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yeah? but whats the explanation really?

🤣🤣🤣

I noticed that too but it didn’t cause me to lol...just a chuckle.😏

We use df primarily when estimating variances, because we know that dividing by n underestimates population variance. To my knowledge, ther is no formal mathematical proof to show that n-1 is necessarily "correct". We can never know it is 'correct", because in the real world we never know the true population values. That said, statisticians have demonstrated the concept using toy data sets for which the population values are defined. With these models, n-1 reliably made the variance estimates better. If n-1 had been better at the job, they would have chosen it. It's the mathematical equivalent if having thermometers that reliably read 10% colder than reality. We are simply compensating for a known bias in the tool.

The no. of Degrees of freedom of sum of squares = no. of independent variables in that sum of squares. Let SS= sum of (yi-ybar )^2 ,i=1,2..n here SS is sum of square of n elements (y1-ybar),(y2-ybar)....(yn-ybar). These elements are not all independent bcz sum(yi-ybar)=0 (which condition for dependence of variable). So we use ' n-1 ' degrees of freedom for SS insted of n.

please correct me,if am wrong

@@niemand262 there are mathematical proofs as to what gives the best estimate on average (i.e. an unbiased estimate). In terms of standard deviations, its called "Bessel's correction" and there is a proof as to why we use n-1. As for using n-p, i.e. some other number of degrees of freedom, I THINK these are calculated by seeing how many of the data points are free to vary and still give us the same statistic. For example, if we calculate the mean of [x1, x2, x3], if we vary any of them, we can just move another one so that the mean stays the same. As we can move any of them, we have n=3 degrees of freedom. If we are estimating population variance from a sample without knowing the population mean, we are solving 2 equations (one for mean and one for variance) with n unknowns. As such, we can "replace" one of the n data points in the equation for standard deviation with some function of the sample mean whilst still technically expressing the standard deviation in the same way. As we can do this replacement of 1 of the data points with one of our statistics, we have n-1 degrees of freedom. This could be slightly wrong (I came to this video hoping for a full mathematical explanation) but I'm fairly sure its the gist of it.

@@henrysorsky thanks for pointing out "Bessel's correction". Your intuitive explanation for degrees of freedom makes sense, but why doesn't the same intuition also apply for the standard deviation of the population? After all, given a set of N observations, if you know the standard deviations of n-1 points around the mean, you know the value of the Nth standard deviation.

That's something most of us indians want -better education

It's better if we adapt the Vedic methods😂😂

He is your professor by choice.

Support the idea

​@@pk-uk5lc Hey there, buddy! It ain't about being Indian or American, it's about the individual's ability to simplify things and make them more understandable. There are tons of examples of amazing Indian educators out there, not just on KZfaq.

Oooo! I like this idea. Might even do a series on bias. Though I'm behind on other series at the moment so STAY TUNED :)

Overestimation can occur only when n, sample size is greater than population size, which by definition is impossible. You can't gather more units to measure than absolute best case scenario, assuming you have available a 100% of information. For example, you can't run a questionnaire through all 8 billion people. And even if you could, you can't hope they all will have answered 100% honestly without biases. If you'd divide your result by 8 billion and 1, your result by default will have a smaller value than the true value. Dividing by a larger value gives you a smaller value. Anything we measure is less than 8 billion people, hence, all of our results will be larger or smaller than the true value. If we wouldn't have measured 1 person out of a total population, that 1 person would be the final measurement before the sample mean becomes a population mean. That one last piece of information increases or decreases the sample mean into a population mean. We divide by n-1, or n-k-1, or (c-1)(r-1) to have our guess be as close to the actual population as possible. We know that any guess we make is not spot on a population guess. Look at what happens with a variance in a perfect population (x-mu)/n with random numbers i.e. mean at zero: (3-0) + (2-0) + (1-0) + (0 - 0) + (-1-0) + (2-0) + (-3-0) = 3 + 2 + 1 + 0 - 1 - 2 - 3 = 0 All of the values cancel out. We square them to get rid of the negative sign and have any kind of usable metric to assess reality. We probably could have use |absoulte bars| with the same result. When you pass 0, i.e. our sample mean passes the population mean. Statistics under/overestimates the true mean mathematically by default. Once your guess is higher than the mean, the now squared distance starts to grow again. 9 + 4 + 1 + 0 +1 + 4 + 9 It does not collapse on itself. Graphically it's a parabola and you've estimated the guess at its bottom point. I guess what you asking is, will we overestimate the variance when our guess size matches perfectly the true population size and no better guess can be made? Firstly you should never assume you can guess the true population value. We have to live in a real life where nothing is perfect. Statistics is not perfect. It simply strives for perfection. Improbable to guess any single continuous value precisely. What is the chance that a next person has a height of 173.48763498456437654405 cm? Impossible to pick a sample this precise. For a sample of n=1 you'd have a undefined sample variance, because in a case of n-1 variance is divided by zero. How far away is a sample from itself? No distance. It is the mean value of itself. Statistics doesn't deal with absolutes and cannot PROVE anything IS because we never know the population at any given moment. Something is always left unaccounted for. If n=0, answer would be negative. Negative value means no sample has been measured. Imagine an equation without the -1 part i.e. a sample of me n=1 writing an an amount of this comment x=1. The average of these two would be 1. The variance (1-1)/1 = 0. No spread from itself. It's nonexistent either way, either you say it's = 0, or infinity, because you divided the spread by 0. Your alternative hypothesis defined by the sample size IS the null hypothesis. You've proven the alternative hypothesis is the null hypothesis. Null hypothesis is not rejected within the significance level of 1, we can have an underestimation or overestimation of the true population mean Having written all this, i still don't think i have answered the question, why an overestimation happens as sample mean becomes the population mean.

0/0 = undefined, not zero, believe it or not!

obvious that it's Prezi software

@@gazzzada Is it? I have used Prezi and wouldn't have guessed that's what was used to create this video. Thanks.

current version it gives even more options