Test Statistics: Crash Course Statistics #26
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- เผยแพร่เมื่อ 7 ส.ค. 2018
- Test statistics allow us to quantify how close things are to our expectations or theories. Instead of going on our gut feelings, they allow us to add a little mathematical rigor when asking the question: “Is this random… or real?” Today, we’ll introduce some examples using both t-tests and z-tests and explain how critical values and p-values are different ways of telling us the same information. We’ll get to some other test statistics like F tests and chi-square in a future episode.
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Every other video on statistics: select playback 2x speed
This video: select playback 0.5x speed
P is low, null must go (P-value is low, reject H0)
Ah, the most difficult aspect of my Statistics class that I took last semester, was never able to wrap my head around test statistics. Too bad this didn't come out earlier, it would have been incredibly useful back before I'd taken the final exam. :)
don't avoid math, math makes the concept easier to understand
Fantastic visualization and excellent breakdown of the concepts!
Thanks a lot, defenitely not a simple concept but somehow the crash course team always knows how to put it in simple terms 🤩. It would have been awesome if you guys explained more how the alpha should be set, when should we opt for 0.01 and when to choose 0.05. Thank you so much!
what a comprehensive lecture. Lov it.
This is great!!!! Thank you for the information!!😎👍
I'm taking Stats in the fall! Very helpful!
For so many years, I thought my biology 12th grade teacher is the greatest teacher of all time, then you came in my life. He is No. 2 now
I don't understand any of this
@2:45 I think there’s a simple word error- you say you expect each observation to be one sd (15) from the mean, the word should be ‘within’ rather than ‘from’. The mean is the expected because it is the value that decreases the summed square of residuals.
wow. really useful info and so much. but i think i would be able to absorb this information much better if the video was slightly longer and had pauses in the dialogue rather than a constant stream of info.
there is a pause button. feel free to use it :)
@@qayxswedcrfv1 my lectures are recorded due to covid19 outbreak preventing physical campus attendance. should i hold my lecturer to lesser standards and be willing to stop the recording incessantly? no i dont think so. the onus is on the presenter to properly structure the presentation.
I like it because it burns through he content at speed, making the video shorter. You can rewatch until you get all of it.
Doing a stats exam today. Thank you!
love the way you present.
This is really helpful, thanks a lot!
My heart broke when you didn't reject null hyopsthesis because the p-value is larger than alpha by 0.0008
still dont get any of it..
Found this when studying for final exams; should've found this when I started the test statistics unit
I hate statistics with a passion but this makes me not want to cry as much haha
You A teacher?
Thank you 🥰
Hi, at 6:01 won't the standard variation formula be 1/(600+400) rather than 1/600 + 1/400. If latter is the case can someone please explain how? Thanks.
I wish this could’ve appeared before I took my Statistics course haha.
Good Content for Education people's in every nations
statistics is the hell lecture - holly molly dudes
This video is awesome , I mean on average.
very good info!!1
I'm just waiting until SPSS gets brought into this and everyone starts crying in a corner.
There is a missing bracket in the formula of the standard error (corrected later in the formula with the concrete numbers).
I'm studying for Six Sigma Green Belt, and the formula at 9:56 looks like the "pooled T-test for sample sizes
You guys should really add mathematical explanation on the flu example 6:10
It’s just so confusing when all of you videos didn’t cover topic of
1. Normal distribution with proportions
2. Z/T test with two different sample or groups with different sample size
At 9:57, you used the t-statistic formula with the standard error in the denominator. You used an alternative version of the SE formula since you are comparing two groups. Why is there a "1" in the numerators of the fractions? Why did you use "1" for the standard deviation?
DAMN YOU STATISTICS!!!
@6:50 Why does alpha fall on the graph at +/- 2 and why does that make the “critical value” +/- 1.96??
Isn't the standard deviation suppose to be devided by square root of n at 7:28 ?
I hope I am wrong but at @6:05 mark, the formula for calculating standard error, shouldn't it be sqrt(p(1-p)/1000) ???
Please do crash course algebra or geometry
I took a level statistics and got an A but I wish I found this series, probably would have helped 😂
I''m in your class and your lying, you got a C
where was this video was i was failing statistics LOL ?!
@10:06 isn that the p value for 2.55,not 2.65?
How did you get a standard deviation of 1 at 8:44? Did you round up the difference?
She did not round up the difference. She is saying that the true standard deviation for both groups is 1 day. In a theoretical setting, she postulates that the wait time for the small repair shop follows a t-distribution with an unknown true mean but a known true standard deviation of 1 day. In other words, she made that up. Similarly, she postulates that the wait time for the larger shop follows a t-distribution with an unknown true mean but a known true standard deviation of 1 day.
I really don't know how to calculate a p value. I am being taught to use the degrees of freedom and a cut off score to the determine the critical t values and use t statistics to determine whether or not to reject the null hypothesis. but my teacher still asks us for a p value with no graphing calculators or ways to solve for it. I'm so confused
let the researcher decide if they can defend the cut off. at a minimum. idk, this feels like a step backwards from bayes. it does need to be covered, i get that.
Can't understand how standard error is being computed at 6:00, why p(1-p)?
That is not trivial. The standard error that is being computed is really the standard error of a random variable that is defined as the difference of the proportion of sick people in the unvaccinated population and that of sick people in the vaccinated population.
In short, each of these 2 proportions is a random variable of the form X / n where X is the number of sick people and n is a sample of n individuals respectively chosen from the unvaccinated population or the vaccinated population. Both random variables follow a normal distribution (according to the central limit theorem) of mean=p and standard error = p (1-p) / n.
To add to the complexity, X is itself a random variable that follows a binomial distribution of parameters n and p. Thus, E[X] = np and VAR[X] = np(1-p). In conclusion, for each of the 2 proportions, you get E[X / n] = np / n = p and more importantly VAR[X / n] = 1/n^2 * VAR[X] = 1/n^2 * np(1-p) = p(1-p)/n.
Finally, because the variance of the difference of 2 random independent variables is the sum of variances, it follows "average variation" (variance) = p(1-p)/n1 + p(1-p)/n2. In other words, the "average variation" (standard error) is the square root of that quantity or sqrt[p(1-p) * (1/n1 + 1/n2)].
@@gregEGO1 😍
wait so are the two tests basically testing the same thing then (but in a different way)? Not sure I understand
josh mcgee depends on what information you have available. If you know standard deviation for the whole population, z is good enough. If you just have a small test group and no prior knowledge about population standard deviation - go for t
Wow this course has so few views. People are probably just scared of all the maths!
please cover how to do ANOVA tests! I need it for analyzing my experiment results! :D Thanks!
We'll get there! (Episode 33)
GlowingEagle if you are trying to learn ANOVA first start with understanding a T-test first, which is basically an ANOVA between 2 groups.
Carl Saltzberg thanks! Will do!
CrashCourse fantastic! HUGE FAN btw!
Quantify.
are those stats on the flu vaccine real?
There is no defnitive way to determine if something is truly random or not random, even if you are 99.9999% sure, you can only say that given your information, this option is more certain than another
Ughhh why tf did I sign up for ap stats
Math hurts my brain
damn, that's a point of view
This is nice and all, but doesn't this imply that our data is normal? What if the given data isn't normally distributed?
t-tests are very robust against violation of the normal distribution assumption, as long as the data is unimodal. But there are different tests, for different sets of data.
Nyt Mare True... I have never been a big fan of hypothesis testing. It seemed similar to a proof by contradiction, but wasn't as intuitive as Bayes theorem.
does john green still make videos on here?
No, because of people like you.
Why has this series repeatedly used IQ as a measurement for examples? Surely a responsible educator should explain how seriously limited and potentially biased such information is? DFTBAQ
Man do I feel stupid. What do you mean by "mean"?
Walter Payne that is another word for Average. Add together your values and then divide by the number of things you added together.
"mean" is what most people mean when they say "average". It is the sum of all the samples divided by the number of samples.
10:00 I am not a fan of that argument. Why does a p-value of 0.0108 constitute as no evidence and 0.0992 as enough evidence, even though both values are basically the same? Alpha levels are arbitrary. I would argue, that a certain p--value suggest a certain weight (no/little/some/strong) of evidence in favour of rejecting the NULL.
Nyt Mare yes, generally we report the p value numerically because we want to evaluate how "strong" it is. But there should allways be caution taken because it is easier to achieve a significant p when you include many samples you are comparing.
You’re right, but she was trying to keep it simple in this video. At the .05 level she would have found significant. when you write your results, you should report it at all three levels just to give the reader more information. Many statistical software denotes this by 1, 2, or 3 asterisks for .05, .01, or .001 respectively (in sociology)
Its too fast for non-english speaker huhuhuhu my brain hurts
Its too fast for english speakers so don't worry
First
Is this the kids version? :|
First!
Cletus Abbot III can you please read what is it in your profile picture
Thanks
But IQs are an ugly fake evil hypothesis.
Isn't IQ just a bunch of racist facts?
(for the record, IQ isn't what you know - or even what you prefer; its your ability, aptitude, not drive. It's almost like saying that we evolved thumbs so we could use pens.)
Higher IQ people are more intellectually curios. You're conflating cause and effect.
Stefan
So what? The why of something is not very mathematical. How do you measure a "why?"
FALSE. In what way does the SPEED YOU LEARN NOVEL THINGS ... indicate your DRIVE to learn novel things? WHO. Is conflating?
Your comment comes off as if you're claiming to know that higher IQ causes you to be more intellectually curious. Maybe more intellectually curious people get higher IQ because they read more?