It would have helped prevent confusion if he had made sure to point out earlier that the denominators are pool sizes and not just arbitrary numbers used to represent the ratio.
Sure, you could figure it out from the fact that the fractions aren't simplified, or from the fact that he SAYS that's what the numbers meant toward the end, but apparently not everyone is that observant.
@BrickChickens: It's not that he is adding the fractions, remember that this is a trial to determine how many people are cured out of a "pool" of individuals. In the two trials 90 people are tested for drug a, 10 for drug b for trial one, and 10 people for drug a, and 90 people for drug b in trial two. If you add the results together, overall 100 people are tested for both drugs, however the results are that drug a cures more people than drug b does testing the same amount. Hence the result.
This comment has received too many negative votesshow
You americans are such a fucking idiots. B drug IS in fact a better drug than A. You can't just add 8/10 + 45/90 like a 5 years old child would do and get a wrong result (53/100) Instead if you calculate it normally you'll get 117/90 OR 128,7/100 if you prefer. That's why there's no fucking way that drug A beats drug B. The uploader is a fucking joke, he trolled all of you.
@RUL1S88 So its efficiency is above 100%. Could you explain what that means in terms of number of people cured out of 100? Also, how the hay did you get the number 117 / 90?
Please Read: Are you wondering how 63/90 + 4/10 = 67/100? It doesn't, but that's NOT the equation he's giving us. The proper equation is 63 + 4 / 90 + 10. This equation DOES equal 67/100. Don't think of math as applying the proper equations to certain problems; instead, think of math as a problem, where you must figure out the equation. If someone can rephrase my last sentence so it's easier to understand, that would be greatly appreciated.
@Zolbat, just forget % for a moment: cure A cured 63 and 4 people, cure B 8 and 45.
And if you want to think about percentage, think about this: compare the percentage when it's reasonable to. Meaning compare the % when the group of people is of the same size:
A: 63/90 while B:45/90
A: 4/10 while B: 8/10
Even from the percentage you can say that cure A on a larger scale is more efficient than cure B.
Just my 2 cents!
P.S. this percentage aren't pure numbers e.g. 1/10 it's not the same as 10/100
I still find Simpson's paradox amazing. I use it as an example that intuitively obvious statements can be false when trying to motivate proof.
I like the example here (partly because the percentages come out nicely without a calculator!). But with such inconsistent performances, I'd want to know if there was some hidden reason why the drugs had both done so much better on day1 than on day 2. If there was, then the overall figures would be unfair on drug B.
I am quite good at mathematics (studying computer science, which contains a lot of that) but to be honest, I don't get what you did there. is this a prank?
no but honestly could you explain it a little better? why are (for A) there only 90 people tested at Day one? where are the other 10? why is it wrong to think in percentages? if it was a medical study you always work with percentages. I'm confused.
im just dumbfounded by the amount of idiocy in the comments. those of you who think that this guy is adding fractions are just plain stupid. maybe its too complex for your puny little brains. go watch dumb videos on youtube.
i feel like you are trolling, obviously the the numbers were taken out of a group surveyed, meaning that this would always be percentage wise, because in lets say the case of drug b being 8/10(80%) if you were to up the group surveyed to for example 50, the number cured would be 40/50, making the results biased, to get an accurate result you would have to survey the same number of people on both days for both drugs to be accurate. and yes i understand that this is a paradox and only hypothetical
@MrHellTard He's not trolling. This paradox is the fundamental basis of the phrase "lies, damned lies and statistics." A number of pharmaceutical companies -- not the majority -- have slipped drugs through the FDA by exploiting this problem -- leading to several class-action lawsuits in the past -- and it's how nearly all of Fox News' sources hide their lies.
@KsClan1234 The fractions mean: 63 people cured of the 90 people and 4 people of the 10. So in total over the 2 days, 100 people got the medication, and 67 got cured.
I thought this was pre portions. wouldn't you have to use common denominators. because 4/10 isn't 4 percent it's 40 percent so i still don't understand how this makes sense to anyone
@dpap314 This is called statistics, it uses the total number of people tested (90 first, 10 second or vice-versa) and looks at their scores as a whole. The equations are not a/A + b/B but (a+b)/(A+B). If you treated them as 1 test instead of 2 you will recieve the answer he gives.
@bansheeflier1015 Ok with out the same # of people you wont be able to compare to results every thing must be the same and only one varible can be dependant ( i think thats the one that is changed pourposley)
Hope my earlier two comments didn't seem too rude. I'm not trying to say that you're all not smart. You're all using the right arithmetic. It's just not what fits the situation. As he says: "It's important you're able to interpret your results correctly."
What cumulative means is that you can't find a common denominator between two fractions. You have to add straight across because the amount of data is increasing each day. Example: Day 1 results: 63/90. Day 2 results: 4/10. This means that out of the total of the two days: 100 people were given the drug, 67 were cured. A mathematical view of it: (63+4)/(90+10)=67/100=67%.
Think of it this way before you post your confusion. The numbers in these fractions all represent tangible objects; in this case, people. The numerator is the number of people that were cured on a certain day. The denominator is the total number of people that were given the drug on a certain day. When adding these sort of "Situational Fractions" you don't use your conventional method: Find common denominator, blah blah. The results are cumulative, which I'll explain in my next comment.
The problem a lot of the commenters are having is that your scenario is unclear. At first, I thought you meant that each drug was given to 100 people on day 1, and drug A cured 63 people the first day and 4 more the second day; similarly with drug B. But that didn't square with the 63 of 90 bit. What I think I understand now is that drug A was given to 90 people on day 1 and 10 on day 2, and the opposite with drug B.
This confusion was exacerbated by labeling the two trials as "Day 1" and "Day 2" rather than "Trial 1" and "Trial 2".
And, of course, if you reverse the days for drug A, so the same number of subjects is getting each drug during each trial, it's much easier to see why drug A is the correct choice. Small-number statistics has shown its bite.
numbers dont make sense, if u compare everything while having 90 in the denominator you get day 1 - drug a 63/90 and drug b 72/90 day 2 drug a 36/90 and drug b 45/90, your curing more people then the amount of people with the disease!
Oh!! DRUG... not JOKE. Makes a lot more sense now. I was sitting here thinking more about "that's one hell of a JOKE if it cures people!" than the actual problem. lol
It's appalling how many people how many people try to correct you, even though you are right, which is really no surprise given you're a mathematician...
People really need to stop considering themselves experts in just whatever subject they have an opinion of!
Your videos are a great attempt at educating the world!
(BTW: I would love to see you talk about real group theory, I really hope you would, it would be without a doubt extremely interesting!)
Even though drug A on the first day has a less percentage, It has cured more people and a better percentage compared to Drug B's 90 people with only 50%
omfg you're such a fucking idiot. You can't just sum numbers like that, by doing so you get AN ERROR! I can't even imagine how the fuck you can take those numbers in overall, that's an obvious mistake, only dumb americans like you will think this is correct.
@singingbanana vinnyc is actually right. even tough it seems strange, drug B is owning. I mean, if I used your way of solving stuff, then 1/2 + 2/4 = 3/6 which is totally wrong, as 0.5 + 0.5 = 1, not 0.5 :P
He explains that this is what we observe. Just think, if you have a drug that will cure 1/2 on day one and 1/2 again on day two, you won't cure everyone, you'll cure half of those coming in on the first day and half of those coming in on the second day, which means half of all.
Hey, I understand it. Kind of. To get the "efficiency" you count the people coming in on a day and divide the people cured by it, to get the total you use the totals of both and then divide.
I must then ask the question, what about people not cured the first day? They'll come back, and they could survive that long, so why are they not counted?
@AdolfHitlerGaming Dear Adolf, I attempt to murder 10 people in Germany, I succeed in killing one. The next day, I attempt to kill 100 people, I succeed in killing one. According to your system of analysis on a problem like this, I killed 11 out of 100. We're not adding 1/10 and 1/100. We're finding the average rate of success between our two results; the percentage.
Meaning, from your example, you cure 1 out of 2, then 2 out of 4. You cured half of them; a 1/2 success rate.
@vinnyc88934 are you for real?? Total sample size in both tests is 100 people. You cannot just add the fractions. Adding the fractions is the same as adding the percentages. Take the total sample. I really do hope you were not being for real. Sad day for society if you were not.
@vinnyc88934 That's why he says you have to look at the TOTAL NUMBER. Not the 2 seperate. That's where your logical goes wrong: 63/90+4/10 is indead 67/100 and NOT 11/10, which in fact is impossible
if you switched the amounts of people so that you gave more people drug b on day 1 and more people drug a on day 2, wouldn't your results be vastly different? and over a number of tests where the numbers of people are always different, wouldn't they average out so that the percentages really matter rather than this final result?
@singingbanana A "7" with a strike through it makes it look rather much less of a number and pisses me off when people do it. Where is when you write the number "1" with a line on the base of it. If you type the number "1" It only has a little curve at the top of it, no base platform thing. Both of these just makes those two numbers look absolutely stupid.
you're still missing the point. It is not a paradox, no, thats what I said. There is no adding fractions together. You're taking the average of 70% and 40% and the average of 50% and 80% without weighing them. Starting to think you're a troll.
You really need to learn basic math before uploading an video! You cannot just add x/10 and x/100... you need to even it first so you can add up, so its 10X/100 + X/100= 11X/100... So its: Drug A saves 103 people and drug B saves 125 people... You fail at math...
... but on the other hand, I like how green (thumbs up) bar represents the math "knowledge" of average YouTube user... So you kinda win with this video :D
@D3w10n Well done, but I'm not adding the fractions together. 63/90 = 70% plus 4/10 = 40% is 110%. If you did add the fractions together the answer would be nonsense (or it's a drug that cures 110% of people! Wow!) . Altogether, drug A cures 67/100 people, that's 67%. Please think about the maths more clearly before judging.
@singingbanana Yes, but in that case you did a test on 200 people, so you cannot really add percentages if there were different conditions... if you did test on same people, than it would be 40% of the 63 people that survived in the first case, so its 63/90~75% (74.44%), so on 100 people ~ 75 survives... and when you subtract 60% on that you get that 30 people... On second case its 40 people... Before doing all this you should find a common division for numbers 10, 90 and 100, and that is 900...
@D3w10n ... than it goes 630900=70%; 360/900=40%; 720/900 and 450/900 (this is necessary for adding; you can only add up fractions with same base)... Your "paradox" happens when there are different number of people under different conditions, and that's why drug A saves more people than Drug B... Even if drug B is more efficient... in this case you use average efficiency (55%A; 65%B; not 110%A and 130%B)... if you test this correctly you will see that everything is correct and no paradoxes here.
@D3w10n you are exactly the reason why this is a 'paradox'. Simple misinterpretation of facts. He is not 'adding' fractions, he is totalling the number of people cured and the total number of people applied. If he were to add fractions like you are, you obv get the wrong answers and this creates the 'paradoxialishness' of this problem.
@frankvdg But that this is not paradox, this is simple math! If you gave 80% cure to 100 people and deadly poison to 10 people, and cure "kills" 20 people and poison kills 10; using his "method" it would came out that is better for all of us to just kill ourselves! (no stupid Reply please)
@D3w10n he isn't adding fractions, he is adding a total of people so in the first day drug A get 63 of 90 and in the second day get 4 of 10 so the number of subject is 100 and the saved ones is 67, as you can see in Drug B xD
@D3w10n drug A does not literally saves people 103 ...it save 55%.....while drug B saves 65%....either way your both wrong i guess...because you timed the 4 and 8 by 10 then u added up...what you actually have done was only times by 9
Didn't get this one... If the drug B is most effective on day 1, but is only applied to 10 people while the drug A is applied to it's fullest (applied to the most people when it's most effective), it's normal that drug A would have better results.
But what you get from there is not that drug A is better, but that drug B is not using it's 'full power'.
I really enjoyed this one! I can't tell you how many medical based statistics I've seen over this past year. This video put a smile on my face. =) Thanks!
There is a far easier way to solve this. On day 1 drug A cures 63% of people or 63/100 while drug b cures 8% 8/100 people. On day 2, same thing, drug A cures 4% while drug B cures 45%. But if you take it out of 200 drug A cures 67/200 while B cures 53. This however assumes that the 90 in day 1 are different from the 10 in day one and vice versa in day two and that the 100 in day 1 are different than the 100 in day 2. These are safe assumptions to make as any medical statistician will tell you
@projektaquarius This is a way of getting to the right answer in the wrong way, will confuse everyone and gives people and false mathemetical sense. There are no 100 people on day 1 in group A, and neither in group B, there are 90 and 10 people. The correct way to understand this, which also becomes apparent when you think about the problem, is that all percentages gotten have a certain weight/importance. The 80% in day B1 looks great, but you should realize that it was only tried on 10 people,
@frankvdg so it's not very large in importance. In fact, the percentage gotten in day 2B is 9 times more important. If we calculate by weight we get 1x80%+9x50% = 530. divide by 10 weight parts = 53. Mr. singingbanana has explained it well. The thought to keep in mind is that not all percentages in the problem are as important/weight as much.
After an initial 'WHAT?!', I can finally agree with your conclusion. But anyway I have another question (as I'm not a native english speaker). You say 'cured x out of y people' - does this always mean, you tested exactly y people?
Otherwise it's crucial (al least I think so) to mention, that the trials were exactly carried out with y people. I'm not a mathematician but an engineer, so forgive me any stupid questions.
@Neatod He says cures. The whole time I was wondering what kind of sick world this is where the drug that kills more people 'wins'. Then I realized he was saying cures.
I showed this to my dad, he said "the people don't matter it's the percent" I said "but they're comparing unlike things, only 10 people took the drug b on day 1, while 90 took drug A" his response"numbers don't matter, percent matters" me "well if 1 basket ball player took one shot, and made a 3 pointer, and another took 15, and made 10 3 pointers, which would you pick?" dad "these are to very different things" HOW? (I was interrupted when my mom made me leave)
It would have helped prevent confusion if he had made sure to point out earlier that the denominators are pool sizes and not just arbitrary numbers used to represent the ratio.
Sure, you could figure it out from the fact that the fractions aren't simplified, or from the fact that he SAYS that's what the numbers meant toward the end, but apparently not everyone is that observant.
ZizooMoDaI 6 hours ago
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dbrckovic 13 hours ago
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dbrckovic 13 hours ago
fuck... I'm going to sleep.
3463sl 15 hours ago
nice
lyac 21 hours ago
@BrickChickens: It's not that he is adding the fractions, remember that this is a trial to determine how many people are cured out of a "pool" of individuals. In the two trials 90 people are tested for drug a, 10 for drug b for trial one, and 10 people for drug a, and 90 people for drug b in trial two. If you add the results together, overall 100 people are tested for both drugs, however the results are that drug a cures more people than drug b does testing the same amount. Hence the result.
DirtyWhyteBoy 1 day ago
Outdated pop culture references from 15 years ago (which I totally lived through) + Danger Mouse tee shirt = PURE AWESOME
e2theeyepie 1 day ago
I want to be you when I grow up
JacobShulman 1 day ago
Wait... I'm pretty sure you added the fractions wrong. You can't just add the denominators, you have to find a GCF, right? Correct me if I'm wrong.
BrickChickens 1 day ago
@singingbanana
In other words, you have to take a weighted average of the probabilities(0.9*0.7+0.1*0.4=0.67 compared to 0.1*0.8+0.9*0.5=0.53)
siddharthjoshi91 2 days ago
Well actually no I can't say that. Recklessly using weighted averages is not the way to go.
notThePiper 2 days ago
weighted averages are fucked up
notThePiper 2 days ago
im rly growing on all these interesting maths vids :D
therealjordiano 3 days ago
This comment has received too many negative votes show
You americans are such a fucking idiots. B drug IS in fact a better drug than A. You can't just add 8/10 + 45/90 like a 5 years old child would do and get a wrong result (53/100) Instead if you calculate it normally you'll get 117/90 OR 128,7/100 if you prefer. That's why there's no fucking way that drug A beats drug B. The uploader is a fucking joke, he trolled all of you.
RUL1S88 3 days ago
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halcyonacoustic 3 days ago
@halcyonacoustic no they are fractions which is the ratio of 2 integers.....
qwert4327able 2 days ago
@RUL1S88 So you're saying that if 100 people are treated with drug B, 128,7 people are cured? You must realise this is imposible.
MinecraftPuzzleMaps 3 days ago
@MinecraftPuzzleMaps
That's a percentage of effectiveness, not the number of people cured.
RUL1S88 3 days ago
@RUL1S88 So its efficiency is above 100%. Could you explain what that means in terms of number of people cured out of 100? Also, how the hay did you get the number 117 / 90?
MinecraftPuzzleMaps 2 days ago
@RUL1S88 How do you cure 117 people out of 90 people? You're fucking stupid.
skinn44 3 days ago
@RUL1S88 Not sure if trolling or just stupid...
DanyKreep 1 day ago
@RUL1S88 Stop embarassing yourself
MrBronyface 1 day ago
@MrBronyface
I'm not, but you are.
RUL1S88 1 day ago
@RUL1S88 Really.... REALLY?!
haloKINGSstudios 1 day ago
@haloKINGSstudios
HIV positive.
RUL1S88 1 day ago
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MrBronyface 1 day ago
This has been flagged as spam show
@RUL1S88 excellent comeback, because I'm the one with the negative votes
MrBronyface 1 day ago
@RUL1S88 LOOOOOOOOOL
LamaPaj 1 day ago
Please Read: Are you wondering how 63/90 + 4/10 = 67/100? It doesn't, but that's NOT the equation he's giving us. The proper equation is 63 + 4 / 90 + 10. This equation DOES equal 67/100. Don't think of math as applying the proper equations to certain problems; instead, think of math as a problem, where you must figure out the equation. If someone can rephrase my last sentence so it's easier to understand, that would be greatly appreciated.
NoNameC68 3 days ago
@Zolbat, just forget % for a moment: cure A cured 63 and 4 people, cure B 8 and 45.
And if you want to think about percentage, think about this: compare the percentage when it's reasonable to. Meaning compare the % when the group of people is of the same size:
A: 63/90 while B:45/90
A: 4/10 while B: 8/10
Even from the percentage you can say that cure A on a larger scale is more efficient than cure B.
Just my 2 cents!
P.S. this percentage aren't pure numbers e.g. 1/10 it's not the same as 10/100
JohnThePetru 5 days ago
I still find Simpson's paradox amazing. I use it as an example that intuitively obvious statements can be false when trying to motivate proof.
I like the example here (partly because the percentages come out nicely without a calculator!). But with such inconsistent performances, I'd want to know if there was some hidden reason why the drugs had both done so much better on day1 than on day 2. If there was, then the overall figures would be unfair on drug B.
JoelFeinstein 5 days ago
go duff man lol
stephenoes 5 days ago
I am quite good at mathematics (studying computer science, which contains a lot of that) but to be honest, I don't get what you did there. is this a prank?
no but honestly could you explain it a little better? why are (for A) there only 90 people tested at Day one? where are the other 10? why is it wrong to think in percentages? if it was a medical study you always work with percentages. I'm confused.
Zolbat 6 days ago
I facepalmed so much reading only 1 page of comments... come on now people, use your brains before you write something stupid :/
pilchtastic 6 days ago 12
I wish the people saying he was wrong would realize that he's not adding fractions. :o
ColdIce009 1 week ago
Is this the guy from the Numberphile channel?
TheBrimic 1 week ago 2
@TheBrimic Yes.
QuasiBelgium 1 week ago
im just dumbfounded by the amount of idiocy in the comments. those of you who think that this guy is adding fractions are just plain stupid. maybe its too complex for your puny little brains. go watch dumb videos on youtube.
shyrwinsteelsia 1 week ago 2
Danger Mouse shirt, ftw
joeloud1 1 week ago
backlighting makes the subject too dark. Shoot with light on the subject to correct.
PlasteredDragon 1 week ago
You remember me of someone... Sheldon?
finster796 2 weeks ago 2
DANGER MOUSE!
HaslamCorp 2 weeks ago
i feel like you are trolling, obviously the the numbers were taken out of a group surveyed, meaning that this would always be percentage wise, because in lets say the case of drug b being 8/10(80%) if you were to up the group surveyed to for example 50, the number cured would be 40/50, making the results biased, to get an accurate result you would have to survey the same number of people on both days for both drugs to be accurate. and yes i understand that this is a paradox and only hypothetical
MrHellTard 2 weeks ago
@MrHellTard He's not trolling. This paradox is the fundamental basis of the phrase "lies, damned lies and statistics." A number of pharmaceutical companies -- not the majority -- have slipped drugs through the FDA by exploiting this problem -- leading to several class-action lawsuits in the past -- and it's how nearly all of Fox News' sources hide their lies.
MultiPaulinator 1 week ago
Thats very simple.. (63/90)+(4/10) does not equal (67/100), because those two fractions do not have like denominators
KsClan1234 3 weeks ago
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@KsClan1234 The fractions mean: 63 people cured of the 90 people and 4 people of the 10. So in total over the 2 days, 100 people got the medication, and 67 got cured.
HerrCaZini 2 weeks ago 2
@KsClan1234 He wasn't adding the fractions; he summed up total number of people cured and then the total number of people altogether for Drug A.
64+4=67 cured people
90 people (day one) + 10 (day two) people = 100 all together
Common sense should tell you that 70% + 40% can't be possible.
MrXenitha 2 weeks ago
very well explained !!! thanks for posting.
sg04f 3 weeks ago
It's a terrible experiment that's the problem. I guess the testers have never heard of keeping the variables constant.
xNajda 1 month ago
Every time you say "cure," to my stupid American ears, it sounds like "kills"
Azkadaz 1 month ago
Well that's 3:39 of my life I'll never get back
ugadawg777 2 months ago
I thought this was pre portions. wouldn't you have to use common denominators. because 4/10 isn't 4 percent it's 40 percent so i still don't understand how this makes sense to anyone
or at least thats why i learned in my school
dpap314 2 months ago
@dpap314 This is called statistics, it uses the total number of people tested (90 first, 10 second or vice-versa) and looks at their scores as a whole. The equations are not a/A + b/B but (a+b)/(A+B). If you treated them as 1 test instead of 2 you will recieve the answer he gives.
PoketoMtg 1 month ago
This has been flagged as spam show
SHELDON!
nuthigg00d 2 months ago
well i dont thing that honestly fair. your not using the same # of people . . . per day and per drug use
Brandon101Realize 2 months ago
@Brandon101Realize As he explains in the video, it's not about each individual day, it's about both days together.
bansheeflier1015 1 month ago in playlist More videos from singingbanana
@bansheeflier1015 Ok with out the same # of people you wont be able to compare to results every thing must be the same and only one varible can be dependant ( i think thats the one that is changed pourposley)
Brandon101Realize 1 month ago
@bansheeflier1015 or atleast compare them accuratley
Brandon101Realize 1 month ago
I love this guy. If he is my classmate, He would be my bestfriend.
MrGreedIsGood 2 months ago
@MrGreedIsGood he's a teacher actually :p
Sandman267 2 months ago
At the begining i could not understand if he said kills or cures...
FluffyKittenMittens 2 months ago
Hope my earlier two comments didn't seem too rude. I'm not trying to say that you're all not smart. You're all using the right arithmetic. It's just not what fits the situation. As he says: "It's important you're able to interpret your results correctly."
MJBfromCCC 2 months ago
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MJBfromCCC 2 months ago
What cumulative means is that you can't find a common denominator between two fractions. You have to add straight across because the amount of data is increasing each day. Example: Day 1 results: 63/90. Day 2 results: 4/10. This means that out of the total of the two days: 100 people were given the drug, 67 were cured. A mathematical view of it: (63+4)/(90+10)=67/100=67%.
MJBfromCCC 2 months ago
Think of it this way before you post your confusion. The numbers in these fractions all represent tangible objects; in this case, people. The numerator is the number of people that were cured on a certain day. The denominator is the total number of people that were given the drug on a certain day. When adding these sort of "Situational Fractions" you don't use your conventional method: Find common denominator, blah blah. The results are cumulative, which I'll explain in my next comment.
MJBfromCCC 2 months ago
Comment removed
MJBfromCCC 2 months ago
The problem a lot of the commenters are having is that your scenario is unclear. At first, I thought you meant that each drug was given to 100 people on day 1, and drug A cured 63 people the first day and 4 more the second day; similarly with drug B. But that didn't square with the 63 of 90 bit. What I think I understand now is that drug A was given to 90 people on day 1 and 10 on day 2, and the opposite with drug B.
Oh, and let me not fail to say, "DangerMouse!"
pseudorandomly 2 months ago
This confusion was exacerbated by labeling the two trials as "Day 1" and "Day 2" rather than "Trial 1" and "Trial 2".
And, of course, if you reverse the days for drug A, so the same number of subjects is getting each drug during each trial, it's much easier to see why drug A is the correct choice. Small-number statistics has shown its bite.
pseudorandomly 2 months ago
Comment removed
pseudorandomly 2 months ago
It's even easier to comphrehend if you change the numbers a little bit:
Imagine giving the cures to only 2 guys (one A and one B) on day one:
The one who got B was cured and the other wasn't. This means that B has a 100% successrate compared to the 0% of the A cure.
On day 2, give the drugs to two groups of 99 people:
The A drug cures 98 people and B crues none.
So, considering seperate days, A had 0%/98,8% successrate while B had 100%/0%. Yet, B cured 1 guy and A cured 99. I'd pick A!
ZiqqiPH 2 months ago
Well if you're going to die on day one from poor drug efficiency from drug A, might as well use drug B?
razerburst 2 months ago
numbers dont make sense, if u compare everything while having 90 in the denominator you get day 1 - drug a 63/90 and drug b 72/90 day 2 drug a 36/90 and drug b 45/90, your curing more people then the amount of people with the disease!
kvn89 2 months ago
lol im not used to british accents, i hear joke instead of drug, and kills instead of cures :)
thedarrch 3 months ago
great video. this happens ALL the time... the punchline is that variability is important.
joeyavankuiken 3 months ago
Wow...your smart!
saramadi100 4 months ago
I dont see the paradox.
Eckendenker 5 months ago
Oh!! DRUG... not JOKE. Makes a lot more sense now. I was sitting here thinking more about "that's one hell of a JOKE if it cures people!" than the actual problem. lol
IbeLangley 5 months ago
I love how you bring it. keep up the great work you have inspired me.
tastyrInc 5 months ago
this really helped! thank you for not being confusing and not going all mr.-math-professor-with-statistical-vocabulary on us!!! ;)
zaffroni 5 months ago
It's appalling how many people how many people try to correct you, even though you are right, which is really no surprise given you're a mathematician...
People really need to stop considering themselves experts in just whatever subject they have an opinion of!
Your videos are a great attempt at educating the world!
(BTW: I would love to see you talk about real group theory, I really hope you would, it would be without a doubt extremely interesting!)
ImaginaryMdA 5 months ago 2
Even though drug A on the first day has a less percentage, It has cured more people and a better percentage compared to Drug B's 90 people with only 50%
LakersBeast22 5 months ago
*facepalm* so many fails ...
Flubadoodoo 6 months ago
Watch the video again and listen to what he says.
"OVERALL, Drug A cured 67 out of 100 people."
"OVERALL, Drug B cured 53 out of 100 people."
He didn't say, "Let's add two percentages together to get a meaningless number!"
rowseeden 6 months ago 9
@rowseeden
omfg you're such a fucking idiot. You can't just sum numbers like that, by doing so you get AN ERROR! I can't even imagine how the fuck you can take those numbers in overall, that's an obvious mistake, only dumb americans like you will think this is correct.
RUL1S88 3 days ago
I see... Indeed, the given fraction/percentage sample given, doesn't give a dyagnosis of the totality.
Cookielooky 6 months ago
Ahhh, starting to remember my stats class. lol.
neogeo328 6 months ago
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Lol fail, you can't even sum numbers correctly.
RUL1S88 6 months ago
@RUL1S88 Quickly. I am not adding the fractions which is why I do not say the word 'add'.
singingbanana 6 months ago 44
@singingbanana
sum and add are not the same thing you asshole!
RUL1S88 3 days ago
@RUL1S88 i love it when some people think they can best a cambridge mathematician on basic arithmetic.
mignik01 3 days ago 13
common denominator, people.. that is all u need
LuiBui 7 months ago
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63/90 + 4/10 is not 67/100, it's actually 99/90 which is 11/10
8/10 + 45/90 is not 53/100, it's actually 117/90 which is 13/10
So Drug B is the better drug, not Drug A.
vinnyc88934 7 months ago
@vinnyc88934 According to your arithmetic, Drug B cures 130% - that's a very good drug.
singingbanana 7 months ago 108
@singingbanana I guess it is a very good drug lol
But do you see what I am getting at?
vinnyc88934 7 months ago
@singingbanana XD
Everyvideo123 5 months ago
@singingbanana Owned!
MechanismProduction 3 months ago
@singingbanana vinnyc is actually right. even tough it seems strange, drug B is owning. I mean, if I used your way of solving stuff, then 1/2 + 2/4 = 3/6 which is totally wrong, as 0.5 + 0.5 = 1, not 0.5 :P
AdolfHitlerGaming 1 week ago
@AdolfHitlerGaming
He explains that this is what we observe. Just think, if you have a drug that will cure 1/2 on day one and 1/2 again on day two, you won't cure everyone, you'll cure half of those coming in on the first day and half of those coming in on the second day, which means half of all.
Hey, I understand it. Kind of. To get the "efficiency" you count the people coming in on a day and divide the people cured by it, to get the total you use the totals of both and then divide.
Quintinohthree 1 week ago
@Quintinohthree
I must then ask the question, what about people not cured the first day? They'll come back, and they could survive that long, so why are they not counted?
Quintinohthree 1 week ago
@AdolfHitlerGaming Dear Adolf, I attempt to murder 10 people in Germany, I succeed in killing one. The next day, I attempt to kill 100 people, I succeed in killing one. According to your system of analysis on a problem like this, I killed 11 out of 100. We're not adding 1/10 and 1/100. We're finding the average rate of success between our two results; the percentage.
Meaning, from your example, you cure 1 out of 2, then 2 out of 4. You cured half of them; a 1/2 success rate.
WoahItsTibig 1 week ago
@vinnyc88934 wtf your math is so wrong its funny
shadows1029 6 months ago
@vinnyc88934 are you for real?? Total sample size in both tests is 100 people. You cannot just add the fractions. Adding the fractions is the same as adding the percentages. Take the total sample. I really do hope you were not being for real. Sad day for society if you were not.
euphoria651 5 months ago 2
@vinnyc88934 he is not adding the fractions, he adds up the people, who were cured...
perfectarif 5 months ago
@vinnyc88934 That's why he says you have to look at the TOTAL NUMBER. Not the 2 seperate. That's where your logical goes wrong: 63/90+4/10 is indead 67/100 and NOT 11/10, which in fact is impossible
yabeva 1 month ago
@vinnyc88934 you are an idiot.
house1098 3 weeks ago
@vinnyc88934 How on earth have you got it so wrong? I dont understand in the slightest.
Surely you must have figured you got it wrong when you had a success rate higher than 100%.
passwordresetisbroke 6 days ago
That's not the way to add fractions my friend
vinnyc88934 7 months ago
This why you have controls :P
TheSniperofDeath 7 months ago
if you switched the amounts of people so that you gave more people drug b on day 1 and more people drug a on day 2, wouldn't your results be vastly different? and over a number of tests where the numbers of people are always different, wouldn't they average out so that the percentages really matter rather than this final result?
pocketsk3824 7 months ago
Comment removed
auiuiuify 7 months ago
How often did you get in trouble for writing a 7 the way you do? (aka writing it almost like a "1") :P
uschi17 7 months ago
@uschi17 That's normal in the UK. I believe 7 with a strikethrough is more common on the continent.
singingbanana 7 months ago 25
@singingbanana A "7" with a strike through it makes it look rather much less of a number and pisses me off when people do it. Where is when you write the number "1" with a line on the base of it. If you type the number "1" It only has a little curve at the top of it, no base platform thing. Both of these just makes those two numbers look absolutely stupid.
Contherage 3 months ago
@singingbanana
Writting 7 like u is good cause we know where it cames from.
How is it to write 5 like this ٥.
MrZbaser 1 month ago
@uschi17 probably never, because he writes the one like a stick =), plus he uses less ink for both digits! a good fact,indeed.
progrocky 6 months ago
Yaaay! Got this one right!.. but then again, its pretty simple..
halokinger 7 months ago
Simple- same effect!
lemonzing234 8 months ago
I fail to see how my way is wrong. Its simple statistical expansion with a little bit of causality.
projektaquarius 8 months ago
you're still missing the point. It is not a paradox, no, thats what I said. There is no adding fractions together. You're taking the average of 70% and 40% and the average of 50% and 80% without weighing them. Starting to think you're a troll.
frankvdg 8 months ago
You really need to learn basic math before uploading an video! You cannot just add x/10 and x/100... you need to even it first so you can add up, so its 10X/100 + X/100= 11X/100... So its: Drug A saves 103 people and drug B saves 125 people... You fail at math...
... but on the other hand, I like how green (thumbs up) bar represents the math "knowledge" of average YouTube user... So you kinda win with this video :D
D3w10n 8 months ago
@D3w10n Well done, but I'm not adding the fractions together. 63/90 = 70% plus 4/10 = 40% is 110%. If you did add the fractions together the answer would be nonsense (or it's a drug that cures 110% of people! Wow!) . Altogether, drug A cures 67/100 people, that's 67%. Please think about the maths more clearly before judging.
singingbanana 8 months ago 38
@singingbanana Yes, but in that case you did a test on 200 people, so you cannot really add percentages if there were different conditions... if you did test on same people, than it would be 40% of the 63 people that survived in the first case, so its 63/90~75% (74.44%), so on 100 people ~ 75 survives... and when you subtract 60% on that you get that 30 people... On second case its 40 people... Before doing all this you should find a common division for numbers 10, 90 and 100, and that is 900...
D3w10n 8 months ago
@D3w10n ... than it goes 630900=70%; 360/900=40%; 720/900 and 450/900 (this is necessary for adding; you can only add up fractions with same base)... Your "paradox" happens when there are different number of people under different conditions, and that's why drug A saves more people than Drug B... Even if drug B is more efficient... in this case you use average efficiency (55%A; 65%B; not 110%A and 130%B)... if you test this correctly you will see that everything is correct and no paradoxes here.
D3w10n 8 months ago
@D3w10n you are exactly the reason why this is a 'paradox'. Simple misinterpretation of facts. He is not 'adding' fractions, he is totalling the number of people cured and the total number of people applied. If he were to add fractions like you are, you obv get the wrong answers and this creates the 'paradoxialishness' of this problem.
frankvdg 8 months ago
@frankvdg But that this is not paradox, this is simple math! If you gave 80% cure to 100 people and deadly poison to 10 people, and cure "kills" 20 people and poison kills 10; using his "method" it would came out that is better for all of us to just kill ourselves! (no stupid Reply please)
D3w10n 8 months ago
@D3w10n Are you part of the red bar then, Mr. Superior?
bugshirt4 7 months ago
@D3w10n owned xD ^^ singingbanana is cool and he makes mathe interresting .look his other vids befor you say that he is bad at math ;)
o0RedBull0o 7 months ago
@D3w10n he isn't adding fractions, he is adding a total of people so in the first day drug A get 63 of 90 and in the second day get 4 of 10 so the number of subject is 100 and the saved ones is 67, as you can see in Drug B xD
ThiagoMarksMendes 7 months ago
@ThiagoMarksMendes Please read my other comments in this video before commenting...
D3w10n 7 months ago
Comment removed
sharuto 7 months ago
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@D3w10n drug A does not literally saves people 103 ...it save 55%.....while drug B saves 65%....either way your both wrong i guess...because you timed the 4 and 8 by 10 then u added up...what you actually have done was only times by 9
sharuto 7 months ago
@D3w10n wow you are so dumb lol
valdas0 7 months ago
@valdas0 And I love the amount of arguments that you put in your comment.
D3w10n 7 months ago
why would this ever be a paradox? let alone a mathemetical one.
adsfasdkjfh 8 months ago
Didn't get this one... If the drug B is most effective on day 1, but is only applied to 10 people while the drug A is applied to it's fullest (applied to the most people when it's most effective), it's normal that drug A would have better results.
But what you get from there is not that drug A is better, but that drug B is not using it's 'full power'.
I don't think this is a fair comparison...
Joao92 8 months ago
Come on, this is not a paradox.It's really easy.
cinqueottavi 8 months ago
When in doubt always choose C
MrTheLBoy 8 months ago
Sample size, it's damn important.
subach 9 months ago
Solution: you can't just add up like that... adding percent and whole numbers are like saying that Obama and Osama should make government...
MrJeberg 9 months ago
mind fuck
Shukria123 9 months ago
I learned this in AP stats! happy to say one of things I knew before hand when watching one of your videos (:
SirWilliamCo 10 months ago
This is exactly why the electoral college system is broken
lokoluis15 10 months ago
and this is how bush won the election...
GhettoAttack1 10 months ago
I really enjoyed this one! I can't tell you how many medical based statistics I've seen over this past year. This video put a smile on my face. =) Thanks!
chrissytinalalala 10 months ago
There is a far easier way to solve this. On day 1 drug A cures 63% of people or 63/100 while drug b cures 8% 8/100 people. On day 2, same thing, drug A cures 4% while drug B cures 45%. But if you take it out of 200 drug A cures 67/200 while B cures 53. This however assumes that the 90 in day 1 are different from the 10 in day one and vice versa in day two and that the 100 in day 1 are different than the 100 in day 2. These are safe assumptions to make as any medical statistician will tell you
projektaquarius 11 months ago
@projektaquarius This is a way of getting to the right answer in the wrong way, will confuse everyone and gives people and false mathemetical sense. There are no 100 people on day 1 in group A, and neither in group B, there are 90 and 10 people. The correct way to understand this, which also becomes apparent when you think about the problem, is that all percentages gotten have a certain weight/importance. The 80% in day B1 looks great, but you should realize that it was only tried on 10 people,
frankvdg 8 months ago
@frankvdg so it's not very large in importance. In fact, the percentage gotten in day 2B is 9 times more important. If we calculate by weight we get 1x80%+9x50% = 530. divide by 10 weight parts = 53. Mr. singingbanana has explained it well. The thought to keep in mind is that not all percentages in the problem are as important/weight as much.
frankvdg 8 months ago
Hey, you got a Danger Mouse shirt, I haven't seen that show in 30 years.
guss1470 11 months ago
Thank you sooo much! You explain the Paradox so easily, I understood it immediately. Neither my book nor google was able to to that ;)
dorospatz 1 year ago
but... drug 2 is better because if the same amount of ppl tried the drugs... like
Day 1:
A:70/100 cured
b:80/100 cured
Day 2
A:40/100
B:50/100
therefore b is better... ovbiously i know that you see this... so i'm just curious how drug a is better??
fatescure 1 year ago
@fatescure
no but you have changed the fraction .. 100 people where not tested in day 1 nor day 2 in a or b.
you are still using the percentages, but in another form.
the trick is to not multiply both numerator and denominator but, add another fraction to your current one to bring it up to the wanted denominator
MasterA55a55in 11 months ago
woah...
ballcapmusicbox 1 year ago
I love the simpson paradox!
BryceKurtis 1 year ago
After an initial 'WHAT?!', I can finally agree with your conclusion. But anyway I have another question (as I'm not a native english speaker). You say 'cured x out of y people' - does this always mean, you tested exactly y people?
Otherwise it's crucial (al least I think so) to mention, that the trials were exactly carried out with y people. I'm not a mathematician but an engineer, so forgive me any stupid questions.
WvBraun 1 year ago
Great video. Great accent.
Pumabrand90 1 year ago
wow i became smarter than the math teacher lol
holdingspace 1 year ago
i wonder can i make money witht this trick or parodox or whatever
kariukarys 1 year ago
when you compare the efficiency of two things you take exactly the same sample of the things that they effect or the things that you exam etc...
but general you are right
gogogino 1 year ago
Wait, how can you add fractions with different denominators? It seems like that is what you just did.
Zeldakitteh 1 year ago
@Zeldakitteh If you added them like the way you think he should have, then the results would be misleading.
He did: 63+4=67, and 90+10=100 for drug A.
Add the numerators, then seperately add the denominators.
Then put the two sums in a fraction.
That's how he did it
IPwnAllAndLeaveNone 1 year ago
Good to see a video about the basics. For my job I'm only using basic maths.
Also nice about this video is seeing I was doing it ok all along.
WhatforNameIsThat 1 year ago
Take them both lol
Rayden440 1 year ago
thank you!
jeroenve 1 year ago
6666 veiws... O_o...
MetallicaRTL666 1 year ago
Take both drugs. x)
Zeldakitteh 1 year ago
@Neatod He says cures. The whole time I was wondering what kind of sick world this is where the drug that kills more people 'wins'. Then I realized he was saying cures.
Zrowny 1 year ago
This video gave me the BSOD...
iPodOperator 1 year ago
I showed this to my dad, he said "the people don't matter it's the percent" I said "but they're comparing unlike things, only 10 people took the drug b on day 1, while 90 took drug A" his response"numbers don't matter, percent matters" me "well if 1 basket ball player took one shot, and made a 3 pointer, and another took 15, and made 10 3 pointers, which would you pick?" dad "these are to very different things" HOW? (I was interrupted when my mom made me leave)
miniwars123 1 year ago 19
@miniwars123 Haha. You're right though. Percentages can be misleading :)
singingbanana 1 year ago 7
@miniwars123 We're all thinking it, I'mma just say it. Your dad is WAY too stuck up. He couldn't admit he was wrong >.<
froggythebob 1 year ago