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

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2
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2answers
31 views

The Mean of the number of times until an event occurs

Lets say we have 6 cards in a hat, that are all red. Now each time, we blindly take a card out of the hat: - If the card is red, we take it out of the hat and insert a blue card. - If the card is ...
0
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0answers
8 views

How to test adjusted mean in R?

I have got eight adjusted means for eight subgroups in a survey study, but I don't know how to test the differences of these eight adjusted means. Any suggestion is appreciated. Thanks!
6
votes
1answer
111 views
+50

Can we use leave one out mean and standard deviation to reveal the outliers?

Suppose I have normally distributed data. For each element of the data I want to check how many SDs it is away from the mean. There might be an outlier in the data (likely only one, but might be also ...
2
votes
1answer
46 views

Why does a confidence interval including 0 mean the difference is not significant?

Could someone please explain why zero being inside or outside the confidence interval tells you whether or not the difference is significant?
2
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0answers
16 views

with two EWMA means, can we reconstruct any EWMA mean?

EWMA is defined as follows(1, 2, 3, 4, 5): $$ \mu_{N} = \frac {1}{N} \Sigma_{i=1}^{N}x_i $$ $$ =\frac {1}{N} \Sigma_{i=1}^{N-1}x_i + \frac{1}{N}x_{N} $$ $$ =\frac {N-1}{N} \frac{1}{N-1} ...
1
vote
1answer
25 views

Sequence of Random Variables

I am confused about how to approach sequence of random variables that are not identically distributed. For example, consider a sequence $X_1, X_2, \dots, X_n$ with the pdf: $$ f(X_n)= \begin{cases} ...
0
votes
0answers
43 views

What is the multivariate analog of the median?

There is a univariate mean: sum the points and divide by the count. There is a multivariate mean analog - the centroid, a point in a multidimensional space. (1). For the median one sorts the list ...
4
votes
1answer
157 views

Can the mean lie outside the the interquartile range (Q1 and Q3)? and if so what does it do to the distribution

Can the mean lie outside of the interquartile range? I realize that extreme outliers can affect or pull the mean, but can it pull the mean outside of the interval from the first quartile to the third ...
0
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0answers
20 views

Mean centering variables NOT in a moderation/interaction term [duplicate]

I am trying to assess the impact of multicollinearity in a regression because I have two separately measured variables which have the reversed signs problem (one predictor is +b regression weight, the ...
0
votes
0answers
15 views

Mean independence and full independence

What is an example of two random variables x and u that are NOT fully independent but such that E(u|x) = 0? Many thanks!
0
votes
0answers
61 views

Distributions where higher variance in sample estimates leads to smaller loss when estimating mean

Let's say I have an unknown distribution a. I do not know the shape, mean or variance of this distribution but I have access to another distribution ...
2
votes
1answer
21 views

Distribution of Sample Means Compared to Population Mean

Assumptions I have a population (n=5000) and I know everything about it (all point values, mean, standard deviation, etc.) From this, I will sample 1000 items. I can calculate the mean of the sample ...
1
vote
1answer
58 views

how to use arima to do mean model

I am learning arima by this site: http://people.duke.edu/~rnau/411home.htm and I want to get the same result as following notes: ...
1
vote
1answer
25 views

Deriving the formula for the mean of a stratified sample

The formula for the mean of a stratified sample $\bar Y_s$ is: $$\bar Y_s = \frac 1 N \sum_i N_i \bar Y_i$$ where $N$ is the sample size for all strata, and $N_i$ and $Y_i$ are the sample size and ...
0
votes
1answer
50 views

Using Bootstrap to estimate confidence interval of the standard deviation

I am trying to compare two different methods of estimating confidence intervals: a parametric approach that uses the assumption that the sample is t-distributed (i.e. the formulas that are given here: ...
7
votes
3answers
143 views

How can I interpret a plot of trimming percentage vs. trimmed mean?

For part of a homework question, I was asked to calculate the trimmed mean for a dataset by deleting the smallest and largest observation, and to interpret the result. The trimmed mean was lower than ...
1
vote
2answers
64 views

Adding two (or more) means and calculating the new standard deviation

There are a load of discussions online about adding means and recalculating the standard deviation, but on none have I found answer to this question. I have two sub groups with mean $x_1$ and $x_2$, ...
1
vote
2answers
58 views

Comparing normal with non-normal

I have two sets of data for setup time of a machine, one is setup time when fixture is running alone, another is when another fixture is running alongside. For fixture running alone the data I ...
0
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0answers
17 views

Mean in Cumulative frequencies distribution

Monthly expense Cumulative Freq. up to 50 7 up to 80 25 up to 120 49 up to 200 58 over 200 60 Calculate ...
-1
votes
1answer
28 views

Can Coefficient of Variation be used to verify the representativeness of the mean?

I have a sample with approximately 45 million elements, with 4,410 as the mean and 1,657 as the standard deviation. I am not confident whether or not the mean well represents the sample due to the ...
0
votes
1answer
14 views

Correlation on mean values

Please note: the variables named in this example do not correspond with actual variable type values, but are simplified for clarity purposes. I have 13 groups, each containing values X of, say, the ...
1
vote
1answer
59 views

Can I use z-scores in right skewed distributions?

I have a right-skewed distribution that represents that number of "likes" on a certain car category for a number of users. What I am trying to do is a sort of classification based on z-scores. For ...
0
votes
0answers
17 views

Testing if the mean of one data set is bigger than the mean of the other data set [duplicate]

I have two data sets, i.e., the number of flowers measured in field A and in field B. Each data set has about 40 samples. I want to do a test to check the hypothesis that field A has more flowers than ...
1
vote
0answers
13 views

Plotting raw data, but running statistics on log-transformed data

My data is non-normal, I want to show my raw data, in a scientific journal, by median +/- mad, to show the true nature of the data. However, if log-transformed, the data is normal. Can I then ...
0
votes
0answers
12 views

real time object tracking

I have correlation value of object using mean and standard deviation, now i want to normalized that correlation value. how can get normalized correlation in terms of percentage vale?
5
votes
1answer
134 views

$\bar{X}$ versus $\mathbb{E}(\bar{X})$?

I was not able to find this question here, so I am going to ask this: What is the difference between $\mathbb{E}(\bar{X})$ (expected value of $X$ bar) and the actual $\bar{X}$? I am very confused ...
0
votes
1answer
6 views

Best method of estimating the output rate of a group

I have a sample dataset consisting of 2 fields, output volume and input time (in hours) for different persons performing an identical task several times each. What is the best method of estimating ...
0
votes
0answers
11 views

Histograms With No Final Interval Upper Limit

If you have the following histogram, how do you calculate the mean if you do not know the upper limit of the final interval: ...
0
votes
0answers
11 views

Assign attributes / categories to users based on their activity / likes

I have a very practical classification problem for which I need some help. I have a database of users along with their activity / likes for a number of car models. I also have the category each of ...
1
vote
1answer
55 views

Standard error bars overlap but significance - estimated marginal means versus observed means

I'm running a Mixed effects model ANOVA with two fixed factors (condition, repetition) and one random factor (subject). Subsequently, a Tukey multiple comparisons test is performed. Now I'd like to ...
2
votes
1answer
73 views

First order statistics (min) of n non-identical but independent normal variates [duplicate]

While I have seen papers and posts about mean and variance of n i.i.d normal random variables, I am looking for the first order statistics of $n$ (specifically $11$) normal, non-identical (different ...
0
votes
0answers
80 views

Finding the value of the pressure to maximize mean

The peel strength ($Y$) of photo resist in the lamination process of PCBs depends on the pressure ($x$) and temperature ($z$) by the relation: $$Y = 50 + 5x + 10z + (20xz)-(.01(x^2)\cdot (z^2))$$ ...
3
votes
2answers
232 views

Outliers and the mean

I would like to know what the following example is called in mathematics: In a gymnastics competition the judges scored a competitor as 10, 8, 3, 7, 7, 9, and 8. I recall that the ending score was ...
2
votes
1answer
37 views

How to measure if a mean is stable

Background I am a physics major, however I am currently interning at a psychiatry/neuro-imaging laboratory. The primary area of research in my lab is diffusion tensor imaging (DTI). A lot of the ...
2
votes
1answer
32 views

Run Many Small or a Few Big Simulations to Estimate the Mean?

I was just running some simulations on tossing a coin given certain conditions, to test out some ideas I had. I was trying to find the ratio $\frac{\mathtt{successful\ tosses}}{\mathtt{total\ ...
1
vote
1answer
25 views

Assuming the true mean

I've collected fluorescence data from some bacterial cells. Each cell has a gene in it which can be induced to fluoresce. However, even without being induced, the gene will still fluoresce a little. ...
1
vote
0answers
43 views

Mean imputation/estimation of missing data

Could someone please refer me to papers that have imputed the mean to missing values of a continuous variable? (i.e. papers that have used mean imputation) I have imputed my missing IMD values using ...
2
votes
2answers
144 views

How do I calculate confidence intervals for a non-normal distribution?

I have 383 samples that have heavy bias for some common values, how would I calculate the 95% CI for the mean? I the CI that I calculated seem way off, which I assume is because my data does not look ...
0
votes
0answers
10 views

Standard error for expected value [duplicate]

I have a computer simulation from which I get a sample of values of some microscopic quantity $X$, i.e. $\{ x_1,\ldots,x_N \}$. I'm interested in estimating the expected value of $X$, i.e. $E[ ...
0
votes
0answers
21 views

Mean squared error / Max error squared

I'm use this metric for variation that is similar to CV, but it is guaranteed to be on a 0 to 2 scale for positive numbers, where 2 is "all over the place" and 0 is "perfectly even". Since its ...
5
votes
1answer
76 views

Why are Winsorized random variables independent?

While studying trimmed mean I understood that if I have some random variables $X_1, X_2, .., X_n$ by ordering them and trimming, the variables are no longer independent. However it is said that "by ...
0
votes
1answer
93 views

High Standard Deviation for Leave one out cross-validation?

I am using the leave one out cross-validation technique to evaluate my model. If the prediction on the test sample is right the output is 1 otherwise 0. So I have a array of N samples with 0's and 1's ...
2
votes
1answer
55 views

Standard Deviation After Subtracting One Mean From Another

I've got two sets of data from some fluorescent cells. The first set is when the cells don't have their fluorescence switched on, but they are still faintly glowing. The second set is when they do ...
4
votes
3answers
129 views

Estimating the ratio of cell means in ANOVA under lognormal assumption

I am conducting a two-sample test (1-way ANOVA with 2 treatments), and the goal is to estimate the ratio of cell means assuming that the data are lognormal. A simple approach is to log the response ...
1
vote
1answer
39 views

How to Test if the Difference between Two Means from Different Samples are Significant?

here are distributions of four samples: and the following is the table of data: I would like to test: (1) if the difference between means of "Give" and "Work-Give" samples is significant; and (2) ...
0
votes
1answer
19 views

Given MTTF and Number of Items, how to calculate failing parts with Time?

I am wondering how to make use of MTTF Here is the situation, I am given an MTTF for an item type x and a certain demand for that item in the next 25 years, say 100 parts that will be in operation ...
0
votes
0answers
5 views

Contribution of residuals to the mean error

I have data for 1000 students' performance over 10 different tests on a scale of 0 -100 (a 1000 rows X 10 col matrix). I calculated the mean score and the associated std. deviation for each student. ...
2
votes
0answers
68 views

Average of predicted values with logistic regression

I have a large unbalanced dataset (the target has ~1500x more 0's than 1's) on which I train a logistic regression algorithm to predict the probability of success (Not a binary outcome but a real ...
3
votes
3answers
213 views

Should I use t-test on highly skewed and discrete data?

I have samples from a highly skewed dataset about users' participation (e.g.: number of posts), that have different sizes (but not less than 200) and I want to compare their mean. For that, I'm using ...
7
votes
1answer
791 views

Should I use t-test on highly skewed data ? Scientific proof, please?

I have samples from a highly skewed (looking like an exponential distribution) dataset about users' participation (e.g.: number of posts), that have different sizes (but not less than 200) and I want ...