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Quantopian Lecture Series: Confidence Intervals (Professor Collaboration)

In statistics, confidence intervals are used to represent a range in which a right answer is likely to exist. The are an elegant way of quantifying uncertainty, and ubiquitous in many parts of statistical testing. This notebook comes out of a collaboration with Professor Jeremiah Johnson at the University of New Hampshire. He coordinates their new data science curriculum, and uses Quantopian as a teaching tool.

Find all of our lectures at https://www.quantopian.com/lectures

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4 responses

hey(: i am new to quantopian and currently following the lecture series. i was just browsing through the notebook for this new tutorial and stumbled across something. shouldnt this line "Where σ is the sample mean and n is the number of samples" read "Where σ is the sample standard deviation and n is the number of samples"? because the standard error is calculated using the standard deviation not the mean. or am i missing something here?
best,
luis

Hi Luis,

That is indeed a very confusing typo. I apologize and will work to get it fixed ASAP. Your interpretation is correct.

Thanks,
Delaney

okay, thanks for the quick reply. and thanks for the lecture series btw - it is a great resource!

"Assuming our data are normally distributed, we can use the standard error to compute our confidence interval. (...) When the samples are large enough (generally > 30 is taken as a threshold) the Central Limit Theorem applies and normality can be safely assumed; if sample sizes are smaller, a safer approach is to use a t -distribution with appropriately specified degrees of freedom."

The CLT does not require the distribution being sampled from to be normal. The less normal and more skewed the distribution, the higher n required for CLT to hold. But on the other hand, if the CLT does hold, and the mean of the samples is normally distributed, that does not mean the underlying distribution is normal. (It could be Poisson, or a t with fatter tails, for example).