Questions tagged [trimmed-mean]
A k-trimmed mean is a mean where the largest and smallest k% of the observations are removed before the mean is calculated.
36
questions
0
votes
0
answers
41
views
How can I draw a interaction plot using trimmed means?
I am conducting two-way ANOVA in r using the t2way function in WRS2 packages for my thesis.
t2way function, as you know, uses trimmed mean to escape from the severe problem of heterogeneity of ...
- 1
3
votes
1
answer
279
views
How does the 30% trimmed mean of this equal 6.167?
[6, 3, 7, 11, 5, 3, 8, 7, 2, 6, 9, 13, 10, 4, 3]
So I'm going through some revision for stats, one of the questions asks to find the trimmed mean of the above data. I've worked it out but my answer ...
- 31
1
vote
1
answer
262
views
Calculating the trimmed mean as an estimator
My book provides the following steps to calculate the $ 100 \alpha$ percent trimmed mean for a sample data of $n$ measurments:
1-Order the measurments.
2-Discard the smallest $100\alpha$ percent and ...
- 37
2
votes
2
answers
470
views
If we are taught to not remove outliers without investigation, how do robust methods (median, trimmed mean) can be even suggested?
I just saw an article, which taught to nor remove outliers without investigation, because it may be a unusual but valid observation or naturally skewed data, for example in chemistry or medicine. Only ...
7
votes
1
answer
4k
views
Use and misuse of Winsorization
I am doing research on Winsorization (and trimming), which has been broadly applied in many fields, but I think many researchers didn't do it in a "rigorous" way. Or maybe even worse, they misuse it. ...
- 693
3
votes
1
answer
70
views
If all trimmed means are equal does this imply equal distributions?
I am trying to prove the following:
Given that $\forall \alpha\in [0,1]$:
$$\int_{F_S^{-1}(\alpha)}^{\infty}xf_S(x)\,dx = \int_{F_0^{-1}(\alpha)}^{\infty}yf_0(y)\,dy$$
where $F_S^{-1}(\alpha)$ and $...
- 33
6
votes
2
answers
1k
views
An X% trimmed mean means?
Rand Wilcox in Fundamentals Of Statistical Methods, 1st. edition, gives a formula which says that for a 20% trimmed mean, you would trim away 20% of one end of the ranked data, and 20% of the other ...
- 459
0
votes
0
answers
52
views
When is it better to exclude outliers and calculate the mean of the data instead of using the median?
I already searched on when to use the mean and median and I often see that median might be better than mean when the data is skewed, ordinal, include outliers, etc.. even tho, this might not be always ...
- 103
2
votes
0
answers
242
views
Skewed data: Is trimming the means necessary when using bootstrapping to compare means?
I want to compare four different groups on one dependent variable. Normally I'd do a one-way independent ANOVA, except that this time the normality assumption isn't met at all (see the below ...
- 481
3
votes
1
answer
2k
views
Treatment of outliers in financial data
I have a data set with financial panel data from 150 companies. I want to analyse the data using linear repeated measures ANOVA and OLS Regression (so far). For this, I want to use the absolute values ...
- 41
6
votes
2
answers
2k
views
Mean vs. Trimmed mean in the normal distribution
In a simple experiment with the normal distribution in R I ran 500 iterations of a simulated normal distribution with N=100 each. For each iteration from the 500 iterations, I calculated both the ...
- 213
13
votes
1
answer
3k
views
Downweight outliers in mean
I have a bunch of points $x_i$ and would like to calculate a kind of weighted mean that deemphasizes outliers. My first idea was to weight each point by $1/ (x_i - \mu)^2$. However, the problem is ...
- 301
3
votes
1
answer
839
views
Does the Hodges-Lehmann estimator perform better than trimmed/winsorized means?
I've been reading about the HL estimator, and a question came to mind. I could fairly easily create a mean-estimator where I trim or clip 29% of the data on either side and have a statistic with a ...
- 75
2
votes
2
answers
2k
views
What is the difference between GAS ( Generalized Autoregressive Score) model and a GARCH?
I am trying to analyze some data about Brent Oil volatility. So far I have managed to fit a GARCH(1,1) model and an EGARCH. However, someone has recommended to use a GAS model, Generalized ...
- 1,116
3
votes
0
answers
759
views
How to calculate a confidence interval for a trimmed mean
I try to get the sample size that presents the population, I averaged randomly the 10 and then the 20 readings then I used the formula CI = 1.96 * std/root n, that gave me the CI at any (n), but how ...
- 31
0
votes
0
answers
481
views
Using trimmed means and Winsorized variances to compute standardisation of data
I am looking into the pros and cons of each normalisation technique for work and it got me thinking. What if I used trimmed means and the sqrt of Winsorized variances to compute the standardised data? ...
- 307
0
votes
0
answers
111
views
Trimming, Winsorising and manipulating biological data
So I have an experiment with multiple groups (groups 1-6), individuals in each group (n=10), and read outs per individual. Eg. below
Group 1: 28.1, 28.6, 29, 30.3,30.4,30.6,30.7,31.1.34
Group ...
- 587
9
votes
1
answer
658
views
Sampling distribution of sample trimmed (truncated) mean
It is elementary probability theory that the sample mean of an i.i.d. sample follows normal distribution, if the background distribution is normal. But what about the trimmed mean? Is there any result ...
- 3,403
10
votes
2
answers
10k
views
Trimmed mean vs median
I have a data set with all the calls made to an emergency service and the response times of the ambulance department. They admitted that there are some mistakes with the response times as there are ...
- 103
0
votes
1
answer
67
views
Trimmed mean for specific groups
I have a dataset with all the calls to an emergency service in a period of time.
I have information about the time (in seconds) that it took to respond to that call and the area where the emergency ...
- 103
12
votes
3
answers
1k
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 ...
- 255
5
votes
1
answer
708
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 ...
- 6,804
3
votes
2
answers
694
views
Modeling trimmed mean
In OLS, the conditional mean $E(Y \mid X)$ is modeled as a function of some regressors $X$, i.e.
$$
E(Y \mid X) = X \beta.
$$
Is there a regression technique that allows to model the conditional ...
- 11.6k
37
votes
5
answers
33k
views
What are the relative merits of Winsorizing vs. Trimming data?
Winsorizing data means to replace the extreme values of a data set with a certain percentile value from each end, while Trimming or Truncating involves removing those extreme values.
I always see ...
- 631
2
votes
0
answers
417
views
How to investigate properties of the trimmed mean for a Cauchy variable?
Let $X_1,X_2, \dots,X_n$ be a sample from a population with distribution function $F(x-\theta)$, where $F$ is symmetric around $0$. The $\alpha$ trimmed mean $T_n(\alpha)=\dfrac{1}{n-2\lfloor n\alpha \...
- 2,090
9
votes
2
answers
2k
views
Given independence, is the median of a product equal to the product of the medians?
Question: Assume $X$ and $Y$ are independent random variables. Is $Median(XY) = Median(X) \cdot Median(Y)$? If so, how would one prove this? If not, what conditions would be sufficient for this ...
- 807
3
votes
1
answer
614
views
7
votes
3
answers
1k
views
Mean has lower standard error than 5% trimmed mean?
I'm investigating using a trimmed mean to measure the location of various distributions. The distributions sometimes are heavily contaminated and sometimes not. Usually they follow something similar ...
- 165
2
votes
0
answers
325
views
Do methods based on trimmed means require homoscedasticity?
I understand (from Wilcox' book [1]) that methods using the trimmed means are robust to distributional assumptions.
Do the methods (e.g. bwtrim, from the ...
- 837
1
vote
0
answers
790
views
Examining the relative efficiency of the trimmed mean
Using the following reference A survey of sampling from contaminated distributions, I am trying to investigate the relative efficiency (RE) for the mean vs the trimmed mean, given the following ...
- 133
8
votes
2
answers
692
views
For what distribution is a trimmed mean the maximum likelihood estimator?
The sample mean is the maximum likelihood estimator of $\mu$ for a normal distribution $\text{Normal}(\mu,\sigma)$. The sample median is the maximum likelihood estimator of $m$ for a Laplace ...
- 6,760
3
votes
2
answers
2k
views
How to interpret output from least trimmed squares estimate and compare it to OLS?
I have to compute and compare the least squares method on a model to the least trimmed method.
The LS model results were:
...
- 41
4
votes
1
answer
2k
views
Is it allowed to use a 5% trimmed mean for analyzing data from a creativity task (quantity of ideas)?
For my research I conducted a creativity test and measured the quantity of ideas subjects had. Some people are extreme outliers as they have a lot of ideas or only 1 or 2 ideas. Intuitively I wanted ...
- 460
1
vote
1
answer
703
views
Measure of central tendency for an ex-gaussian distribution
I know there won't be a clear answer to that question but I'm really curious to know your opinion on that matter. I deal with reaction times, and finding a good measure of central tendency is ...
user5084
3
votes
2
answers
9k
views
Is R's trimmed means function biased?
I've been trying to understand how R's trimmed mean function works. I suspect it might be biased, but would like to get feedback here before I file a bug-report (if this is an inappropriate forum for ...
- 4,957
10
votes
2
answers
89k
views
How to calculate the truncated or trimmed mean?
How can I calculate the truncated or trimmed mean? Let's say truncated by 10%?
I can imagine how to do it if you have 10 entries or so, but how can I do it for a lot of entries?
- 471