# Questions tagged [geometric-mean]

A measure of central tendency that represents the typical value of a set of numbers when those numbers are thought of as multiplicative in nature.

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### Interpreting differences in log-transformed data when constant has been added first

I have performed an ANOVA on some log-transformed data. I had planned to transform the mean differences in the log-transformed data back to the original scale and interpret them as ratios of the ...
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### How to calculate an average from three distinct but related samples?

I am trying to find out how to average price information stemming from three different types of products belonging to three distinct groups: Red Cars, White Vehicles and Blue Vehicles. The information ...
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### How can I compare differences between geometric means?

Background: The HDI (Human Development Index) is a geometric mean based on 3 variables (each normalized to a value between 0-1). There is a fair description of the details here. I copy below the ...
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### Is expected value different in meaning from central tendency? Isn't both about “typical values”?

I was taught, that for any distribution having the 1st raw moment defined, the "expected value" is equal to it and it's also the arithmetic mean. "Expected value" sounds to me like "typical value". ...
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### How is that possible that simple arithmetic mean works well even for strongly skewed distribution?

I was taught, that the arithmetic mean is sensitive to outliers and skewness. This was natural to me - the observations lying far from the "central point" of the distribution "pull" the measure ...
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### Why summarise right-skewed distributed (log-normal) data with geometric mean rather than its expected value?

I am very confused. The first raw moment calculated from sample, the arithmetic mean, is the BLUE estimator of its expected value. So there is no better one. At the same time, I was told that the ...
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### Geometric mean: Why root instead of divide? [closed]

I use the geometric mean to create standardized ranking between several disparate variables, so I can compare different variables combination: the higher the GM, the higher all the variables will be. ...
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### Geometric mean intuition and interpretation

When simple mean is generally quite an intuitive term, and may be interpreted among others as average value in terms of distance, central value in terms of weight, expected value in terms of ...
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### Geometric mean and geometric standard deviation

When summarizing normalized data (for example, percentage data), one must use the geometric mean instead of the arithmetic mean. Thus, instead of using the arithmetic standard deviation, one shall use ...
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### Compare 2 sets of numbers by Ratio of Geometric means rather than Student t-test

In a medical article published today(!), ratio of geometric means and its confidence interval is used to compare 2 independent groups rather than Student t-test. My specific questions are: What ...
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### Which test should I use to compare three geometric means?

I'm trying to use some test to compare three geometric means of some dataset, to see if there are significant differences. I want to compare A with B, B with C and A with C, but I'm unsure of which ...
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### Most “statistically sound” method for finding the average of multiple different metrics [duplicate]

If I have 3 different metrics and I wanted to find an "average" (not necessarily arithmetic mean) of the 3 metrics so that observations can be ranked, what would be the most "statistically sound" ...
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### What does it mean by “approach the performance of the Bayesian gold standard”?

It is a sentence in Dropout paper(Dropout: A Simple Way to Prevent Neural Networks from Overfitting). "This can sometimes be approximated quite well for simple or small models, but we would like to ...
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### What comes after the geometric mean?

The geometric mean is a multiplicative alternative to the arithmetic mean, which we could call additive mean, thereby calling the geometric mean multiplicative mean. My question is the following: what ...
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### Comparing performance of 2 comparable tests

So I have sets of data, 15 responses for test A and 15 separate responses for test B. Tests A and B have 6 perception questions and the object is to compare the performance of representing data one ...
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### How can we simulate from a geometric mixture?

If $f_1,\ldots,f_k$ are known densities from which I can simulate, i.e., for which an algorithm is available. and if the product $$\prod_{i=1}^k f_i(x)^{\alpha_i}\qquad \alpha_1,\ldots,\alpha_k>0$$ ...
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### Transformation among power-means

It is well-known that arithmetic and geometric mean are strongly related via logarithmic transformation, i.e. if we take arithmetic mean of logarithmic-transformed values we get the same as if we take ...
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### Geometric Mean Standard Error [duplicate]

I read from wikipedia that the geometric standard deviation is $$\sigma_g = \text{exp}\left( \sqrt{\frac{\sum_{i=1}^n\left(\frac{A_i}{\mu_g}\right)^2}{n}}\right)\,,$$ where $\mu_g$ is the geometric ...
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### Robinson's Geometric Mean Test

I am reading this book: Ending Spam: Bayesian Content Filtering and the Art of Statistical Language Classification by Jonathan A. Zdziarski page 78 is about the Robinsons Geometric Mean Test. This ...