# 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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### Back Transformation of Predicted Y from Log 10 Transformed Model Data

I am using a General Linear Model for Analysis in Minitab. I have two questions. I had two responses variables which I transformed using Log10 as there was evidence from the residual plots of some ...
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### Why is taking the mean RMSE sometimes so far off overall RMSE?

I'm working with a multi-threaded program, which splits a dataset into N chunks, and evaluates some regression model's performance, predicting a score for each item in each chunk. I'm using RMSD as ...
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### When to calculate the bias corrected geometric mean

Most sources give a simple equation to compute the geometric mean (GeoMean) of data samples from a lognormal distribution. GeoMean = exp(m) where m is the mean of ...
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### converting data from geometric LS mean and confidence intervals to mean and SD

I Hope this letter finds you well. I am conducting a meta-analysis, and some of the studies have reported data in geometric least squares mean and confidence intervals, while others have presented ...
305 views

### When summarizing data from a lognormal distribution, when does it make sense to report the arithmetic mean vs. geometric mean

When data are sampled from a lognormal distribution with a reasonably large geometric standard deviation, the distribution is asymmetrical and the arithmetic mean will be distinct from (and larger ...
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### Central tendency of survey results and geometric mean

I recently conducted a survey asking users about their music listening habits at different times of day. Here are the results from 6am in the morning: Taking a weighted average, 32.14% seems quite ...
101 views

### Calculating proportion

I have a dataset of 10 people who share the cost of a service at the end of each month. The cost of the service is constant. Is there a fair way to split the cost of the service such that the ...
1 vote
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### Geometric mean "flipped" at arithmetic mean?

Due to the inequality $2\sqrt{xy}\leq x+y$, the geometric mean is always closer to the smaller value than the arithmetic mean. In my situation, I need a "mean" that is closer to the larger ...
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I have been working to try to get means adjusted for covariates. I've seen examples such as this one, but I haven't seen an example that has Dr. Lumley's survey ...
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### Percentage Change values for Prices in a given basked: Gemoetric mean vs arithmetic mean to get "mean" Prices

Lets say i have a Timeseries of data for different goods in a basked. Af first, i do not want to calculate an index value to answer the question "How much more expensive is the basked compared to ...
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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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### Estimate weights given a weighted geometric median

Problem 1 Given a set of points and their weighted geometric median, find the weights associated with each point. For instance, given the points ...
1 vote
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### Geometric vs. arithmetic mean [duplicate]

I'm not sure if this is the best place for this question, but when averaging data, how do you know if the geometric or arithmetic mean is more appropriate for taking the average? Do you need to know ...
1 vote
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### average of geometric and harmonic means

I have a stochastic simulation model in which three types of mean (arithmetic mean, geometric mean, and harmonic mean) are calculated for three different variables. I run the simulation 1000 times so ...
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### Sample Geometric Mean and Sample Median of a Log-Normal Random Variable

The Wikipedia article for the log-normal distribution states that the geometric mean and median of a log-normal random variable are equal. However, when I simulate log normal data with a small N, ...
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### Geometric mean of log10 values

I have the following series of log10 numbers: ...
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### Kruskal Wallis test or ANOVA for G-mean?

I currently working on the data (4 groups), which requires the evaluation in Geometric means. I transform the data into logarithms (which is non-normal distributed), then I wonder whether to use ANOVA ...
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### How to calculate percentage difference of geometric means with emmeans?

I want to estimate the estimated marginal means (EMMs) of a log-normal variable across different groups. Let’s take the dataset of pigs from ...
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1 vote
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### Geometric mean vs geometric mean rate of return

Consider the rate of return for an investment in year 2000 increased by 105% and in 2001 it increased to 42%. what is the average rate of return in 2000-01. I'm confused as to which formula to use (1) ...
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### I have expected stock returns on US and globally ex-US. How do I combine them?

Edit: If US stocks are 56% of world stocks and they have a 5.09% expected return, while the other 44% have a 2.31% expected return, how do I calculate the expected return of world stocks, the 100%? ...
537 views

### How to calculate the confidence interval for the difference between geometric means?

I am comparing the amount of leaf area eaten by herbivores between two groups of plants. This data is very zero-inflated (many leaves had no herbivory) with some very large values that skew the ...
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### what is the standard deviation of the geometric mean sample distribution?

I wrote a python script to take a population distribution of a random variable in the interval (0,1) to be uniform and make 2 sample distribution: The fist is the distribution of the arithmetic mean ...
137 views

### quasi-poisson / Neg.Bin / Chi-square for analysing annual count data?

I'm interested in looking at annual trends. The numbers represent the total number of a particular animal species that have been counted in that year. We see a decreasing trend, and I would like to ...
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### Average of geometric mean across subsamples

I am looking for a simple closed-form expression simplifying the sum (or average, if you prefer) of the geometric means of all subsamples $A\subset X$ of cardinality $|A|=k$ from a grand set $X$, \...
1 vote
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### Calculating the mean or median "whereabout" of a joystick

I have recently collected data using the NASA TLX tool, which includes a tracking task, where subjects have to keep the joystick deadcenter while having to react to multiple tasks. The raw data looks ...
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### Which variation estimate to prefer: SD, geomSD, CV?

I have a case where we see regional disparities in median received services. Services is a lognormally distributed variable. Plot is based on a lognormal model, examining y and sigma. You can see that ...
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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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### 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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### How to show the geometric mean times of divided by the 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 ...
1 vote
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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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### What is the definition of the geometric mean of a random variable?

I haven't found any definition online although searching for hours: So here is the thing: The geometric mean(GM) of an (iid) sample drawn from some random variable is given by: \text{GM}(X_1,...,...
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### How can I calculate confidence for a multiplicative (growth) dataset?

I have a dataset of daily price changes, represented as decimals. Perhaps: 0.5, 1.5, 2.0. That's to say it lost 50%, then it gained 50%, then it gained 100%. I'd like to know how confident I should ...
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### Arithmetic mean from geometric mean

For the data set the geometric mean is 10 then arithmetic mean will be? I tried hard to calculate the arithmetic mean from geometric mean which is given as 10 but unable to find it.
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### How would I calculate a combination of the Binomial and Geometric Distributions?

To be specific with my problem, I'm calculating a formula for a game. There's 6 independent trials, each with an independent probability of success = 0.34. I know that from the Geometric distribution, ...
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### Is it dangerous to take the mean of ratio measurements?

I'm going through a Computer Architecture course and in one of the lectures they mention that when measuring the difference in runtime performance between two systems, using for example multiple ...
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### In R, find geometric mean of monthly data converted into quarterly data

Looking to find geometric mean of monthly data that's been converted into quarterly data. I've tried several methods but only provide simple arithmetic mean as shown below. Thanks. ...
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### Combining both arithmetic and geometric mean in dataset with zeros and extreme values

I have a some datasets that I want to take an average of - a typical dataset might look something like this: 0 0 0 1 100 100 10000 30 10 10 0 0 0 0 0 Ordinarily ...
1 vote
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### Find $E(x^2)$ given $E(\log(x))$

Suppose I have a blackbox generating values $x_n$. If I take mean($x_n^2$) it flies all over the place as new values are added -- a supermassive 48-digit value could suddenly ramp up a previously ...
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### How to calculate confidence interval for a geometric mean?

Apologies if this is confusing at all, I'm very unfamiliar with geometric means. For context, my data set is 35 month-end portfolio values. I found the month to month growth rate [Month(N)/Month(N-1)] ...
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### Estimating with the geometric mean

I heard about an interesting technique for making ballpark guesses: If you need a variable that you have no idea about (like the average number of pianos per household), you can try to come up with ...
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