The expected value of a random variable; or a location measure for a sample.

learn more… | top users | synonyms

2
votes
1answer
113 views

Best way to estimate mean of RV from independent samples

Suppose we have N independently drawn samples from an unknown random variable $X$. What is the best way to estimate the expectation of $X$? For simplicity, we can assume that $X$ only returns values ...
1
vote
1answer
76 views

Constrained mean variance optimization

I have some numbers $X={x_1,x_2,...,x_n}$. I add some small numbers to them and get $Y={y_1,y_2,...,y_n}$ where $y_i=x_i+\epsilon_i$. How can I find $Z={z_1,z_2,...,z_n}$ to minimize ...
0
votes
1answer
101 views

How to add prediction intervals to describe the variability in monthly samples of data?

The data analyzed here is a sample of individuals collected on a monthly basis. What would be the best way to compute "prediction intervals" for the monthly sample means, in order to indicate the ...
4
votes
0answers
87 views

How to test whether mean and variance is the same in two small samples?

I would like to test two relatively small samples against the null hypothesis that both their means and variances are the same. The alternative would be that they in fact differ. I saw a post on this ...
0
votes
0answers
37 views

Control mean lower than treatment mean in a list experiment — why?

I have a list experiment with N=150. The control group was given 3 factors and the treatment group was given 4 factors, with random assignment to these groups. Each group had to report how many ...
4
votes
1answer
238 views

Estimation of mean, variance and mean squared error of a histogram that poorly models real distribution

I'm having a basic statistics problem. I'm running an experiment using a photon counting detector to measure a diffraction pattern. I want to calculate the centroid of each diffraction spot and the ...
2
votes
2answers
464 views

Help with Anova of categorical and continuous variable in R and SPSS output

I am having some trouble running an Anova on categorical variables in R and matching SPSS output. What I need to do is run an anova on the dataset below (its a made up data set). But, I need to know ...
1
vote
3answers
93 views

Testing whether two groups formed from a continuous variable differ on a binary outcome

18 people, who have been divided into 2 groups based on the semiquantitative expression of a protein (low vs high). Group 1 (low protein levels) has 6 people, Group 2 (high protein levels) has 12 ...
1
vote
0answers
114 views

Mean and variance of call center data

I have a fairly involved homework question, I was wondering if I could get some help. There are two types of phone calls arriving at a switch, long-duration and short-duration. Each day the number ...
1
vote
1answer
50 views

Mean and variance of number of tries required

So the question states that I'm trying something with an 85% chance of success, if I don't succeed I try again until I do. What is the mean and variance of the number of tries necessary until I ...
0
votes
2answers
85 views

Simple homework question about normally distributed variables

The question states: Consider a set of random variables $X_i$, where $i=1,...n$. Each $X_i$ is normally distributed with mean $0$ and variance $1$, i.e. $X_i$ are $\mathcal N(0,1)$. What is ...
0
votes
2answers
112 views

Why do we refer to our estimates in terms of precision?

Open any statistics textbook and it will urge the need to check the 'precision of our estimates'. Take the following random variable: ...
2
votes
0answers
119 views

Best estimate for a decile or quintile mean from a known distributional family?

Suppose you have a population drawn from a known distributional family f with a vector of unknown parameters θ. You may also assume that the distribution is strictly non-negative and skewed, with a ...
2
votes
1answer
365 views

Test for comparing “mean of means”

I have a treatment and a control group. Both groups consist of several teams, each with several individuals. When I want to compare the performance between the groups, I could run a t-test or Wilcoxon ...
0
votes
0answers
95 views

What statistical method used to compare mean and inspect developmental changes?

I use a multiple mediator model in describing my data, and age is the independent variable (IV). I want to see if there exist developmental changes at the level of my dependent variable (DV) that are ...
0
votes
1answer
286 views

Mean of means -> error propagation or uncertainty or both?

my problem is as follows. I have a simulation of a neural network which creates activity patterns, learns them and then tries to retrieve previously learned patterns one by one. The performance of ...
0
votes
0answers
78 views

equating problem with instrument that have two version

I want to measure metacognition (as a whole construct and per subscale, (knowledge of cognition (KC)) and regulation of cognition (RC)) development in children using the Jr MAI inventory. The Jr MAI ...
6
votes
2answers
124 views

Robust mean estimation with O(1) update efficiency

I am looking for a robust estimation of the mean that has a specific property. I have a set of elements for which I want to calculate this statistic. Then, I add new elements one at a time, and for ...
2
votes
1answer
943 views

Interpretation of mean in this example

I recently presented a national test and the company in charge of preparing the test then does a standardization to provide the final scores for each person. These are the values they gave at the end ...
2
votes
2answers
164 views

What should I do when a confidence interval includes an impossible range of values?

Let's say I'm analyzing the mean number of students per class for a school district. The district has imposed a hard limit on the maximum ratio: there can never be more than 30 students in a class. ...
1
vote
0answers
78 views

Can the proof of the central limit theorem be expressed as the limit of a convolution with an operator

The central limit theorem, as I understand it (engineer, non-statistician), says that the distribution comprised of means of some other reasonably behaved distributions converges to a normal ...
0
votes
1answer
181 views

Regression on means of log-transformed variables

Suppose that I want to study the relationship between two variables $Y$ and $X$ using the linear model $Y \sim X$. Unfortunately, both $Y$ and $X$ are not normally distributed, say they are both ...
0
votes
0answers
2k views

How to report results from Friedman's test including post-hoc results

I have performed comparison of repeated measures for a group using Friedman’s test (K-related-samples test) and additional post-hoc analysis with Wilcoxon signed-rank test and Bonferroni correction. I ...
0
votes
1answer
732 views

How to derive p-value from standard error between two group means?

Data was collected on binary variable and continuous variable. The binary variable represents two groups. Group 1 has a sample size $n_1$ and mean $\mu_1$ on the continuous variable Group 2 has a ...
0
votes
1answer
130 views

Given weighted mean and raw data, derive weights to minimize error

Imagine I have a set of data from an experiment: Observed Measurement 1: 5 Observed Measurement 2: 6 Observed Measurement 3: 7 Observed Measurement 4: 8 Observed Measurement 5: 9 I have a target ...
2
votes
1answer
371 views

Standard deviation of revenue where numbers are only positive

Is there a way for standard deviation to ignore negative numbers? In other words, how can you make it so that 2 or 3 deviations do not extend into negative territory? When looking at a set of only ...
-1
votes
2answers
105 views

can I compare standard deviation and mean?

I hope no question is too simple. I am just learning, and I came across an expression that compared standard deviation and mean of a distribution. I thought that it makes no sense to compare them, ...
1
vote
0answers
517 views

Ordinal data, different scales, comparison between variables

I would appreciate any help you could give me I have ordinal data which I want to standardise in order to compare averages and data spread between variables. I need to standardise since the variables ...
12
votes
4answers
2k views

Is it appropriate to plot the mean in a histogram?

Is it "okay" to add a vertical line to a histogram to visualize the mean value? It seems okay to me, but I've never seen this in textbooks and the likes, so I'm wondering if there's some sort of ...
0
votes
0answers
48 views

Removing data above the mean

I am working with a data set, for which to remove noisy data I take the average of the sample itself and cut anything above that average. What I'm trying to understand here is does this have a name ...
3
votes
1answer
91 views

Distribution family of the mean of iid random variables

Let $X_1,X_2,...,X_n$ be $n$ iid random variables following some distribution family $A$ (beta, gamma, normal, etc.). Does the mean $\bar{X}=\frac{1}{n}\sum{X_i}$ also follow a $A$-like distribution ...
0
votes
0answers
53 views

Appropriate tests for finding a diffference between the scores of two groups of questions

I am testing whether there is difference between the scores of 2 groups of 12 questions on a Likert-scale questionnaire. Each question from one group has a corresponding question in the other group ...
0
votes
2answers
781 views

Mean comparison for statistical significance

I was told to come here by a friend to ask a stats question. I took Social Stats and Methods of Social Research about 4 years ago and to be honest, I don't remember much about it. Now I'm writing a ...
1
vote
2answers
200 views

Mean of a function of $K$ Gaussian random variables

Consider $K$ Gaussian random variables $Z_1, Z_2,\ldots,Z_K$ that are mutually independent with $Z_1 \sim \mathcal{N}(\mu,\sigma^2)$ and the remaining random variables $\sim \mathcal{N}(0,\sigma^2)$. ...
0
votes
1answer
187 views

Show that $E(XY) = σ_{XY} + μ_Xμ_Y$?

Let X and Y be two random variables with means $μ_X$ and $μ_Y$ , variances $σ^2_Y$, $σ^2_X$ and covariance $σ_{XY}$ . Show that $E(XY) = σ_{XY} + μ_Xμ_Y$? I tried the Covariance formula with: ...
3
votes
1answer
1k views

How is finding the centroid different from finding the mean?

When performing hierarchical clustering, one can use many metrics to measure the distance between clusters. Two such metrics imply calculation of the centroids and means of data points in the ...
0
votes
1answer
241 views

Plotting means and standard deviations

Does it make sense to look at a scatterplot of means versus standard deviations in terms of looking for outliers or changepoints? So the mean is on the x-axis and the standard deviation is on the ...
1
vote
0answers
90 views

Variance explained for averaged values

I am trying to work out how good my particular model is at explaining some observed data. The problem here is that the observed data takes the form of averaged (mean) values for each of my predictive ...
3
votes
2answers
173 views

Finding mean and standard deviation

Experience raising Labrador puppies revealed that the weight of the puppies at six months follow a normal distribution. The subsequent weights (in pounds) of a small sample of seven six-month puppies ...
6
votes
3answers
7k views

R: Calculating mean and standard error of mean for factors with lm() vs. direct calculation -edited

When dealing with data with factors R can be used to calculate the means for each group with the lm() function. This also gives the standard errors for the estimated means. But this standard error ...
1
vote
1answer
66 views

Average rate versus average period

I am working on a project where I need to do workload balancing, and to see how well my approach is working I want to compute both the average amount of time between requests for a workload and the ...
1
vote
1answer
248 views

Compare means of two groups with a variable that has multiple sub-group

I was unable to understand how to compare multiple mean values in each group. Within the subgroup the mean values influence each other (If one changes, the other changes automatically). I collected ...
2
votes
2answers
132 views

Interpretation of an equation

I'm trying to describe the equation in the attached screenshot in my own words. $\lvert(\overline\chi_1-\overline\chi_2)\rvert > s_1(t_{1 @ 99 \%}) + s_2(t_{2 @ 75 \%})$ The equation tests ...
1
vote
0answers
54 views

Assessing the consistency of an estimator of the average path length of a large network

I have found the following in a network-science article and would like clarification of what the authors are claiming: We observe that the root mean square of the difference between the empirical ...
1
vote
1answer
158 views

Comparing many means in JMP

I'm trying to compare several sets of experiment data, by comparing means. I read there are several different tests such as Each Pair, Student’s t and All Pairs, Tukey HSD, which give different ...
2
votes
1answer
121 views

Normal distribution in R

I am trying to check what is the probability that a new observation is anomalous or not? Suppose I have the following set of observations: ...
0
votes
5answers
769 views

How can I find distribution from mean and variance

If I know the mean and variance of a discrete random variable $\in \{0,1,\dots \}$, How can I find the distribution?
9
votes
5answers
895 views

If not a Poisson, then what distribution is this?

I have a data set containing the number of actions performed by individuals over the course of 7 days. The specific action shouldn't be relevant for this question. Here are some descriptive statistics ...
0
votes
1answer
50 views

What number minimises RMSD between itself and randomly generated numbers?

Let us assume that we have a random number generator given by its probability density function. Now, we need to use this distribution to generate a number that has the following property. It minimises ...
8
votes
2answers
5k views

Mean absolute error OR root mean squared error?

Why use Root Mean Squared Error (RMSE) instead of Mean Absolute Error (MAE)?? Hi I've been investigating the error generated in a calculation - I initially calculated the error as a Root Mean ...