A beautiful demonstration of the Feynman technique .... And you actually explained WHY we were doing it to begin with rather than just the technique. Thanks heaps
I have gone through around 15 websites before coming here. Thanks so much for the crystal clear explanation. I am now 100% confident that i have understood it right
... Nice explanation with example...!!! I was trying to understand how bootstraping work and how to preform the calculations for several days but NO ONE is so clear and to the grain. Thank you.
Much clearer than other explanations I've seen. However, "Having said that, an XX% confidence level does not mean that for a given realized interval there is an XX% probability that the population parameter lies within the interval!"
Clear, concise and informative - thank you. Would it be possible to add the links to the previous/next videos to the video description (or maybe even a list of the videos in a topic?). Thanks - excellent work. :-)
Super! Just a double check, if you can. In your specific example, the pet survey, I think you could also calculate the confidence interval analytically, without resorting to bootstrapping. As (stdev of the sample mean) = (stedev of the 40 original samples) / SQRT(40). Is that right? I appreciate you picked this simple example for teaching purposes, but I want to double check that bootstrapping is actually superfluous here (while it is very useful for more complex cases, where you cannot easily calculate the statistics analytically). Thank you (and sorry in advance in case I got it all wrong and I'm just waisting your time 😌)
That is correct -- on any sample you could use either a simulation/bootstrap approach or a normal curve/analytical approach, but the normal curve really breaks down when your basic assumptions for normal curve-friendly samples are not met (with proportions, usually when you get close to either 0% or 100%). However, unless someone is preventing you from using a computer to do your job, just bootstrapping everything is faster and easier. The exception is probably when dealing with confidence intervals of means, you have a sample that is a bit wonky, and you have strong reason to believe that the population looks more normally distributed than your sample -- then you're basically "overriding" the sample data to match a model, which has some validity once in a while.
Statkey is just running a basic simulation (sample without replacement) from the data you feed it. Nothing too fancy -- I had a high student build their own version of the calculations in a few weeks as a project. The magic of their tool is the fantastic visuals and ability to study a single resample at a time -- fantastically built (so is their curriculum if your school does that).
Very great tutorial, thank you! I've got a question on the bootstrapping procedure though: Instead of multiplying your sample of 40 elements to represent your population and then iteratively select 40 elements a high number of times, would it be conceptually wrong to leave your original sample of 40 elements, and iteratively select eg 20 elements a high number of times and do the analysis the same way? The difference here is htat your new sample size will be smaller (ie 20 instead of 40 elements). Am I right? Thank you very much!! Simone
sbch179 Hi there, the answer is "not quite." The size of your new samples needs to be equivalent to the size of the original sample, or else the confidence interval will not be the same. One way of maintaining the sample size is to draw from your original sample "with replacement", that is, you could get the same element twice in your new sample. This is equivalent to "copy and pasting" your original sample to the size of the population, like he did in this video. Hope this helped!
+sbch179 This is a *hair* late to the party, but for the benefit of future viewers, it is important to use the same sample size for each resample. In a small sample, there will be more variation between samples, and thus suggest a larger confidence interval. A set of larger samples will have less variation amongst themselves. As an extreme example, imagine a sample of 5. Being 1 off of the expected value of 60% gives you 40% or 80% with no chance of being somewhere closer. With a sample of 500, there are many ways to be less than 1% away from 60%. This is the logic for why larger samples make better predictions of population values.
Thanks so much this video was really helpful. I do have one question that was kind of addressed in the comments, but not quite. You mention "copying and pasting" the original sample to create a sort of mock population that you can then resample from. From most resources that I've found, the resample method is just resampling with replacement from the original sample. So I'm wondering if the "copy-paste" part was just to sort of conceptually explain the idea of using the original sample as a best estimate of the true population, or if it should be taken more literally. (A lot of the other resources I've found on this are a bit vague/confusing, which is why I'm not sure how to interpret this.) I.e. If I'm making making a bootstrap program in python for a cs class, would I simply resample with replacement from the original dataset? Or would I concatenate the original dataset with itself many times to create a mock population, then resample from that with replacement, each resample being the size of the original dataset?
Alexa Murray You are exactly right -- copy-paste is a conceptual way to think of sampling with replacement from the original sample (since a normal sample does not use replacement but does have a much larger population). For your simulation, just sample with replacement.
I get what you have done but I am concerned about some aspect of this idea. The bootstrapped proportion has no link to your research question. It could be 40% prefer the dog; 40% prefer a particular mobile phone etc. The bootstrap outocme would be the same irrespective of what is being considered.
OriginalJoseyWales why do you think it matters if it's a dog or a phone? You are dealing with estimation of proportion here, it makes no difference of what.
+Indrius Right -- the entire purpose of bootstrapping is to estimate the spread of a sampling distribution of a given sample size. If you were dealing with a quantitative variable, the values from the original sample would probably be more unique than yes/no data and the calculations would be more "personalized" to the problem, if you want to call them that.
I think it is a too simple example, barely informative. Get 40 ball and 16 of them are red. The confidence interval for 40% actually has a close form, and only depends on the sample size.
