Student's t-test

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  • Опубліковано 23 гру 2024

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  • @cheekyboyz8121
    @cheekyboyz8121 3 роки тому +200

    "...so, instead of this being known as the Gosset's t-test, it's known as the -"
    *cue smooth electronic beat*

    • @Anton_Pietro
      @Anton_Pietro 3 роки тому +6

      Bozeman really turning science into a tv drama, lol.

    • @beboldbored2099
      @beboldbored2099 9 місяців тому

      Student T Test

  • @zainabmohammed1141
    @zainabmohammed1141 8 років тому +222

    I just started my PhD in Psychology and the program is extremely quantitative. It's been years since I've taken a stats test and watching your videos have seriously helped in me remember the basics. I'm so going to keep you in my prayers! Thank you for making it seem less scary.

    • @burtons9922
      @burtons9922 3 роки тому +7

      How did your PhD go?

    • @zainabmohammed1141
      @zainabmohammed1141 3 роки тому +21

      @@burtons9922 just finishing. I propose my dissertation on the 27th!

    • @catherinepattersonmcelroy8336
      @catherinepattersonmcelroy8336 3 роки тому +7

      @@zainabmohammed1141 Congratulations!! And good luck next week!

    • @yonisabdull
      @yonisabdull 3 роки тому +4

      @@zainabmohammed1141 How did the dissertation go?

    • @zainabmohammed1141
      @zainabmohammed1141 3 роки тому +16

      @@yonisabdull I’m a PhD candidate and defend next month Insha’Allah

  • @HafizBahar
    @HafizBahar 2 роки тому +7

    Finally! Someone who speaks english! Perfect video showing the real world applications and methodology to come to a conclusion, thank you so much for the entertaining lecture!

  • @simongonzalez4946
    @simongonzalez4946 4 роки тому +6

    This man needs ALL THE AWARDS.
    Bruh got me through high school, college, and continues to help me refresh for job relating stuff.
    This dude is single-handedly responsible for a quarter of millennial contribution to GDP. xD

  • @donovanlucibello6420
    @donovanlucibello6420 6 років тому +13

    Mr. Andersen, I have had the privilege to meet you in person and tell you, "Thank you!," but it bears repeating here.
    You have no idea how much you have helped me over the years to understand fundamental concepts that are glossed over in lecture leaving my head spinning unable to follow along. I get home, come to UA-cam and watch you unravel the whole thing in < 15 minutes.
    You are an exceptionally talented teacher, and your work does not go unnoticed. Thank you for your gift of quality instruction to complete strangers on the internet over many years now. I wish that more teachers would watch your style and emulate that rather than trying to rip through slides or go off on pointless rabbit trails during lecture. "Thank you!"

  • @technoterror1129
    @technoterror1129 5 років тому +388

    Dude somehow you don't make me want to die while learning this stuff haha, I wish my professor was more like you, thanks for the help!

    • @ArjunSingh-rn3wh
      @ArjunSingh-rn3wh 3 роки тому +3

      Awesome explaination.

    • @mrtoast244
      @mrtoast244 2 роки тому +4

      fr, my prof is so boring even though he's done some seriously cool engineering work in the past

  • @DrChrisAbraham
    @DrChrisAbraham 7 років тому +15

    Was that helpful??
    God! You have no idea how much I have struggled to wrap my head around this whole Statistics topics. And again, you have no idea what a boon your videos are turning out for me! Many many thanks, Bozeman! You the boss!

  • @mostinho7
    @mostinho7 4 роки тому +4

    Fantastic thank you
    3:00 t-value formula compares difference in means to difference in variance of the samples. Like a signal to noise ratio.
    4:55 once we have a t-value, we can read from the table and see what p-value that t-value corresponds to. That is the t-test, seeing if our t-value is high enough to give us a low p-value (and if so, then the difference in means is statistically significant and we can reject the null hypothesis)

  • @sj26843
    @sj26843 4 роки тому +128

    ...I still have no clue 😭😭 Probably going to re-watch this a dozen times, cause it explains it better than my lecturer this year

  • @Ureyeuh
    @Ureyeuh 5 років тому +2

    I just learned a semesters worth of work for my research in psych class from your account. I have used this account all throughout college. I owe you my tuition.

  • @michaelsoriano5340
    @michaelsoriano5340 3 роки тому +36

    Thank you so much Coach Steve Kerr for this lecture video. Despite your busy schedule as the GSW Head Coach, you were still able to find time and record this important topic in Research.

  • @shraddha3108
    @shraddha3108 5 років тому +45

    Crystal clear description of t- Test. I could finally understand this concept. Thank you !!

  • @nickkraw1
    @nickkraw1 8 років тому +810

    Thank you for posting this! You explain statistics far better than most teachers!

    • @ResilientFighter
      @ResilientFighter 3 роки тому +8

      i have taken over 10+ stats courses, this was very very well explained

    • @hogrideeeeer
      @hogrideeeeer 3 роки тому +1

      @@NostalgicHearts deez nutz

    • @gordonramsayjr
      @gordonramsayjr 3 роки тому +2

      Completely agree with you. He can explain in one short video what most teachers try to explain in one week's lecture.

    • @nihalkhan2541
      @nihalkhan2541 2 роки тому

      0.05 probability means that if we will conduct the experiment 100 times, 95 times we will reject the null hypothesis and 5 times accept....
      Why?

    • @picassoofai4061
      @picassoofai4061 2 роки тому

      Approuved.

  • @osamaomer9106
    @osamaomer9106 2 роки тому

    Honestly I understood more by listening to you for 10 min, than I have my whole life listening to mundane lectures or reading notes. And the best thing is that listening to u some how doesn't make me wanna die while studying t-test. Truly u r a gem. Thank you so much

  • @Blueberrypancake306
    @Blueberrypancake306 2 роки тому +5

    This was so helpful! I haven't taken stats in years and have had to partially watch so many videos before finding this one. I really appreciate the clarity and step by step approach!

  • @Alchemist10241
    @Alchemist10241 Рік тому

    I'm a data scientist, there are a lot of channels which are dedicated to data science, but none of them can explain t-test this much simple and compact.

  • @serenkuner1280
    @serenkuner1280 3 роки тому +6

    Watched this during my second undergraduate year, come back as a PhD. student to watch it again :)

  • @naeemullah6976
    @naeemullah6976 Місяць тому

    This is the best explanation of t test, explained to me by anyone until now.

  • @lilyliu1231
    @lilyliu1231 8 років тому +5

    This is the best way of introducing Student T-Test I have ever seen! Every easy to understand! Thanks!

  • @trongnhantran3358
    @trongnhantran3358 4 місяці тому

    It had been 7 years and this knowledge still helping me a lot

  • @eugenaharley7103
    @eugenaharley7103 4 роки тому +6

    I’ve learned more in this 10 mins then I have all semester 😩😩 Thank You so much🙏🏾

  • @ritikaparekh9627
    @ritikaparekh9627 2 місяці тому

    Finally someone who makes sense !!! I have my exam in two days and I'm now finally confident about t-test. It is all making sense !!! I wish I had seen this video before

  • @bolajiadedasola6369
    @bolajiadedasola6369 8 років тому +11

    you are indeed a great teacher. I love this video. I got a t critical which is greater than my t statistics and this establish the claim of the null hypothesis to be true, so I fail to reject the null hypothesis which means that there is no statistical significant difference between the samples. also, my probability value is greater than my alpha value, so this also tells me that my null hypothesis should not be rejected.

  • @salmanalbaloushi630
    @salmanalbaloushi630 5 років тому +1

    This man deserves genuine respect from students. I wish he was my professor.

  • @tousifazmain6205
    @tousifazmain6205 5 років тому +3

    Finally a video that clearly explained t test. thank you!

  • @netflixtvb
    @netflixtvb 4 роки тому

    It is a very great video, i learn t test in high school, pre-uni, year 1, master degree...........now i graduate for 4 years and finally understand this after watching this video, i love youtube!

  • @ivantoroman60
    @ivantoroman60 8 років тому +377

    What does it meeeaaan? Thanks for the video man

    • @nickw22689
      @nickw22689 6 років тому +23

      What does that meeEEEeaaAAn?

    • @gabor6259
      @gabor6259 6 років тому +17

      We calculate the mean but what does that MEAN? (why so mean?)

    • @hubert3802
      @hubert3802 6 років тому +15

      a comment I anticipated after watching this video haha

    • @freedom9729
      @freedom9729 3 роки тому +1

      literally

    • @ethandaltonofficial267
      @ethandaltonofficial267 3 роки тому +2

      mate I was saying the same thing too myself ahah

  • @sams8502
    @sams8502 3 роки тому +2

    I've been watching and reading lectures for hours, this is by far the best lecture I've seen

  • @タカノユウイチ
    @タカノユウイチ 5 років тому +7

    This video's explanation is excellent! Though I am Japanese, I could not understand T-test, P-value and etc by reading Japanese textbooks of statistics. But now I have understood of them by watching this video. I think, Japanese Professors of all university and college are really bad at explaining in the lectures and
    of books written by themselves. Thank you a lot!

    • @lilideedee
      @lilideedee 3 роки тому

      funny my Professor is Japanese

  • @eefkemariaduijst2051
    @eefkemariaduijst2051 3 роки тому

    i love people who make the time to make these videos so much

  • @seanmcc15
    @seanmcc15 2 роки тому +7

    Excellent example in 10 minutes. Thank you

  • @SuperLslam
    @SuperLslam 6 років тому +1

    I'm working on a lab report requiring statistical analysis for my data, your 10 minute video did two hours of work for me!

    • @HE-cm8kt
      @HE-cm8kt 6 років тому

      Salman Syed I’m working on a lab report too lol

  • @ztk7789
    @ztk7789 6 років тому +11

    I think its 95% of the time we fail to reject and 5% we would reject since it's based off the null at 5:48

    • @ajaykushwaha6137
      @ajaykushwaha6137 5 років тому +1

      I had the same doubt while watching the video. Did you find the answer to your query?

    • @samsung6980
      @samsung6980 5 років тому +5

      I believe the explanation in the video is correct. If the t-test gives you a value that is less than the p-value, then you reject the null hypothesis(the difference between the samples is statistically significant). In other words, you compare the p-value with the critical value (0.05 or 0.025), but compare the t-value(the result after putting the numbers in the formula) with the corresponding cell from the distribution table.
      If the t-value statistic is 'greater' than the corresponding value in the table -> you reject the null hypothesis.
      If the p-value is 'lesser' than the critical value (0.05 or 0.025) -> you reject the null hypothesis.

    • @Tony-qw1df
      @Tony-qw1df 4 роки тому

      @@samsung6980 THANK YOU. I HATE STATS SO MUCH

  • @tootscarlson
    @tootscarlson 4 місяці тому

    For a person who really struggles with equations and statistics in general, you've explained this very well.

  • @ajaykushwaha6137
    @ajaykushwaha6137 5 років тому +3

    No doubt, the teaching, the content, delivery and everything else was incredible. This is one of the best videos I ever found with complete knowledge. I have just one doubt at 8:35 you mentioned that 0.95 is the probability of rejecting the null hypothesis. But I was unable to grasp it as it always seemed that it is the probability of the acceptance region. Is it different from Z- test? And it will be great if you could make a video on Z test. :)

    • @pradeepwhistles
      @pradeepwhistles 2 роки тому +1

      You are RIGHT! It is the probability of accepting the Null hypothesis. That is how we frame the hypothesis by giving more weightage to Null hypothesis.

  • @TheStrossicro
    @TheStrossicro 5 років тому

    Bozeman, I congratulate you.
    I am horrible at statistics and it is my achilles heel. I can do wonders with data in R, trully. But when it comes to demonstating significance etc...
    This demonstration (and others) really clarified what was going on and why and where.
    You know how to teach.

  • @Precious211
    @Precious211 8 років тому +19

    I got:
    t=0.206
    t-test(p-value)=0.83814447
    Therefore, I fail to reject the null hypothesis, meaning there is no statistical significant difference between the two samples.
    I had a question though...on the excel spreadsheet do I type in: =ttest(plant A, plant B, 2, 2) or (plant A, plant B, 2, *3* )? The last number is for the "type" and excel reads to put in "3" instead of "2" if the variances are not equal for the two-tailed test. The variances I got seem pretty far apart: *Plant A variance= 138.69 and Plant B variance= 226.29*. Your variances were closer to 1, so I see why you put in "2" for the type. When I put in "3" my p-value turns out to be slightly different= 0.83820433 than 0.83814447. Which is more accurate?

    • @vaibhavghegade7557
      @vaibhavghegade7557 6 років тому

      hmm.... Same question here....

    • @artemioosorio9045
      @artemioosorio9045 5 років тому

      I got he same results as you did. I had to type in the 2 in place of the 3

    • @woodchuk1
      @woodchuk1 4 роки тому

      Actually, a variance ratio of 2 isn’t all that uncommon...the t-test is rather robust to unequal variance as I recall, and you probably don’t need to worry until your variance ratio is over 3, in my experience. If you’re in doubt, you can always use the unequal variance option regardless of your variances, since the statistical power of the two methods is pretty much the same. But since the unequal variance option reduces the degrees of freedom compared to the equal variance option, the corresponding critical value for the unequal variance option will be slightly higher., and thus the p-value will be affected as well.

  • @tinsleyadams9251
    @tinsleyadams9251 2 роки тому

    Sir, I have been putting off my most important math paper of the year, and I wholeheartedly forgot how to do these tests. Thank you for being my lord and savior while trying to graduate, I hope your life is amazing because you deserve it.

  • @mHassanAbdelwahed
    @mHassanAbdelwahed 8 років тому +38

    you saved my ass, for my exam is tomorrow

  • @paldenwangchuk6790
    @paldenwangchuk6790 3 роки тому

    in the exercise you have given, t value is 0.042 where as critical value is 2.02. in this if i correct, we fail to reject null hypothesis. awesome teacher

  • @CountGrishnakh
    @CountGrishnakh 6 років тому +6

    Thank you so much, very detailed video, and explained perfectly. I had a biology lab report and I haven't taken a statistics course yet, so I had no clue what to do in Biology X since most kids are older than me !

  • @truegrit7697
    @truegrit7697 7 місяців тому

    Wow - I love the way you crunch the numbers instead of using a methods software. Now I understand the PROCESS. It makes so much more sense now. Thanks!

  • @AlAmin-lc6fs
    @AlAmin-lc6fs 4 роки тому +5

    Meaning of 95% confidence level, the meaning that I wanted

  • @rocketrider1405
    @rocketrider1405 8 років тому

    I like that t-table link you gave because it gives df all the way up to 100 without skipping any values in between

  • @marektomanek1913
    @marektomanek1913 6 років тому +7

    Giving you a big like man :) really great explanation .... I learned the T-Test at university but haven't used it for several years so wasn't sure how to count it and you brought it back to my mind ..... really great video man :)

  • @oot007
    @oot007 6 років тому

    by far the best t test video on youtube.

  • @parisithapliyal1501
    @parisithapliyal1501 6 років тому +16

    Tomorrow is my chemistry exam for which I m watching ur lessons thanks a lot for this understandable video

  • @differdiffer7498
    @differdiffer7498 3 роки тому +1

    Bozeman, this is amazing. I learnt and solved a problem in minutes. I had a problem on biostat on my desk and needed solution and this video just helped clear it all. I'm super grateful

  • @breakdancerQ
    @breakdancerQ 6 років тому +6

    I wish I somebody showed me this damn video instead going through a readers hundred times and not getting it. Thank you! 🤜

  • @shekelboi
    @shekelboi 11 місяців тому

    Student's t-test is such a weird name, glad you mentioned the history of it in the beginning

  • @GregRainsMedia
    @GregRainsMedia 8 років тому +8

    I actually get it!!! You sir are amazing. I've been reading all this in my textbook and just not getting it. Thank you so much.

  • @billmichae
    @billmichae 5 років тому

    This Prof. is No.1 !!!! Fast and simple lecture that cannot be better!

  • @EH_888
    @EH_888 5 років тому +4

    Thank you so much! I have to do this for quantitative analysis, and you've made this process so much easier! Again, this video is much appreciated!

  • @momnamaryam2220
    @momnamaryam2220 Рік тому

    Best vedio on youtube about t test that has cleared all my doubts

  • @autumnrose8091
    @autumnrose8091 6 років тому +4

    My dude!! THANK YOU SO MUCH we really really appreciate your channel! God bless you xx

  • @pradeepwhistles
    @pradeepwhistles 2 роки тому

    For the leaves problem, t-value(0.05 significance level,2 tail test, independent type)=0.803, t-critical value(dof=40,0.05 significance level, 2 tail test)=2.021. Since the (t-value < t-critical value), we fail to reject the Null hypothesis(Leaves in both the plant have the same parameter for which it is tested). Hence, there is no significant difference between the leaves of two plants

  • @Emeraldxx
    @Emeraldxx 8 років тому +30

    omg... lol I was having trouble with this subject & BAM I get a notification of you uploading this video. THANK YOU.

  • @pradiptaguptaindia2026
    @pradiptaguptaindia2026 3 роки тому

    This is gold, best explanation of statistics, ever

  • @stiarait
    @stiarait 3 роки тому +3

    I don't know how but I understand this now.

  • @damian9303
    @damian9303 3 роки тому

    I love how I had to grind my Statistics class so hard I’m being recommended videos like this

  • @a.z5381
    @a.z5381 5 років тому +8

    Oh my god thank you so much! My biology teachers made zero sense when explaining this!

  • @flynnl
    @flynnl 9 місяців тому

    God level video, the bit at 4:16 is just so clear

  • @magalihovsepian3169
    @magalihovsepian3169 8 років тому +6

    You are a genius explaining statistics! ;)

  • @peasem7
    @peasem7 8 місяців тому

    This video was amazingly helpful for my studies this week. Thank you so much for taking the time to make it!

  • @VanWarren
    @VanWarren 5 років тому +4

    this is freakazoid clear. thank you. dropbox link is dead tho, so can't run the example.

  • @InsideTheBox3
    @InsideTheBox3 2 роки тому

    This was a lot better than watching my lecturers 1 and a half-hour lecture on t-tests, thank you (:

  • @davidchoi33
    @davidchoi33 8 років тому +4

    I want to see if I am understanding this correctly. We have a t-value of 0.211, p value of 0.838, and df value of 40. Even though the critical value for p=0.05 and df=40 is 2.02, do we say that we don't reject the null hypothesis because it probably won't go below 0.211? Or are we comparing the t-value and p-value directly, which doesn't seem to make much sense to me?

    • @bolajiadedasola6369
      @bolajiadedasola6369 8 років тому

      no

    • @bolajiadedasola6369
      @bolajiadedasola6369 8 років тому +2

      we are looking at the value of the t stat and the t critical

    • @bolajiadedasola6369
      @bolajiadedasola6369 8 років тому +2

      if t stat is less than t critical, you don't reject null hypothesis and vice versa. likewise, you can use p-value and alpha value to make judgment as well. if your pvalue is greater than your alpha value, you must not reject your null hypothesis.

    • @patelkumar3524
      @patelkumar3524 7 років тому

      the p value and t value both go inverse to each other

    • @karansingh-nn1zv
      @karansingh-nn1zv 6 років тому

      thank you sooooo much. these 3 lines by bolaji enabled me to get rid of all doubts.

  • @sujinpark2623
    @sujinpark2623 7 років тому

    I think you are the best in the industry! I speak Korean and English, but I am not confident of translating this to professional words in Korean. One day, I want to be able to help you with this! Thank you, You save me for this class ( my professor is very poor at explaining! )

  • @ksparikh9807
    @ksparikh9807 8 років тому +69

    BOZEMAN BACK AT IT AGAIN WITH THE SCIENCE ;)

    • @Bozemanscience1
      @Bozemanscience1  8 років тому +37

      +Ks Parikh Been traveling for the last few weeks. Feels nice to be home uploading videos again.

    • @ksparikh9807
      @ksparikh9807 8 років тому +8

      +Bozeman Science
      people like us always love the science, statistical analysis and other education videos
      Thanks Bozeman

    • @AA-ge6vo
      @AA-ge6vo 6 років тому

      هه

    • @AA-ge6vo
      @AA-ge6vo 6 років тому

      اوحه

  • @calm_compost
    @calm_compost 2 роки тому +1

    Came for the t-test, stayed in awe seeing the capabilities of excel..😄

  • @sujinpark2623
    @sujinpark2623 7 років тому +4

    the link to the excel file does not work. it says 'File not found
    Sorry, that file doesn’t live here anymore. It might have been moved or made private.'

  • @mackeylin9387
    @mackeylin9387 Рік тому +1

    For those of you who don’t quite get the null hypothesis (H0) yet… Essentially, rejecting it means that the data you found is NOT due to random error. Which means that the difference you’re seeing is real and not something that happened by chance.

  • @erikazetina8857
    @erikazetina8857 8 років тому +39

    I would like to know about ANOVA

  • @brianwisniewski9012
    @brianwisniewski9012 3 роки тому

    Commenting to help the algorithm. Thank you! This was clear, concise, and thorough.

  • @keonkim
    @keonkim 3 роки тому +3

    This was incredibly helpful! Thank you so much for this amazing lesson!

  • @codybitme
    @codybitme Рік тому

    For someone who just wants to brush up on my old statistics (and have fun), i get this the first time. Omg thanks.

  • @ButterflySimmer
    @ButterflySimmer 5 років тому +13

    "use a spreadsheet" oh I wish 😂. Gotta do this in my exam 😂. Thank you.

    • @loveurself.speakurself.1017
      @loveurself.speakurself.1017 5 років тому

      You have done your test already but if you were allowed to use a calculator than it could have done it for you.

  • @vivichan3930
    @vivichan3930 5 років тому

    I have been reading biostats for 3 hours and this one video cleared all my queries regarding mean, sd, variance, t test, tests of significance altogether

  • @Tominatorr
    @Tominatorr 8 років тому +6

    Thanks Mr. Bozeman! You really helped me out! I have actually been studying this and I could never understand it.

  • @jameskim5716
    @jameskim5716 4 роки тому

    Thank for your short lecture, it is the best t- test lecture that i have ever seen.

  • @marj736
    @marj736 8 років тому +7

    I found this video too late. I have just passed my STAT class. This video would have helped.

  • @afolabiadetoun2860
    @afolabiadetoun2860 2 роки тому +1

    You are simply the best teacher in the world, you just made my life very easy right now. Your explanation is amazing!! Every step is so simple, straightforward and less stressful. God bless you for this video.
    How complicated some teachers can be? They make things so hard to learn and scary such that I feel like flying away..Haba.... Please make videos on SPSS, R and non-parametric test such as Mann-Kendall test whenever you have the time. Remain great!!

    • @adebayoolufemi2074
      @adebayoolufemi2074 2 роки тому

      as a graduate student, i was confused on the difference between unpaired and paired samples. Thanks to this video, i understood everything in less than 5mins.

  • @yoshic3177
    @yoshic3177 7 років тому +3

    What does that meeeean?

  • @yubaiyuan4832
    @yubaiyuan4832 2 роки тому

    Thank you for helping my interview!

  • @Amiinerz
    @Amiinerz 8 років тому +17

    GOD BLESS YOU

  • @mohammedluqman6954
    @mohammedluqman6954 7 років тому +2

    Your explanation is simply amazing, in the sense that you answer any question that pops up in my mind at any point of doing the solution! a heartfelt thank you!

  • @hitylerlake
    @hitylerlake 7 років тому +19

    I injected mariweed and I dieded

    • @richardwu9013
      @richardwu9013 6 років тому +3

      Which one of your joints had a higher average high?

  • @calebdoner
    @calebdoner 2 роки тому

    Learned more here than the entire statistics course I took in college.

  • @firstnamenotimportant1818
    @firstnamenotimportant1818 7 місяців тому

    first I wanna thank you for the wonderfull explaination , I did the test and it showed me a 0.838 and that indicats No significant difference and we dont reject the null hypothesis

  • @CHANTI8947
    @CHANTI8947 7 років тому

    Best 10 min explanation of any statistics concepts so far..I liked the usage of visual aids in explaining and demonstrating the calculations. Thank you!

  • @huseyinyilmaz1155
    @huseyinyilmaz1155 6 років тому

    I have watched many videos about this topic, this one is different. Visualization and simple explanation make this difference. Thank you,​ Mr.Bozeman

  • @georgewang7770
    @georgewang7770 5 років тому +1

    WOW. This is the best explanation I have come across so far. Thank you so much. The analogy SNR is fabulous.

  • @dddivi84
    @dddivi84 7 років тому

    i was long searching for a video on statistics. none of them explained as simple n neat as you sir.. thanku so much. you are an awesome teacher..

  • @kylefisher-grant9806
    @kylefisher-grant9806 7 місяців тому

    This was great-- Nice work on this video. I've been a teacher for a long time and you really hit all the bases-- Thanks for this!

  • @toyinkezia5181
    @toyinkezia5181 3 роки тому +2

    Hello, I tried clicking the link for the excel file but I couldn't find it anymore

  • @marksbluerpd
    @marksbluerpd 2 місяці тому

    Wow, a video that actually explains how this works. Who would’ve thought

  • @salvadorassar7170
    @salvadorassar7170 6 років тому

    I swear this guy has gotten me out of so many academic jams! Teach on brother !!!

  • @amalraj4157
    @amalraj4157 3 роки тому

    You don't know know how helpful this is. Thanks a lot❤❤

  • @villejunttila1425
    @villejunttila1425 2 роки тому +1

    Thank you so much for actually explaining the equation. First time I've seen this. It's so difficult for me to use a formula without understanding why it looks the way it does!

  • @nominkh3346
    @nominkh3346 6 років тому +2

    These kind of videos make me feel like we should drop the unis and get the true knowledge through an UA-cam :) thanks for the great video !