# Questions tagged [intuition]

Questions that seek a conceptual or non-mathematical understanding of statistics.

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### Mean of geometric distribution is odds?

Context: I mean the $P(X=k)=(1-p)^k p$ not the $P(Y=k)=(1-p)^{k-1} p$. Apparently the mean of the 1st kind of geometric is $\frac{1-p}{p}$ instead of $\frac{1}{p}$ for the 2nd kind of geometric. I ...
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### What does conditional independence mean semantically?

I've just spent the last 3 hours reading every post, question, Medium article, and textbook entry on conditional independence, and I still don't really understand it. Can somebody explain what it ...
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### What exactly does the Box-Cox transformation do to a time series?

If I were to try and rephrase the argument in the original Box-Cox paper in my own words, I would say something like the following: given a model $$y = x \beta ,$$ if the residuals do not appear to ...
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### Why do we need a smaller sample size to detect a smaller proportion?

The plot below shows the sample size needed to detect a proportion with a precision 0.01 for various true proportions: This assumes an infinite population size, and the confidence intervals are fixed ...
1 vote
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### Why PCA is invariant under rotation

Lets say that we have a matrix of variables (the columns are variables and rows are the observations) called X whenre X = [x1, x2, ...., xp] where ...
1 vote
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### Does the number of samples, as opposed to the sample size in each sample, matter for the Central Limit Theorem? [closed]

(1)So here is a formula that describes CLT I found at https://en.wikipedia.org/wiki/Central_limit_theorem. According to the first part of the explanation, n as in Xn describes the number of samples(i....
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### Why is my intuition about probability in this regard so flawed? [closed]

Take the following example: Take a sample from 100 people and measure their height. Assume that we know that height is approximately normally distributed, with a sample mean of 175 cm and sample ...
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### What's complicated about regression to the mean?

Note: I am a bit of a novice when it comes to statistics and data analysis. Reading the chapter on regression to the mean in Kahneman's Thinking Fast and Slow, I came across the following passage: ...
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1 vote
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### Intuition about the relation between joint distribution, marginal distribution, and conditional distribution

The wording "intuition" might be a bit imprecise. I want to discuss how we visualize in our head going from one to another among the joint PDF, marginal PDF, and conditional PDF. To make the ...
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### Is the exact value of any likelihood meaningless?

While reading about likelihood, I have heard that "the exact value of any likelihood is meaningless" why? So, because of that we may use the likelihood ratio. So, my question is, why the ...
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### What is the intuition behind the odds scale?

What is an intuitive explanation of the odds scale? In a logistic regression such as $$logit(p) = \beta_0 + \beta_1 x$$ we often interpret $\beta_1$ by looking at the odds ratio, $e^{\beta_1}$, which ...
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### An Intuitive Explanation of Multifractality in Financial Time Series

Can anyone please give an intuitive explanation of multifractality in financial time series? Most definitions I came across are either purely mathematical or not in relation to finance. As for the ...
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### Central Limit Theorem - intuitive explanation without deep math [duplicate]

The Central Limit Theorem says that the distribution of the sample mean is approximately normal. Is there any intuitive explanation for why this should be so? I know it can be proven with deep math, ...
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### Per-variable $p$-value in MLR and $p$-value in SLR

Suppose I fit a linear model Y ~ X1 + X2, and the output looks like ...
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1 vote
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### Why to calculate $\mathbf{weighted}$ average of the leaf node impurities in decision trees? Why not to just add entropies up without weights?

In decision trees why do we calculate weighted average of entropies of each leaf when we calculate the entropy of target variable given some feature? The question is: "Why is it weighted average? ...
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### number and size of eigenvectors in PCA

As I understand, the size of eigenvector produced in PCA should be min{n,N}, where N=number of samples and n=dimension of each sample (Right?). However, I have seen in couple of cases that this size ...
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### Intuitive explanation of Choquet Integral for data aggregation

I've recently stumbled upon this python package that implements Choquet integral as a way of aggregating data. Does anyone have an intuitive way of explaining how does this integral work in this case?
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### Intuition for correlation of N≥3 dimensional Normal distribution

What is an intuitive way to think about the covariance matrix in an N≥3 dimensional Normal distribution? In two dimensions the covariance matrix can be visualized by plotting a region of constant ...
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1 vote
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### Intuition: Variance of the sum of R.V's and correlation

I have many questions that seems basic to me but I just cannot wrap my head around it. Say we simulate 100 R.Vs that comes from a symmetric distribution with mean 0 $(X)$. Say we build another random ...
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### Relation between variance, square difference and CLT

NEW EDIT TO CLARIFY THE QUESTION My initial question was about why square difference was used instead of absolute value in the formula of the variance... But I ...
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### How to explain intuitively to a lay audience that the variance is an unbiased estimator?

I have data for the concentration of several chemicals in the milk of 10000 cows and have to explain to policymakers and the lay public (i.e. people with no or limited knowledge of statistics) that ...
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### Intuition for why LDA is a special case of naive Bayes

The naive Bayes classifier assumes the regressors to be mutually independent, while linear discriminant analysis (LDA) allows them to be correlated. James et al. "An Introduction to Statistical ...
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### Understanding the Importance of "Sufficiency" within Statistics

I am trying to better understand what it means to be a "sufficient statistic". "In statistics, a statistic is sufficient with respect to a statistical model and its associated unknown ...
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