @kennedykalaluka2470
    @kennedykalaluka2470 8 месяцев назад

    Thank you so much. Enjoyed the lecture.

  • @chrisadrianachera7014
    @chrisadrianachera7014 10 месяцев назад +1

    Hello sir! Is it possible that the within groups is much higher than the between groups? Is it valid?

    • @greenbeltacademy
      @greenbeltacademy  10 месяцев назад +1

      Hey there! No, that's not a valid outcome.
      If there is variation within a group, then that within-group variation will naturally cause some between-group variation, and then those two estimates of variation will be nearly identical.

    • @chrisadrianachera7014
      @chrisadrianachera7014 10 месяцев назад

      @@greenbeltacademy So sir, it means we cannot continue perform ANOVA? If it is not valid, why do some researchers still use and perform ANOVA? Is there a solution to do it? Or we better use the non-parametric equivalent of ANOVA which is the Kruskal-Wallis? Note: Assumptions of ANOVA are met.

    • @CQEAcademy
      @CQEAcademy 10 месяцев назад

      Are you working with a situation where your within-group variation is much higher than your between group variation? Or are you asking hypothetically?
      Another assumption of ANOVA is that your data set is normally distribution, when that assumption is not met, the Kruskal-Wallis test can be used.

  • @learnwithob
    @learnwithob 6 месяцев назад +1

    I need to request a refund from my school fees because you explained that my lecturer used 2 hours to confuse me in 30 minutes, and it was awesome

    • @greenbeltacademy
      @greenbeltacademy  6 месяцев назад

      hahahaha thanks!!! I appreciate that!
      I'm happy to help!

  • @khushboosurana6229
    @khushboosurana6229 Год назад +1

    Thanks Andy, the example really helps

  • @yenkonaga7493
    @yenkonaga7493 10 месяцев назад +1

    But you need to calculate the MSE for each group, right? How did you do it in the video?

    • @yenkonaga7493
      @yenkonaga7493 10 месяцев назад +1

      I see,so it's simply the sum between the groups.

    • @greenbeltacademy
      @greenbeltacademy  10 месяцев назад +1

      @@yenkonaga7493 Yes, you need to calculate MSE by including data points from all of the different treatment groups. Go to 21:04 to see the equation for the SSE (Sum of Squares of the Error), and then you take that value and divide by the DFE (Degrees of Freedom of the Error).

  • @HopeNestu
    @HopeNestu 8 месяцев назад +2

    Thank you so much

  • @pariesque
    @pariesque Год назад +2

    Great video, thank you

  • @Abzarad
    @Abzarad 10 месяцев назад +1

    Thank you

  • @angelicagnzalzr
    @angelicagnzalzr 5 месяцев назад +1

    Oh, wow, what a nice video.

    • @greenbeltacademy
      @greenbeltacademy  5 месяцев назад +1

      Thank you so much! I"m glad you enjoyed it!

  • @benedictansiahfrimpong84
    @benedictansiahfrimpong84 Год назад +3

    👏👏👏Great video, I just came across it and it’s informative. Thank for the patience in explaining every step in details.

  • @GuthrieJenkins-f3i
    @GuthrieJenkins-f3i 8 месяцев назад +1

    The data doesn't "prove it," but rather, suggests it... because a Type One error is still possible. That's why we say reject the null hypothesis and not disprove the null hypothesis. The reject/fail-to-reject language points to the difference between proof and evidence. But still... a very nice video!

  • @sakshiabrawl
    @sakshiabrawl 4 месяца назад +1

    This is excellent. A question- Can i run anova on an independent variable and a principal component as the dependent variable? Thanks

    • @greenbeltacademy
      @greenbeltacademy  4 месяца назад

      That’s a good question, and I’m honestly not sure. I’ve never personally setup an Anova analysis that used a principle component as the dependent variable.

  • @vini202710
    @vini202710 8 месяцев назад +1

    awesome. Thank u so much

  • @renesubieta2862
    @renesubieta2862 6 месяцев назад +1

    where is the Excel file for the calculations? I do not understand how to calculate GM the grand mean

    • @greenbeltacademy
      @greenbeltacademy  6 месяцев назад

      The grand mean is simply the average of all of the measured values within the experiment.

  • @basseybassey6834
    @basseybassey6834 9 месяцев назад +1

    How do I get the Excel calculation spreadsheet and cheat sheet, please?

  • @SRAVANKOTTA
    @SRAVANKOTTA Год назад +1

    query: the way f test works to my understanding is, we compare mst (biased if null rejected) and mse(unbiased in any case) estimate of variance (sigma square), if they are different, the test show.
    what i wanted to know is what is sigma variance of? the larger population the means are from if null is true? if null is false how is it that mse still gives sigma, when one of the sample isn't from the population at all? or do the means belong to a general population regardless of null or alternate hypothesis?
    thank you for your videos by the way, it was really easy to grasp and went indepth

    • @greenbeltacademy
      @greenbeltacademy  Год назад +1

      Thanks for the reply, I"m glad you enjoyed the video. To be honest, I don't think I fully understand your question.
      Generally with ANOVA we're evaluating a factor, to see if that factor has an effect on our response.
      If that factor does not have an effect (null is true), then the MST will equal the MSE.
      If that factor does have an effect on the response (null is false), then the MST will be much larger than the MSE.
      If the null is false and the factor does have an effect, then the MSE still reflects the population standard deviation because of how the MSE is calculated - which is the variation WITHIN each sample group.
      That MSE calculation does not consider or include any variation from the factors themself, and is thus unaffected by any effect that the factor has on the response.
      Did that answer your question?

    • @SRAVANKOTTA
      @SRAVANKOTTA Год назад +1

      @@greenbeltacademy yes that clears up a lot of doubt, thanks for the quick response !
      To rephrase my doubt, i was under the assumption that the null and alternate hypothesis was (intuitively, I understand its true purpose is to measure factor effect) a test to determine whether or not the sample means belong to a singular general population
      Now i understand thats not the case, we just create a imaginary population where all samples are a part of and MST takes into account difference between means to calculate variance while MSE does not

  • @sureshmurugesh5783
    @sureshmurugesh5783 3 месяца назад

    Excellent explanation..! Hats off to you..!
    Could you pls explain how we can get Critical F - value distribution for the degrees of freedom with 5% significance level..?

    • @greenbeltacademy
      @greenbeltacademy  3 месяца назад

      Thanks, i appreciate that!
      The best way to see these critical values is to use create them in excel.
      You can use the function: FINV

  • @bhavishanthsuresh3298
    @bhavishanthsuresh3298 Год назад +2

    Great Content. But I think there is a small calculation mistake, (1831 + 148), should sum to 1979 right?

  • @mireyajones810
    @mireyajones810 5 месяцев назад +2

    We do NOT say that the NULL hypothesis is FALSE. We say that with a given degree of certainty (probability; confidence) we can REJECT the null.

    • @greenbeltacademy
      @greenbeltacademy  5 месяцев назад +2

      Great feedback, and you're right, if I said that the null hypothesis is false, I misspoke, I should have said that we can reject the null hypothesis!

    • @lamnorman7610
      @lamnorman7610 4 месяца назад +1

      You are not alone!! Same thing with me

  • @benhiggins811
    @benhiggins811 11 месяцев назад +2

    nice video boss

  • @JaredCavazos-l1p
    @JaredCavazos-l1p 2 месяца назад +1

    There is lots of discussion on estimating population variance, but no definition for the population. Is the population all of the cars that use octane? Are there different populations for each octane rating?

    • @greenbeltacademy
      @greenbeltacademy  2 месяца назад

      In this case the population would be cars using any octane of gas, that mirrors our null hypothesis with assumes that the octane gas will have no effect on HP.

  • @jerrychen8715
    @jerrychen8715 Год назад +1

    Great video, thanks Sir. A question migjht to ask, where we can calculate the critical f-value? how this 2.866 was calculated?

    • @greenbeltacademy
      @greenbeltacademy  Год назад

      Hey Jerry! That critical F-value comes from a table of critical values for the F-distribution.
      Here's a link to the NIST website where you can find all of these critical values - depending on your alpha risk, and degrees of freedom.
      www.itl.nist.gov/div898/handbook/eda/section3/eda3673.htm

  • @sudhanshharkut353
    @sudhanshharkut353 2 месяца назад +1

    How is number of treatments 4? it should be 10 right?

    • @Olibuckets
      @Olibuckets 2 месяца назад +1

      The treatment is different octane gas, so there’s 4 groups of data in different treatments, making the number 4. 10 is the treatment sample size mentioned in sum of squares calculation.

    • @greenbeltacademy
      @greenbeltacademy  2 месяца назад

      That is correct

  • @Blitzkrieg_one8
    @Blitzkrieg_one8 11 месяцев назад +1

    good

  • @dr.aimanmukhtar2171
    @dr.aimanmukhtar2171 9 месяцев назад +1

    thanks

  • @sidtamang4728
    @sidtamang4728 10 месяцев назад

    Since alternate hypothesis means that atleast one mean is not equal, does it also mean the group that has different mean is not impacting horsepower at all and there might be other unknown factors in play, causing mean of that group sample to be different from actual dataset mean?

    • @greenbeltacademy
      @greenbeltacademy  10 месяцев назад +1

      Great question, so typically with ANOVA, we're doing that analysis at the end of a DOE (Designed experiment), and if you're designing your experiment properly, you should be blocking out many other potentials factors that might be affecting your experiment. So hopefully there is not some unknown factor at play. It also usually takes additional analysis (Beyond ANOVA) to actually define the relationships between inputs/outputs for a process.

  • @stanleyugah8479
    @stanleyugah8479 Год назад +2

    i really wish i saw this material much earlier.

  • @luuuuukez
    @luuuuukez 2 месяца назад +2

    Whyyyy couldn’t our professor teach us like this instead of using a bunch of boring textbooks!!!😭

    • @CQEAcademy
      @CQEAcademy 2 месяца назад

      Hahahaha, thanks! I appreciate the positive comment. I'm glad you enjoyed that video.

    • @greenbeltacademy
      @greenbeltacademy  2 месяца назад

      Hahaha thanks!

  • @hikikomorihachiman7491
    @hikikomorihachiman7491 11 месяцев назад

    The reason we do variance when it’s talking about mean,
    Isn’t it still doing mean calculations?
    Since variance = some form of Geometric mean?

  • @ronaksingh3602
    @ronaksingh3602 9 месяцев назад +1

    Sir i want you to advice me that i have a degree with stats , econ. , maths stream so after graduation , what will be the opportunity for me nd sir your ANOVA table is my favorite😍❤

    • @CQEAcademy
      @CQEAcademy 9 месяцев назад

      Thanks for the positive feedback!
      To be honest, I'm not very familiar with Economics/Math fields of study, so it's tough to recommend a career path.

  • @MsiziBongimpilo
    @MsiziBongimpilo Год назад +1

    Where was this Last Month😢

  • @rznt1082
    @rznt1082 11 месяцев назад

    Is this applicable to two-way anova with interactions?

    • @greenbeltacademy
      @greenbeltacademy  10 месяцев назад

      No, the calculations change somewhat with two-way anova with interactions. The principles are the same, but the calculations change slightly.

  • @khantimalkangiriya7803
    @khantimalkangiriya7803 Год назад +1

    How the "SUM OF SQUARES OF THE TREATMENT" IS COMING; 1831 , I have calculated over and over but still i am not getting 1831 instead i am getting 729 as MST. can YOU please clarify this.

    • @khantimalkangiriya7803
      @khantimalkangiriya7803 Год назад

      at 20:19

    • @greenbeltacademy
      @greenbeltacademy  Год назад

      What value did you calculate for the grand mean?
      @@khantimalkangiriya7803

    • @linkxue201
      @linkxue201 Год назад

      @@greenbeltacademy I got the same 729. take the average of 4 treatments's mean as GM then calculate the SQUARE of each treatment by square (mean-GM). sum the 4 SQUAREs up is 182, then times 4 get 729. Please advise. Tks.

    • @greenbeltacademy
      @greenbeltacademy  Год назад +2

      Hey There!! @@linkxue201
      Okay, so you take the difference between the mean and the grand mean, then multiply by n (10).
      n there is the treatment sample size, which I see now is a confusing term. I meant the sample size within a treatment, not the number of individual treatments).
      So for the first average value it would be (169.7 - 178.7)^2 = 81.3 * 10 = 813.
      For the second average, it would be (175.3 - 178.7)^2 = 11.3 * 10 = 113.1
      Then on and on, until you get 1830.6 (rounded up to 1831).

    • @linkxue201
      @linkxue201 Год назад +1

      @@greenbeltacademy thank you so much Andy for the detailed explanation 😀