How to Calculate a Two Way ANOVA (factorial analysis)

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  • Опубликовано: 25 янв 2025

Комментарии • 270

  • @bro.jdfrancisco
    @bro.jdfrancisco Месяц назад

    I'm surprised that this was posted way back 11 years ago, and it still continues to help people up to this day. Thank you so much!

  • @MetropolitanChic
    @MetropolitanChic 4 года назад +85

    7 years later, and your still helping me in 2020. Passing my final exam now.

    • @mj2625
      @mj2625 3 года назад +7

      Felt in 2021

    • @milcahkwenda
      @milcahkwenda Месяц назад

      I’m here in 2024

  • @statisticsfun
    @statisticsfun  11 лет назад +89

    Thanks! I use a variety of different software including photoshop, illustrator, HTML5, Final Cut, GarageBand and a few other products. Each video takes me a long time to create. My rule of thumb is each minute of video takes about 12 hours to create, so a 7 minute video takes me about 84 hours of development time.
    Good luck on your presentation.

  • @Persplained
    @Persplained Год назад +4

    Still useful 10 years later. Best use of video to explain a topic in a lecture style way, no useless animation but perfectly understandable. That must take a lot of work. Thank you for making these video's. Best video's on youtube for stats

  • @abnormia
    @abnormia 4 года назад +2

    I watched 2 x 2 hour lectures from my uni about factorial analysis and had no idea wtf he was talking about. I watch this youtube video which is 18 minutes and understand it... you are a life saver! Thank you!

  • @statisticsfun
    @statisticsfun  11 лет назад +13

    You are welcome, welcome, welcome! I really appreciate hearing from students and it does make my day to hear that my videos are helping.

  • @stavanmehta1285
    @stavanmehta1285 9 месяцев назад +1

    one of the only few genuinely decent and complete explanations of two-factor ANOVA

  • @huichen6461
    @huichen6461 5 лет назад

    extremely high quality, very intelligent, and elegant. The speed is great. not slow at all. I can watch it while thinking. I would absolutely ignore any not constructive comments.

  • @SilenceDestroier
    @SilenceDestroier 2 года назад

    You know, channel lives up to it's name, dude made me actually have fun with statistics for the first time in a couple of years.
    Great channel and explanations are top notch

  • @paulhan3536
    @paulhan3536 6 лет назад

    searched the website for couple days to try to figure out how to solve this by hand and EVERYWHERE i looked... people did them by excel or other programs and just wrote out the answers without showing any work... thank you SO much for this video. helped a lot.

  • @statisticsfun
    @statisticsfun  11 лет назад +4

    Awesome!!!!! Thank you for spreading the word and congratulations on your A+. You deserve all the credit.

  • @xiaxiading7806
    @xiaxiading7806 3 года назад

    It is my first comment on RUclips. I can not wait to share it with my friends. It is thousands of help. Thanks for the pretty vision and explanation.

  • @afd8507
    @afd8507 8 месяцев назад +1

    Saved Me and my final in 2024, insanely helpful video

  • @IfeanyiUkwuoma
    @IfeanyiUkwuoma 11 лет назад

    Greatest Teacher Ever! Am going to tell the Whole World how Statisticsfun made me get an A+ in my Masters Thesis.. Working with Caterpillar Global Mining and I had to apply statistics to determine the variability between coal production and methane emission...with this Video, I looked like a pro :-)
    Hope to see you someday! You are the Best!!! *So Grateful*

  • @slimahmoud
    @slimahmoud 11 лет назад +18

    Amazing Tutorials!! Many thanks
    I have only one comment (kind of silly), but the square of 1.3 = 1.69 and not 1.8
    Thanks again and they are really very helpful tutorials with great explanation...
    Regards

  • @statisticsfun
    @statisticsfun  11 лет назад +3

    Thank you very much for your compliments. I believe the 1.3 = 1.8 is a rounding error. I don't carry all the digits through the entire problem.

  • @hasben0
    @hasben0 3 года назад

    Really apreciate you for taking the time to make all the graphics, makes the leson easy to digest!

  • @jokertaylor6492
    @jokertaylor6492 3 года назад

    This is so precious, thank you so much for making these and uploading these. I'm gonna pass my exam.

  • @krisghimire6938
    @krisghimire6938 5 лет назад

    Thanks a Lot! helped me understand Two way ANOVA much better from your video than from my professor. Keep making more !!

  • @learnwithamber7765
    @learnwithamber7765 10 лет назад

    It's very clear when you break it down. Now I know what my professor was talking about!. Thanks!

  • @Januaryblues100
    @Januaryblues100 10 лет назад

    This video series helped me understand these concepts better than my professor did, you just saved my Pysch Stats grade. Thankyou, very easy to listen to and understand.

  • @marisawyman9674
    @marisawyman9674 3 года назад

    Currently taking my final and I couldn’t do it without this video 🙏🏼

  • @ObhiReads
    @ObhiReads 9 месяцев назад

    Very helpful. There are minor mistakes still such a long process anyway gets benefit of doubt. Thanks for the easy explanation

  • @statisticsfun
    @statisticsfun  11 лет назад

    I checked! Holy Cow Batman. You have great ears and eyes and a keen perspective on detail. You are correct.

    • @divyatopwal3190
      @divyatopwal3190 4 года назад

      Sir will u help me out to how to analyse the data for crd design if the data is based on germination test done in lab.

  • @sebastianjensch5203
    @sebastianjensch5203 8 лет назад +60

    Advice: Play in x1.25. Great vid!

  • @sarah-louisedench3373
    @sarah-louisedench3373 9 лет назад

    Amazing! Thank you so much. Not only can I do this now but I actually understand the logic behind it, and at a brilliant pace. Thanks! :)

    • @statisticsfun
      @statisticsfun  9 лет назад

      Sarah-Louise Dench You are very welcome. If you get a chance make sure you like and share the videos, it will make it easy for others to find them.

  • @jgrtrx
    @jgrtrx 6 лет назад

    I like the clean presentation style. Very nice work.

  • @kyounokaze
    @kyounokaze 8 лет назад

    Thank you for making statistics so much simpler to understand. Your videos have helped me and thousands more.

  • @DrSarahManvilleWest216
    @DrSarahManvilleWest216 11 лет назад

    thanks again for clarifying that SSW is "error." Not getting that concept can completely wreck a calculation---writing a good interpretation is impossible without it.

  • @carlosp.e.bedson4011
    @carlosp.e.bedson4011 6 лет назад +1

    Such an awesome video. Thank you so much for taking the time to show so simply and transparently how this all works.

  • @summertummer2394
    @summertummer2394 5 лет назад

    Marvellous. You are great. The graphical interface you use is excellent.

  • @CMAuProductions
    @CMAuProductions 11 лет назад +3

    I cannot express my thanks enough. These videos are great!

  • @statisticsfun
    @statisticsfun  11 лет назад

    Jenn, nice to hear my videos are helping you towards your PhD. Btw, what is the subject are of your PhD?

  • @balayet03
    @balayet03 11 лет назад

    You have helped get me one step closer to maybe passing my exam! Thank you!!

  • @bogdandobondi8128
    @bogdandobondi8128 11 лет назад

    Awesome! Purely awesome. You put the fun back into statistics - the fun that got sucked out by the book of John A. Rice. With all due respect to him.

  • @michaeljoppa2155
    @michaeljoppa2155 8 лет назад +18

    at 12:49 in the video you show that the boys score of 6-7= (-2.0)2 Wouldn't it be (-1)2? Plus isn't the sum of squares equal to 31?

    • @JasTheKariol
      @JasTheKariol 4 года назад

      28 is the correct sum of squares if the correct value is considered for (6-7)² = 1 instead of 4.

  • @odalovesjustin
    @odalovesjustin 5 месяцев назад

    Amazing videos! I´m so glad i found these. Thank you for taking so much time in making these :D

  • @bhakthirai8166
    @bhakthirai8166 3 года назад +2

    how did u get the square of -1.3 to be 1.8? even if u round figure it, it must be 1.7

  • @brendapoole8490
    @brendapoole8490 5 лет назад

    I enjoyed watching the video on the two-way ANOVA design. I finally learned how to compute the measured to interpret the data. Also, a big thank you for demonstrating such great examples. Thank you!

  • @statisticsfun
    @statisticsfun  11 лет назад

    Good catch. I hope (I don't think) it makes a difference, but I will correct that when I revise the video. Thanks again for the catch, you have an eve for detail.

  • @ericthehalfabee1
    @ericthehalfabee1 9 лет назад +1

    Thanks very much, sir. Most illuminating indeed! Deeply appreciate your taking the time to help out folks like me, who have been struggling with this.

    • @statisticsfun
      @statisticsfun  9 лет назад +3

      Eric Smith Eric, I always appreciate hearing my videos are helpful. I spend a tremendous amount of time on them (about 8 hours for every minute of video). Hopefully you will like, share, subscribe, If you get a chance could you please like our FB page. www.FaceBook.Com/PartyMoreStudyLess
      It will help others find the videos.

  • @statisticsfun
    @statisticsfun  11 лет назад

    Thanks for that. I will double check the video. I appreciate the help.

  • @christytanner3896
    @christytanner3896 3 года назад

    I was going 2 say you made a mistake on SSe but I see it was just wrong on screen. Thank you for doing it step-by-step bc I've been looking everywhere for someone to break it down 4 me. Math is not my best subject...at all!!

  • @statisticsfun
    @statisticsfun  11 лет назад +1

    Appreciate that! Always good to know my videos are helping.
    Make sure you like MyBookSucks on FaceBook (see link in video description). This will help others find the educational videos.

  • @statisticsfun
    @statisticsfun  11 лет назад

    As always you are very welcome and good luck this week too.

  • @IR240474
    @IR240474 7 лет назад

    Thank you!! This was really cool and well explained - going for part 3 then to bed, Two-Way ANOVA at 10am

  • @shn1804
    @shn1804 5 лет назад

    Thank you so much for this-Its hard to find such a clear presentation on doing two way ANOVA's by hand

  • @Kevin2341
    @Kevin2341 11 лет назад +1

    Oh, and thank you very much for the videos, you explain it very clearly!

  • @ultinatetruustar
    @ultinatetruustar 11 лет назад

    It does seem much easier than I expected. Great videos.

  • @wandaparsons8331
    @wandaparsons8331 Год назад

    Thank-you for your time putting this together, very helpful!

  • @andreib8871
    @andreib8871 4 года назад +2

    Thank you for video! When you calculate Sum of squares for Gender you do this separetly for boys and girls. I expected that for second factor age it would be separate calculation for each category 10YO, 11YO, 12YO. Could you please clarify why it is used different approach for caluculation sum of squares for factor 1 and factor 2?

    • @shobhitverma3290
      @shobhitverma3290 2 года назад

      I had the same question. Although the final answer is correct, calculating means based on Age would have been more intuitive.

  • @statisticsfun
    @statisticsfun  11 лет назад

    I believe that is a rounding error. Keep in mind that in all of statistics we are estimating, so rounding should not make a lot of difference. It is hard to carry more than one decimal when you are doing calculations by hand.

  • @ileanaquintero5002
    @ileanaquintero5002 5 лет назад +2

    Thank you so much! I have an exam this week and my teacher goes through things super fast and textbooks just don't do it for me.

  • @sergioc2989
    @sergioc2989 11 лет назад

    Thank you!!! so much!!! you can't understand how much this video help me!! really! thank you!

  • @statisticsfun
    @statisticsfun  11 лет назад

    I am not sure what Bit string means relative statistics.

  • @emmaobrien7431
    @emmaobrien7431 2 месяца назад

    Thank you! Great video. Why did you use the averages of each age group from which you subtracting the grand mean instead of using the row means to calculate SS age?

  • @hilalozkececi1900
    @hilalozkececi1900 10 лет назад +1

    thanks a lot for the effort, statistics isn't a nightmare anymore!

    • @statisticsfun
      @statisticsfun  10 лет назад

      Hilal özkeçeci Glad that you are no longer having statistics nightmare, best to keep your dreams to happy dreams. Hopefully you will like, share, subscribe, If you get a chance could you please like our FB page. www.FaceBook.Com/PartyMoreStudyLess
      It will help others find the videos.

  • @jamenlong1097
    @jamenlong1097 9 лет назад +3

    At about 7:17, you calculate the first component of the first factor sum of squares. You do this by repeating nine times, the boys average (7.7) minus the grand mean (9) and squaring the result, (7.7-9)^2, then summing all of this to get 16 as the boys sum of squares. It seems that you could get a more granular and accurate measure of the sum of squares if you subtracted the grand mean (9) from the individual scores. Why is this not done? I realize that it would increase the sum of squares and affect the F tests later on, but it seems more accurate. Why is it that using the boys mean in place of each score is acceptable when it seems less accurate?

    • @user-hongkongnews
      @user-hongkongnews 5 лет назад

      I think they are two different things. One is called sum of squares between the group, one is called sum of squares within the group. So basically our goal is to see whether different group are the same. So we compare differences between group mean and ground mean, and differences within the group. If they are very different, we reject hypothesis. Think about this way. You probably have three class , which all have average 81 points, 82 points and 83 points. If you calculate average of (81+81+82) to get your group mean, then the differences between each group mean and your ground mean would be very small. However, it is possible that most of students in group one are around 81, while in group two there are some students get 90, while some get 72, which also give average 81. However, obviously these two groups will be very different even if they have same average.Then you calculate differences between each data point in a group and the mean of the group it is in.(called sum of square within) Then, you compare sum of square between and sum of square within. If the ratio is very large, that means your different group perform very different even if they have similar mean

  • @statisticsfun
    @statisticsfun  11 лет назад

    Hi Hannah,
    Not sure why the link does not work. I did add the links in the video description of this video. Hope that helps.
    David

  • @raiszakirdzhanov2148
    @raiszakirdzhanov2148 3 года назад +1

    at 7:08, how did you get 16? I calculated (7.7-9)^2*9=(-1.3)^2*9=15.21, and by my calculation (-1.3)^2=1.69. So, either I'm not able to understand your calculation or you made a mistake. Please, explain it to me! for what did you round a few your calculation?

  • @kirbyy
    @kirbyy 11 лет назад

    thejamesbond, i wondered the same thing. I calculated the ss for the second factor according to "test scores" and it did give the same result as the method in the video.

  • @coldpineapples9328
    @coldpineapples9328 5 лет назад +1

    great vid!! very comprehensive and easy to understand!!

  • @an-autumn-leaf
    @an-autumn-leaf 3 года назад

    is there any mistake at 8:43? 1.3^2 is actually equal 1.69, and if the result is 1.8 anyway, the sum of squares should be 16.2

  • @yasser19781
    @yasser19781 10 лет назад

    This vedio helped me alot in analyzing my data for my project , many thanks

  • @clockwork4068
    @clockwork4068 4 года назад

    It's actually mindblowing how most of your audience rely on memorization of 'lo-and-behold' facts and consider themselves to be learning the subject

  • @kirbyy
    @kirbyy 11 лет назад

    thanks so much for these videos!! im doing complex analysis for my thesis and these help me a lot in understanding the reasoning behind it all. though its too bad you didnt show how to calculate the interaction by hand i am curious about that too.

  • @hetvimodi6137
    @hetvimodi6137 7 лет назад

    You are so patient with the entire process. Thank you for explaining this topic so well. So do I get an award by mail or what? :D Thanks once again.

  • @Kevin2341
    @Kevin2341 11 лет назад +15

    Around 7:05, you square -1.3, the answer is 1.69 or about 1.7, not 1.8

    • @bonitaliu1030
      @bonitaliu1030 7 лет назад +1

      FUCK ME IVE BEEN SPENDING HOURS FIGURING OUT WHAT I WAS DOING WRONG

    • @nathanielpeter5411
      @nathanielpeter5411 6 лет назад +6

      He used 1.3 to write it down, the actual value is 1.3333333 or 4/3. squaring that makes it 1.8

    • @jayanthychakrapani3553
      @jayanthychakrapani3553 5 лет назад

      Nathaniel Peter ,Thanks a lot!

    • @raizzaannebaria1799
      @raizzaannebaria1799 4 года назад

      how did it became 1.3333333?😭😭😭

  • @statisticsfun
    @statisticsfun  11 лет назад

    I do have an example of doing Two Way Analysis by hand. I have an entire playlist on Two ANOVA. You can find the link to the playlist in this videos description. The first video in the playlist shows how to calculate Two ANOVA by hand.
    Good luck on your thesis as well. Btw, What is your topic of your thesis?

  • @pedantsunited5368
    @pedantsunited5368 3 года назад

    you're a lifesaver

  • @user-xn2hf9re8r
    @user-xn2hf9re8r 7 лет назад

    put simply, thank God you exist

  • @paranjaygulati9661
    @paranjaygulati9661 Год назад

    hi great videos , in 7:13 (-1.3)^2 is 1.7 not 1.8, pls note this calculation error everyone who's watching

  • @susanarios7825
    @susanarios7825 11 лет назад

    Very helpful. I have to present a two-way ANOVA to others in the class next week and had no clue how to... now I do. Thanks!
    Also, what computer program did you use to put the presentation where you can move the data, highlight them, etc.?

  • @woRstbB
    @woRstbB 9 лет назад +1

    Hi, can I have more than two independent variables for 2-way Anova :)?

  • @alexandraxanthopoulou6853
    @alexandraxanthopoulou6853 5 лет назад

    you just saved my day my friend

  • @statisticsfun
    @statisticsfun  11 лет назад +1

    Many thanks for the comment. Make sure you like MyBookSucks on FaceBook (see link in video description). This will help others find the educational videos.

  • @03442279566
    @03442279566 8 лет назад +8

    isnt the square of -1.3, 1.69 at 7:22??

    • @nathanielpeter5411
      @nathanielpeter5411 6 лет назад

      He used 1.3 to write it down, the actual value is 1.3333333 or 4/3. squaring that makes it 1.8

    • @MT-we3fw
      @MT-we3fw 4 года назад

      I also struggled for the same question that -1.3 is 1.69. Thanks Nathan for explaining it. 1.3333333 is indeed 1.8 rounded up.

    • @MT-we3fw
      @MT-we3fw 4 года назад

      @@nathanielpeter5411 but 7.7-9 is -1.3 why did he take 1.3333333?

  • @louism.s.4845
    @louism.s.4845 11 лет назад

    Hell man.. If thats for real, then I have absolute believe in the appropriateness of your name!
    By the way thanks for the great video.
    I hate going to the stats lectures and I do not like the stats book too much either. I usually learn by slides only. They are terrible this year. But guys like you make auto-didaction not only possible but the future!
    Thank you so much for all the time you put into this. Although I am not interesting in creating videos anymore after having heard that ratio..

  • @rehansiddique7291
    @rehansiddique7291 7 лет назад

    When we take the average of a group overall, do we take the average of the averages, or the average of all of the data? For example, if we had a differing number of observations for each factor, Im not sure if the average of averages would work

  • @PatrickQ
    @PatrickQ 9 лет назад +2

    Excellent! Very nice presentation, and very clear. Thank you for taking the time to put this together. I don't suppose you might do a video on the estimation of parameters in linear regression models?

  • @senthilcaesar
    @senthilcaesar 4 года назад

    Thank you so much for this lecture...

  • @robbieklein6162
    @robbieklein6162 5 лет назад +3

    For main effects, it would be clearer if the whole thing were framed in terms of a ratio between between groups/factor variance and within-group variance. But for the age factor, you organize the data by gender. This makes the overall functioning of the f-ratio for the age effect unclear for beginners

    • @saebelorn
      @saebelorn Год назад +1

      I think it may have helped to have mention or emphasise that the within-group variance is calculated for each 'group', 'treatment', however you call it, rather than combining the factors together completely

  • @sylviaemejuru1956
    @sylviaemejuru1956 4 года назад

    Thank you very much Sir! I am so grateful!

  • @anonymous47667
    @anonymous47667 11 лет назад

    Unfortunately, the link for related videos does not seem to be visible. The graphic appears directing to related links, but the link is not visible. Please advise.

  • @speedyraptor9
    @speedyraptor9 11 лет назад +1

    Please give an example of three-way ANOVA, if you do not mind. Your videos are great!

  • @hannahwilliams9983
    @hannahwilliams9983 Год назад

    Is this a type 1, 2 or 3 sum of squares? I know it doesn't matter because it's balanced but I am curious?

  • @mandelanwa7472
    @mandelanwa7472 10 лет назад

    am so happy to watch this.... I really enjoy it Thanks allot
    # PROUDLY A STATISTICIAN #

  • @hanslofgren8199
    @hanslofgren8199 10 лет назад

    Hi there, thank you for a very nice layout. I wonder about 11:00 min in the video, where you have the BOYS mean instead of Girls mean (7 green, 10 Brown, 14 Purple) substracted from the grand mean. I thought that the sum of Squares of the Girls should be 90, and the Sum of Squares of the second factor (age) should be 136,5. That leads to a negative Sum of Squares in both factors of -36,5. Am I right or have I misunderstood something?

  • @arnolddelacruz7822
    @arnolddelacruz7822 5 лет назад

    Awesome video with clear and easy to follow explanation. By the way, is this with or without replication? thanks

  • @carlosaldana6039
    @carlosaldana6039 4 года назад

    Can I use two way anova for solving 3 factor experiments?

  • @kezzu5849
    @kezzu5849 10 лет назад

    does this method still work if the sample sizes are not the same for each set?

  • @statisticsfun
    @statisticsfun  11 лет назад +1

    Thank you for you compliments. It is much appreciated. Make sure you like MyBookSucks on FaceBook (see link in video description). This will help others find the educational videos.

  • @slimahmoud
    @slimahmoud 11 лет назад

    Yes I have noticed that also at the end of the video with the same rounding being made by the software...
    Thank you again :)

  • @jenssoet8382
    @jenssoet8382 5 лет назад

    @statisticsfun maybe a dumb question, but can I calculate the SST as well if I don’t have any individual test scores but only group means? Thanks a lot for the video btw

  • @kevinchyung2026
    @kevinchyung2026 2 года назад

    Thank you for this. This was incredible

  • @allivecars
    @allivecars 7 лет назад

    thankyou u save my life

  • @a.chikkuchimathematics7386
    @a.chikkuchimathematics7386 6 лет назад

    Thank you so much for making it so simple.

  • @smokydingo6362
    @smokydingo6362 4 года назад

    8:37 According to the formula in my textbook, you're supposed to mulitply that sum with the number of levels of factor B, in this case it would be 3 so 32 * 3. Am i missing something?

    • @mukulsinghal6730
      @mukulsinghal6730 4 года назад

      I guess it won't impact because of the number of observations in your data assumes to be the same at both the factor A & B.

  • @silicondecay
    @silicondecay 6 лет назад

    12:46 -- the brown color -- you have two 6-7's in a row while one of them says 6-7 = (-2)^2 and the other says 6-7 (-1)^2

  • @DerickDickens
    @DerickDickens 8 лет назад

    My reward will be some ice cream. I made it! Thanks for the great video.