Questions tagged [units]

units of measurement. Use this tag also for dimensional analysis.

Filter by
Sorted by
Tagged with
7 votes
1 answer
85 views

What are the units of a binomial variable's standard deviation?

I recall that a standard deviation is in the same units as the random variable, which is useful. However, when deriving the standard deviation of a binomial variable, how do we resolve the units of ...
E. Kaufman's user avatar
3 votes
1 answer
40 views

If I do a PCA on centered only variables (of the same unit), does it mean that the principal components created expresses themselves with that unit?

This question might look very trivial, but PCA is still nebulous to me. If I have a set of individuals described by 10 variables: $A, B, C, D, E, F, G, H, I, J$, all quantitative and having the same ...
Marc Le Bihan's user avatar
1 vote
0 answers
33 views

How should I write the units for MSE in its formula and in a plot axis?

I am trying to write a paper for IEEE and would like to know if for MSE, which can have any units, it correct to write "MSE (error^2)" in its formula (i.e. MSE (error^2) = ) and in a plot ...
Baldovín Cadena Mejía's user avatar
10 votes
3 answers
3k views

Can statistical units measured per thousand inhabitants be bigger than 1000?

I found some data on the number of self-employed people per one thousand inhabitants in Europe here. However, in the year 2020, for instance, some statistical units have over one thousand self-...
Anc45's user avatar
  • 103
13 votes
4 answers
2k views

How should variables in statistics be understood?

I had a slightly basic question about variables (particularly in statistics). We would say that “height” is a variable. In my mind, “height” does not just represent different values, like 2, 45, or 75....
Pranav Jain's user avatar
-1 votes
1 answer
52 views

PCA statistical units

I have a school project where I'm required to use a factor analysis. I chose this dataset from FiveThirtyEight about police killings. I want to characterize the places where people have been killed so ...
Lionel Ngoubou's user avatar
0 votes
2 answers
286 views

Effect of units on shape of normal distribution

TL;DR: Is the shape of a bell curve / normal distribution idependent of the units chosen to represent a certain variable? More detail: I was playing around with some data from this paper in excel: ...
Nick's user avatar
  • 101
3 votes
1 answer
2k views

Can ratio data have negative values?

I get the concept of a "true zero" value, but I'm not sure why this implies that there cannot be any negative values—at least that's what most sources say that I found only, with only few ...
Christian's user avatar
  • 197
2 votes
1 answer
27 views

What issues arise when you perform stats on scores attributed to concepts/objects rather than people? (2-way independent ANOVA example)

• Pianos have 5 different types of black note, and 7 different types of white note, on them. • A famous music psychology paper examined the effects of note colour (black vs white) and instrument (...
Sam Leak's user avatar
1 vote
1 answer
83 views

How do the units of the SIR model cancel out?

I was having trouble trying to understand the parameters of the simplest SIR model. If beta is the effective contact rate and s is the percentage of people who are susceptible, then how do the units ...
Krishna Kalakkad's user avatar
0 votes
0 answers
1k views

Units of measurement and the t-statistic

Consider a case in which we want to examine the effect of house value on homeupkeep expenditure using linear regression model, where dependent variable y is the upkeepexpense and ...
Nicholas Heinrich's user avatar
2 votes
1 answer
123 views

How to interpret a scaled response variable as an unscaled response variable?

I'm new to R and I'm having trouble to interpret the estimates of my scaled response variable. I used (scale) function to standardize all my variables (1 response ...
Thalia's user avatar
  • 21
0 votes
1 answer
489 views

Standardizing versus percentile rank with survey data

I am currently working with survey data, collected across different locations, but with slightly different units of measurement. For example, on questions such as "What is your level of education", ...
Charlotte Manin's user avatar
0 votes
1 answer
940 views

Changing units in linear regression

A linear model: $y_{i}=\alpha +\beta x_{i}+u_{i}$ was estimated using least squares and the following estimate was calculated: $\widehat{\beta }=\frac{\sum (x_{i}-\overline{x})y_{i}}{\sum (x_{i}-\...
user3275222's user avatar
3 votes
0 answers
991 views

Probability density function units of the log-normal distribution

In a discussion on this forum lognormal distribution, standard-deviation and (physical) units the cumulative distribution function (PDF) of the lognormal distribution was analysed. The conclusion was ...
mjs's user avatar
  • 152
1 vote
1 answer
363 views

What are the units of a medcouple?

Let's say I have a distribution of some weights in kg. I want to estimate the skewness of this distribution using a robust statistic, the medcouple [ G. Brys; M. Hubert; A. Struyf (2004). A robust ...
zlon's user avatar
  • 718
1 vote
1 answer
3k views

Multiple regression of variables with different units

I'm new in statistical modelling and using R, so please excuse my mistake for this question. I want to make multiple regression model with these variables: Revenue (in million USD) as dependent ...
shawn's user avatar
  • 13
1 vote
0 answers
39 views

Linear unit-transformation (say, from liters to milliliters) of response variable in simple regression

The setting Consider the simple regression model: \begin{equation} y_i=\hat{\beta}_0 + \hat{\beta}_1 x_i + \hat{\epsilon}_i \end{equation} Now, suppose I want to apply a linear transformation to ...
jobrachem's user avatar
2 votes
1 answer
3k views

Units in Principal Component Analysis

If I have a data set with 6 variables (A, B, C, D) all measured in different units (eg. m, kg, s, K) and I perform principal component analysis to transform this into two Principal Axes, how do I ...
FJC's user avatar
  • 143
1 vote
1 answer
65 views

Interpreting regression results for different units of measure

Could you kindly help me with interpreting the results from the Probit model for different units of measure of the covariates? Consider the Probit Model $$ Y=1\{X\beta+\epsilon \geq 0\} $$ with $\...
Star's user avatar
  • 826
2 votes
1 answer
450 views

Sampling Methods/Monte Carlo method and Log-normal distribution

I found a problem from some notes i found online, here is a screenshot: I am trying to understand this question, it seems this function they define as the LIP() function is basically the quartile/...
Palu's user avatar
  • 237
3 votes
1 answer
4k views

Can a ratio level variable have negative values?

According to Stevens (1946) ratio level variables require an absolute zero. The implication, I believe, is that 0 = an absence of the thing being measured. As such, can ratio level scales have ...
gabryll's user avatar
  • 101
2 votes
1 answer
329 views

What do "scales" refer to when comparing correlation matrix to covariance matrix?

In one post it was written that: You tend to use the covariance matrix when the variable scales are similar and the correlation matrix when variables are on different scales. What does scale ...
mavavilj's user avatar
  • 4,109
-1 votes
1 answer
134 views

Dimensional analysis for a qdf/quantile function correspondng to the pdf/CDF (income distribution example)

This question is a duplicate of a question I previously asked, here: Dimensional analysis for a qdf/quantile function corresponing to the pdf/CDF (size distribution of income example). I believe I ...
andrewH's user avatar
  • 3,117
1 vote
2 answers
116 views

Can I use a dataset even if the observations of a variable are not in the same unit?

I am using a dataset where a variable is "height". However, when I read about the construction of the dataset, it seems that some observations in the dataset are labelled in centimetres and others in ...
Jagdish Hilolt's user avatar
3 votes
2 answers
2k views

What are the units of entropy of a normal distribution?

I have a random process that follows a normal distribution. It's parameters are mean = 35 units, std.dev. = 8 units. I've seen from the wiki entry for the normal distribution that there is a formula ...
Paul Uszak's user avatar
2 votes
0 answers
224 views

Change of units in linear regression [duplicate]

Take the following sample linear regression equation: $$ \hat{y} = 20 + 50X $$ I understand how a change of units in X that consists of simple scalar multiplication would alter the regression ...
user1569317's user avatar
8 votes
1 answer
26k views

The unit of Root Mean Square Error (RMSE)

What is the unit of root mean square error (RMSE)? For example if we get an RMSE of 47 from a regression model, what does it tell in terms of unit?
Armo's user avatar
  • 83
1 vote
0 answers
424 views

How to define general covariance with a dirac delta with correct units

I want to define the covariance of a variable, say $X$, which is the integral over $Y(t)$: $$ {\rm Cov}[X,X'] = \int\int {\rm Cov} [aY(t), a'Y(t')] dt dt'.$$ Just as an example, let the variable $...
StevenMurray's user avatar
4 votes
1 answer
705 views

in calculating Kalman gain, what if state and measurement space have different units?

My understanding is that the Kalman gain for a regular multivariate filter is computed as $$ K = \bar P H^T S^{-1} \\ S = H \bar P H^T + R $$ $K$ being the Kalman gain, $\bar P$ being the prior ...
npp1993's user avatar
  • 143
3 votes
1 answer
2k views

What are the units of a convolution?

The convolution of $f$ and $g$ is defined as $ (f * g )(t) \, \stackrel{\mathrm{def}}{=}\ \int_{-\infty}^\infty f(\tau)\, g(t - \tau) \, d\tau $. Let's say that $f(t)$ and $g(t)$ have units of, say, ...
rhombidodecahedron's user avatar
1 vote
0 answers
38 views

Convert LP3 parameters following a unit change

The USGS uses a Log Pearson Type 3 (LP3) distribution to model flood frequency based on cubic feet per second (cfs) annual maximum flow data (AMAX). The result for a gauging station is the three ...
RockyTed's user avatar
2 votes
1 answer
52 views

Compare relationships independent of units

I am trying to compare multiple columns of data with different units graphically. If I z-score the whole dataset am I introducing any error? Can I safely compare from column to column? Eg ...
Rilcon42's user avatar
  • 759
2 votes
1 answer
297 views

Is there a way to reconstitute the unit of measurement in PCA?

I have a data set composed of changes in financial asset prices. Because they are on different levels, e.g., one asset is trading in the 100s, the other in the 5s, the change their prices have vastly ...
A1122's user avatar
  • 227
9 votes
2 answers
774 views

Inconsistency in unit on gradient descent equation

The update algorithm for gradient descent is $$\theta_j = \theta_j - \alpha \frac{\partial}{\partial \theta_j}J(\theta)$$ $ \frac{\partial}{\partial \theta_j}J(\theta)$ have the unit of cost per ...
user411754's user avatar
0 votes
0 answers
48 views

Units of measurement when going back from regression to theory

This is a fundamental question I have, and so far I have not found a convincing answer. My theory is this: $$ w_{ijt} = \theta_{jt} a_{ij} $$ where $w_{ijt}$ is wage of worker $i$ in occupation $j$ ...
luchonacho's user avatar
  • 2,742
2 votes
1 answer
172 views

Are units of the parameter important when considering Fisher information?

This is a follow-up question to one I asked on Math.SE: What are the measurement units of Fisher information? (Dimensional Analysis) When doing calculations with Fisher information in practice, ...
Chill2Macht's user avatar
  • 6,259
6 votes
1 answer
4k views

Is the multiple of a lognormally distributed variable also lognormally distributed?

If $X$ is distributed normally $N(\mu,\sigma^2)$ then the variable $Y = \exp(X)$ is lognormally distributed. If the variable $Y$ is multiplied by some constant $C$: $$D = CY$$ Is the variable $D$ ...
egg's user avatar
  • 1,205
6 votes
2 answers
249 views

Which is the dimension (or units) of the predicted random effects?

Consider a simple panel data (or multilevel model) with random effects. For context, consider a wage regression, where the dependent variable $ln(y_{it})$ is the natural log of wage, where the wage is ...
luchonacho's user avatar
  • 2,742
1 vote
3 answers
639 views

How to predict orders when unit of measure is different across and within months

I have to predict the order quantity for a 6 month time period. The products are available in different unit of measurement and i dont the relationship between the measures i.e i dont know the ...
Raj's user avatar
  • 943
2 votes
1 answer
70 views

Do I really need to put unit on the graphic?

I would like to add unit on this graphic: As stated in many sources, I should place as much of the required information within the figure itself. Unit is a (very) important information so therefore I ...
Ooker's user avatar
  • 329
1 vote
1 answer
111 views

Statistic calculation (Conversion from one unit to another)

I could get the mean using the formulae but not the value of SD and IQR from using the formulae. What is the problem?
Lim Zhi Jian's user avatar
1 vote
1 answer
2k views

Comparing Standard Deviations with Different Units

Given: the standard deviation is 15.5 cents per gallon in one set of quoted prices and a standard deviation of $5.5 per barrel in another set of quoted prices. There are 33.5 gallons in 1 barrel. ...
HyungPark's user avatar
7 votes
1 answer
6k views

If I divide my data by its mean, does it still have a unit?

When dividing a timeseries by its mean value so that its mean becomes 1, does the resulting data still have a unit or is it unitless?
Leo's user avatar
  • 495
2 votes
1 answer
1k views

What are the tests to measure agreement between two methods of measurement when the unit of measurement is different between the two methods?

Bland-Altman plot measure the agreement between two different methods which measures the same variable. As far as I understand Bland-Altman can measure only if the two methods have the same unit of ...
Padmanaban's user avatar
2 votes
2 answers
714 views

Changing the units for an independent variable in a Poisson model

I'm trying to model a dose-response relationship between the incidence of cancer (dependent variable, counts) and the radiation dose (independent variable in gray). Can I change the unit of the ...
Nicolas's user avatar
  • 133
4 votes
1 answer
2k views

lognormal distribution, standard-deviation and (physical) units

I have a distribution of microparticles that follows a lognormal distribution. The cumulative distribution function thus is given by: $$ F_X(x;\mu,\sigma) = \frac12 \operatorname{erfc}\!\left(-\frac{\...
akid's user avatar
  • 143
1 vote
0 answers
560 views

Z-score calculation for a single variable with readings in multiple units

I ran into little trouble transforming a set of data I need for analysis. I have been trying to analyze results of a lab test as Z-scores. I have an output field with a reading and unit field. Data ...
myriadcolours's user avatar
6 votes
2 answers
430 views

Getting the units right for the Pareto distribution of wealth: x = people, dollars, dollars per person?

When people talk about the 80-20 rule in the context of wealth, it is usually expressed, verbally, by stating that the 20 percent of the people with the highest wealth get 80 percent of the wealth, ...
andrewH's user avatar
  • 3,117
3 votes
2 answers
352 views

What is a dimensionless indicator?

What is a dimensionless indicator? I assume it refers to the fact that it is consistent in the way that it doesn't vary disproportionately at the variation of its factors.
Mihai Despa's user avatar