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

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87 views

How to tell if a sample comes from a distribution with infinite mean?

I observe a sample from a distribution that I expect to be the hitting time $$\tau = \inf\{t>0| X(t)>a\}$$ where $X(t)$ is a Lévy process with $X(0)=0$ and $a$ is some constant. $X$ is not a ...
3
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0answers
133 views

How do I forecast a timeseries of data using GARCH(1,1)?

I'm new to GARCH, but I've got daily data of TV Ratings. I've been trying to forecast this for future, and a quick background - the data is non-stationary, has high seasonality (weekly, monthly & ...
3
votes
3answers
2k views

Calculate mean of ordinal variable

I've read in a number of places that calculating the mean of an ordinal variable is inappropriate. I'm trying to get an intuition for why it might be inappropriate. I think it is because, in general, ...
1
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2answers
1k views

How do I estimate the mean of a variable for different groups by controlling for age, gender, education…?

I am trying to estimate the mean of a variable for 2 different groups. If in Stata I use . bys group: sum variable I'll get the mean. However, there are ...
0
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1answer
97 views

Statistically evaluating performance of algorithms

I am working on a problem for which I have come up with a couple of algorithms. To assess which one is the best, I compare a set of algorithm outputs (set of numbers) against the "true" set of values ...
2
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0answers
121 views

Robust estimation of mean with small sample size

Working with a 2D sensor. A row consists of 4096 samples, of which there are 16 reference samples (the rest are active). The reference samples do not measure the signal, but are used to estimate the ...
0
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1answer
36 views

Is it possible to generate means and standard deviations for two groups based on a Cohen's d?

Is it possible to generate means and standard deviation for two groups from a Cohen's d effect size? Even if the means and standard deviations are trivial/meaningless values, I would like to keep the ...
0
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2answers
118 views

Can time series be used to predict series which has a changing trend?

Supposing I have a stock return series from 2000-2013. Looking at the data, it has pattern of long trending bull market: 2001-2008, and 2010-2013, while it also has great reversal in 2008 financial ...
4
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0answers
111 views

Backing out the standard deviation from information on baseline mean/s.d., and coefficient mean/s.d

I am trying to run a power calculation for a randomized control trial. For this I need a mean and standard deviation for our 'baseline'. There are papers out there which would have a mean and standard ...
0
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1answer
42 views

Calculating mean percents

Are there any rules to calculating mean percent or is it the same as calculating any other average (i.e., add all of the percents together and divide by the sample size)?
4
votes
1answer
94 views

How many counts are required to estimate a mean to a certain precision?

I have been photographing bubbles arriving at a fluid surface. The photographs are obtained at rate of one image per minute. Given that the frame of the image is always the same size and the source of ...
0
votes
3answers
123 views

Normality of a lognormal variable having a spike in 0?

I have two very right-skewed datasets which I must study for difference in means. Given the skewness, I transformed using log 10 scale after adding 1 to be able to take the log. In other words: ...
0
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0answers
65 views

Frechet Mean of Multiple Curves

I'm working on determining the Frechet mean of several curves. I am using this equation: $$ \sum_{n=1} (P_a - P_b)^2 $$ but I'm not entirely sure how I would do this across multiple curves. Also, ...
4
votes
1answer
161 views

Notation for sample mean: $\overline{Y}_{\cdot{j}}=\frac{\sum\limits_{i=1}^N Y_{ij}}{N}$

I sometimes see the following notation, e.g., for the mean of the jth variable over N observations: $\overline{Y}_{\cdot{j}}=\frac{\sum\limits_{i=1}^N Y_{ij}}{N}$ My question is: What is this little ...
2
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1answer
42 views

How to best account for population sizes in disease outbreaks

Say one has the fatality and survivor rates of a pathogen in terms of geographical location (e.g., the latest data on the MERS-CoV). ...
14
votes
3answers
748 views

Example of distribution where large sample size is necessary for central limit theorem

Some books state a sample size of size 30 or higher is necessary for the central limit theorem to give a good approximation for $\bar{X}$. I know this isn't enough for all distributions. I wish ...
0
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2answers
98 views

High standard deviation: rule of thumb

I know this is a pretty vague question but I was wondering if there was a rule of thumb relation between the mean and the standard deviation of a given set of values by which you can say "Something's ...
0
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0answers
411 views

Finding the mean difference of two data sets in R, within a confidence interval

I'm analysing benchmark data for some of my R functions, and I'm trying to compute a statistic describing how many times faster my function - group_one - is than a control function - group_two - as a ...
1
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1answer
203 views

how to rank items measured with a likert scale?

I have a 70 or so items all measured with a 5 point likert scale. What I'd like to do is take their mean value and rank the items according to their means but with respect to statistical significance ...
4
votes
1answer
12k views

“Accept null hypothesis” or “fail to reject the null hypothesis”?

I'm trying to conduct a Student's t-test for a table of values while trying to follow the explanation and details found on this website. I understand that if the p-value is <.01 then it's really ...
2
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0answers
126 views

Comparison of dependent but unpaired data sets

I'm trying to find a statistical test that can help me compare the means of two dependent groups. My data: parameter values from white matter region in an in vivo rat brain parameter values ...
3
votes
1answer
162 views

Question about squares of the coefficients of variation

Suppose that $X$ is a random variable with any distribution that takes only positive values. Can the following inequality hold for constants $c_2 >c_1 >0$? ...
0
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1answer
94 views

Simple Mean/Average

I have results from a likert scale 1 - strongly disagree-5 - strongly agree. I also had a N/A and a Not Sure category. How do I calculate the average response? I am thinking to not include the n/a's ...
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0answers
89 views

Marketing research survey results

I added a question about marketing research survey result. There are two questions and two results related to this survey. Can you help me answer these questions about this data sheet.
2
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1answer
117 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
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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
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1answer
104 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
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0answers
90 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 ...
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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
251 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
530 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 ...
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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 ...
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0answers
125 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 ...
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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
86 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
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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
127 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
419 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
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0answers
96 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
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1answer
313 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 ...
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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
127 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
1k 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
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2answers
170 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. ...
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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
183 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
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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
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1answer
751 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
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1answer
135 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
391 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 ...