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1 vote

Can we assume a form of heteroskedasticity and correlation within groups with the sample mean?

Estimation of the sample mean is equivalent to estimating the coefficient of an intercept-only model. Consequently, if you have violations of the usual $iid$ assumption when you calculate the sample ...
  • 39.3k
2 votes

Probability of sample means being equal

By some properties of the normal distribution (make sure you understand which) $$\bar X \sim N(70, 16/4), \quad \bar Y \sim N(70, 9/9)$$ If $X$ and $Y$ are independent, $\bar X - \bar Y = W \sim N(0, ...
  • 4,034
1 vote

Is Median Absolute Percentage Error useless?

TLDR; Here is a point of view in terms of what the median/mean tell about the behaviour of the tails. The median gives little information while the mean does. A related question is Chebychev-like ...
8 votes

Is Median Absolute Percentage Error useless?

I've spent a few years building real estate price regressors, which are known as "AVMs" (Automated Valuation Models). A few comments: Yes, "median absolute percentage error" is ...
6 votes

Is Median Absolute Percentage Error useless?

The potential issue with absolute percentage error is that it is not symmetric with respect to over and underestimating. If you overestimate by a factor of 2 you will get an error of 100%, if you ...
  • 332
8 votes

Is Median Absolute Percentage Error useless?

I would be very careful about percentage errors, especially in the context of skewed distributions in the outcome (more precisely: skewed error distributions). Look at each separate prediction. You ...
14 votes

Is Median Absolute Percentage Error useless?

Be careful with the median for performance metrics! Robustness to a small number of outliers is a good thing in most cases, but if you use the median a method may look good that in fact gives you a ...
0 votes

Let f be a mean 0 variance 1 density. What's the variance of g(x)=f{(x−μ)/σ}/σ?

For mean: $\int_{-\infty}^\infty x f\{ (x - \mu) / \sigma \} / \sigma dx $ for change of variable $z = (x - \mu) / \sigma$ and $dz = 1/\sigma$: $ = \int_{-\infty}^\infty (z\sigma + \mu) f(z) dz $ $ =...
0 votes

Percentage Change values for Prices in a given basked: Gemoetric mean vs arithmetic mean to get "mean" Prices

I think it makes sense to look at the differences rather than summarize the Before basket and the After basket. In a way, this is the same logic as a paired t-test or a paired Wilcoxon signed rank ...
1 vote

Percentage Change values for Prices in a given basked: Gemoetric mean vs arithmetic mean to get "mean" Prices

We would use the geometric mean if it was the same good declining by different prices throughout time (which would be appropriate for averaging growth/decline rates for the same thing), but you have ...
2 votes

t-test where one sample has zero variance?

As others have already said, it would be better to address the issue with rounding to get the original data. However, if you have to work with the data you have here's another fairly simple option ...
  • 3,770
7 votes

t-test where one sample has zero variance?

It requires a bit of explaining how or why this second sample is so "precise" so to speak. Is this rounding error, or are there accidental replications? There is a lot of science going on, ...
  • 55.2k
5 votes

t-test where one sample has zero variance?

One solution is to use a one-sample t-test of the null hypothesis: $$\text{H}_{0}\text{: }\mu_{1} = 4\text{, with H}_{\text{A}}\text{: }\mu_{1} \ne 4$$ If $n_1=26$, $\bar{x}_1=3.865$ and $s_{1} = ....
  • 27.3k
17 votes
Accepted

t-test where one sample has zero variance?

This answer doesn't address the issue of why the second group has no variation (and I really do suggest you get to the bottom of that). If you're comfortable saying the yield of group 2 is definitely ...
  • 7,054
3 votes
Accepted

When would the variance for a probability distribution give the same result as the standard equation?

You are actually applying the same formula for the variance (of a discrete random variable) to two different random variables $X$. Indeed, in the first case, $X$ takes on values $x_{1},\ldots,x_{N}$ ...
  • 4,034
5 votes

When to use Mean(X/Y) versus Mean(X)/Mean(Y)?

I first consider $mean(x/y)$ versus $mean(x)/mean(y)$. As Eoin and dariober suggest, the more practically relevant quantity should be used, which is often the former, although the latter is not ...
14 votes
Accepted

When to use Mean(X/Y) versus Mean(X)/Mean(Y)?

If $x_i =$ number of items consumed on active days (for person $i$) and $y=$ number of active days (for person $i$), then... $\text{Mean}(x/y)$ is the average number of items consumed per person on a ...
  • 7,054
4 votes

When to use Mean(X/Y) versus Mean(X)/Mean(Y)?

In my opinion mean(X/Y) is more meaningful because your experimental unit (not sure this is the correct term) is the individual, not the aggregate. Let's try to see ...
  • 3,770
1 vote
Accepted

Demonstration - normal distribution

If we integrate the probability density function of the normal distribution from $\mu-\sigma$ to $\mu+\sigma$, we end up with about $0.683$: $$ \int_{\mu-\sigma}^{\mu+\sigma} \frac{1}{\sqrt{2\pi}\...

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