instruction
stringlengths
9
38.7k
Does anybody know why it is not possible to compute standardized residuals when estimating a Tobit model? Here is a short example of what I am talking about: > require(AER) # for tobit estimation commands > require(MASS) # for computing standardized residuals > numberofdrugs <- rpois(84, 5)+1 > healthvalue <- rpois(...
Why is the negbin distribution required when the analyzed count data is bounded? I don't really understand the following: "The Poisson distribution can form the basis for some analyses of count data and in this case Poisson regression may be used. This is a special case of the class of generalized linear model...
Suppose you are trying to estimate the joint density $p(x,y)$ based on observed $(X,Y)$. However, you know that the marginal density $p(x)$ is uniform. How can you use this information to improve your density estimate?
I have a series of scores in a signal detection task. For each block of scores (i.e. a set of scores from one participant on one day) I have calculated a d' score which I am using as an indicator of performance. These d' scores rise over time, which is an interesting result. Is there any way I can calculate whether the...
I've got R running on amazon EC2, using a modified version of the bioconductor AMI. Currently, I am using putty to ssh into my server, starting R from the command line, and then copying and pasting my script from notepad++ into my putty session. The thing is, I hate cut and pasting. It feels stone-age and I occasional...
Suppose I have two (possibly biased) coins. I've run an experiment where I flipped each coin N times, and the coins landed heads with proportions p_1 < p_2. Now I want to do a power analysis to figure out how many flips I need to run in a second experiment, in order to have an 80% chance of detecting a difference at le...
I am conducting a Linear Mixed Effects Model analyses to evaluate the efficacy of an intervention. I have a dummy variable 'condition' which I have coded '2' for control group and '1' for intervention group. Is that okay or do I need to use a specific order (.e.g, 0 = no intervention, 1 = intervention)?
is it possible to do stepwise (direction = both) model selection in nested binary logistic regression in R? I would also appreciate if you can teach me how to get: Hosmer-Lemeshow statitistic, Odds ratio of the predictors, Prediction success of the model. I used lme4 package of R. This is the script I used to get t...
I have set $x = {1,2,3,4,5}$ and set $y = {2,3,4,5,6}$. Lets say the correlation of $x$ and $y$ is $0.7$. If I then have set $z = {1,2,3,4,5,2,3,4,5,6}$, and I do autocorrelation using lag $=$ $5$, should I not get the same $0.7$? I have been doing this but I keep getting different results. I'm wondering if I'm doing s...
I am confused about the mixed advice regarding controlling for baseline differences. Would you always control for a baseline between groups difference on a particular variable or only if the variable correlates with the DV? I am using SPSS and conducting Mixed Model analyses to evaluate an intervention. Jeromy, I tri...
I'm trying to find the best model based on AIC using the stepwise (direction = both) model selection in R using the stepAIC in MASS package. This is the script i used: stepAIC (glmer(decision ~ as.factor(Age) + as.factor(Educ) + as.factor(Child), family=binomial, data=RShifting), direction="both") however I got this ...
I'm performing a relatively simple one-way ANOVA as part of a class exercise. I'd like to get pairwise uncorrected p-values out of R, so I can do a sequential FDR test in another package (I realize there are FDR packages in R as well). I've set up my ANOVA as shown below, and it works fine, produces results, but I can'...
Both dependent and independent variables I deal with are nonstationary series that become stationary after differentiating them once. The problem is that I assume that the dependent variable has a certain constant value which does not depend on the explanatory variables' changes and should be estimated as the model's c...
I have completed an experiment measuring the magnetic field of a solenoid. The answer I got was $0.0075 \pm 0.0011$T. The uncertainty by the way was generated from Microsoft Excel's Regression under data analysis and is the standard error of the gradient of some graph. The gradient is the magnetic field, B in Tesla. I ...
Say I have two $n$-vectors $f(t)=(f_1(t), \dots, f_n(t))$ and $f(s)=(f_1(s), \dots, f_n(s))$, both with expected value 0. Let $\operatorname{Cov}(f(t)) = a \Sigma$ and $\operatorname{Cov}(f(s)) = b \Sigma$ with scalar $a,b$. Further assume that the two vectors are not independent and that $Cov(f_i(t), f_j(s)) = c \Sigm...
I wanted to solve such a regression problem: $$Y = Xb + e$$ where $X$ is a $m$ by $n$ matrix, resulting in: b = (X'X)-1X'Y as a solution. Since $n$ is quite large (2400), I can't use the conventional methods to calculate the inverse of $X'X$. So I thought about using LU Decomposition using Crout method. In this link a...
Does a high LL value imply that the model has a high $R^2$? I'm a very beginner to statistics so please excuse my naivete.
I've run a 2-way ANOVA on growth rate data (grams/day) with the factors of year type (good and poor) and site (A and B). Though the data themselves are non-normal and do not have homogeneous variances, the residuals fall pretty nicely along the qq plot, and they are not heteroskedastic. Running the test shows that ther...
I'm fitting a linear model where the response is a function both of time and of static covariates (i.e. ones that are independent of time). The ultimate goal is to identify significant effects of the static covariates. Is this the best general strategy for selecting variables (in R, using the nlme package)? Anything I ...
The problem I'm trying to solve here is very simple but the available data is very limited. That makes it a hard problem to solve. The available data are as follows: I have 100 patients and I need to rank order them in terms of how healthy they are. I only have 5 measurements for each patient. Each of the five reading...
In an attempt to improve the results of Bayesian NNT, I transformed the 7 variables that I have into normal scores (subtracted the mean and divided by SD). Then I used a PCA on the transformed variables to generate new 7 PCs. I used these PCs to run the Bayesian NNT and the classification results improved a little bit....
Does anyone have Stata code they could share with me so that I can run a two-part model to look at health care expenditures? The first part of the model will determine whether or not an individual had any visit and the second part will determine how much individuals spent (estimated on the subset of those who had a vis...
What am I supposed to do when I want to interpret significances, although I know that standard errors are biased because of wrong error term assumptions? I know that there is the possibility to use White estimators, weighted OLS. But my prof told me not to do so. Maybe some extra information: 1.) I am analyzing an OLS ...
I have a web-site, and I found the distribution of user number in a day have an obvious pattern. Not only my own site, I see almost all usage distributions of web-site fit model like this. They look like sine wave. I would like to use the model to predict how many total bandwidth I will use if I know the peak of usage....
$A$, $B$, $C$, $D$ are positive integers. $$A \sim Binomial(p_1, A+B)$$ $$A+C \sim Binomial(p_2, A+B+C+D)$$ My variable of interest is $p_1/p_2$ Could one analytically compute a distribution (preferably exact) for this variable? What would be its mean and variance (how to compute it?).
I am doing Cox regression models and KM plots for a data set where the end point is death. In addition there is information about whether the death was cancer-specific or not. So I have three categories: No death, last seen is the date of censor Death - cancer-specific Death - other cause What I would like to know ...
I am starting a work on electric vehicle to see how the charging process can impact the local electricity network. I would like to know if there exists public data of driving "habits". Ideally, I would like time series data for bigh fleets of vehicles in a relatively big city. For a given car these data could be a ser...
I have been running correlations for a set of data and several subsamples. During this analysis I ran into a situation where the $r^2$ for two groups was smaller in each individual group as opposed to when they are grouped together. Is there any straight forward explanation for how this could happen?
I've collected around 10 numbers of ants from a colony and introduced the same numbers of ants to the same colony (say Colony-1) at their entrance to see their behaviour (whether they accepts or rejects). Again I introduced 10 ants from different colony (say Colony-2, i.e. non-nestmate) to Colony-1 and checked their...
I've collected a data set from the literature. These data are largely binomial: they are clutch sizes of a bird that lays only 1 or 2 eggs in most areas, and in some areas will lay 3. However the only information I have compiled are means, standard errors and sample sizes (# nests) from various sites. Some sites have m...
I am looking at timeseries data in foreign exchange and bond markets (to test for reversion on extreme moves). Unfortunate "tick" data, namely high frequency data, is prone to many problems, and they obviously can significantly mess with the analysis. I'd like to know which R library can help with the following type of...
I have a number of regular daily measurements in a MySQL database that I'd like to manipulate using R. When it's returned from RMySQL, it looks like this: > memdata date vsize 1 2011-04-22 3535.178 2 2011-04-23 5680.516 3 2011-04-24 5468.914 4 2011-04-25 4761.044 5 2011-04-26 4403.515 6 2011-04-27 445...
I have the observations $X(n)$, where $X(n)$ is the realization of a binomial random variable with probability of success $p(n)$, and with $Y(n)$ trials. The observations are independent across $n$. I would like to test the null hypothesis H0: $p(1)=(2)=\cdots=p(N)=0.5$. Is there a standard recommended test? An approa...
I found a list of statistical tests along with practical guidance on Wikipedia. Can anyone point me to something similar, but in a textbook form? I'm interested in particular in practical guidance (along the lines of "should have n>30 for Z-test")
Lets say there is population of measurements X, and 50% of those X = 1, and the the other 50% = 0. Therefore, population mean = 0.5 given a random sample of size n, how do you determine the SE of that sample? Or, in layman's terms, if you flip a coin n times, how far can you expect to deviate from 50% heads and 50% ta...
I've taken a few probability classes and now understand how to calculate some statistical measures like mean and confidence intervals. What I don't know is the what, when, and why of using these measures for specific situations. I'm hoping to put together a good collection of each of these measures, what they're used...
Is there a standard (or best) method for testing when a given time-series has stabilized? Some motivation I have a stochastic dynamic system that outputs a value $x_t$ at each time step $t \in \mathbb{N}$. This system has some transient behavior until time step $t^*$ and then stabilizes around some mean value $x^*$ ...
I have a series of (x1,y1) points. I'm using a 3rd party software tool to which I feed these points. The tool then provides a mechanism for me to get back a series of (x2,y2) points that are on a Gaussian curve that has been fit to the data. I'd like to confirm that the points I'm getting back are correct (because, fr...
I am facing a difficult challenge, given my very low skills at text mining… Basically, I have a list of approx. 200 individuals described in a plain text file following a simple structure: N: (name) Y: (year of birth) S: (sibling) N: (name) Y: (year of birth) S: (sibling) [etc.] Here's the catch: each individual c...
Given the following dataset for a single article on my site: Article 1 2/1/2010 100 2/2/2010 80 2/3/2010 60 Article 2 2/1/2010 20000 2/2/2010 25000 2/3/2010 23000 where column 1 is the date and column 2 is the number of pageviews for an article. What is a basic acceleration calculation that can be done to determine i...
I want to browse a .rda file (R dataset). I know about the View(datasetname) command. The default R.app that comes for Mac does not have a very good browser for data (it opens a window in X11). I like the RStudio data browser that opens with the View command. However, it shows only 1000 rows and omits the remaining. (U...
The classical F-test for subsets of variables in multilinear regression has the form $$ F = \frac{(\mbox{SSE}(R) - \mbox{SSE}(B))/(df_R - df_B)}{\mbox{SSE}(B)/df_B}, $$ where $\mbox{SSE}(R)$ is the sum of squared errors under the 'reduced' model, which nests inside the 'big' model $B$, and $df$ are the degrees of fre...
I am wondering the orthogonal projectors such as Hadamard transform change the statistics of i.i.d. generated data. Consider, i.i.d. generated data $\mathbf{X}$ of length $N$, $$\mathbf{X}_P=\mathbf{P}\mathbf{X}$$ where $\mathbf{P}$ is an orthogonal projector of size $N \times N$ and $\mathbf{X}_P$ is the projected dat...
What is a good statistical test to check if there is a bias in judging in a situation that there is one judge that gave extreme scores (high score for one of the contestant and very low scores on the rest of the contestants)? Here is the actual data in the contest: contestant 1 contestant 2 c...
I have an application for which I need an approximation to the lognormal sum pdf for use as part of a likelihood function. The lognormal sum distribution has no closed form, and there are a bunch of papers in signal processing journals about different approximations. I have been using one of the simplest approximatio...
I have one data sample of non-negative random variable $X$ with unknown distribution and predefined expected value $y$. Is there any test able to check null hypothesis $\mathbb{E}[X]\geq y$ or $\mathbb{E}[X]\leq y$? Actual data samples are gathered in realtime. More specifically, it's an intervals between HTTP-requests...
I have a set of images of same color cars which I have users rate on a scale from 1-5 (integers only) based on how attractive they think the car design is. For each image I have a set of parameters about the cars in question, mostly various ratios of dimensions (say height at middle, width at trunk, curviness of hood, ...
I'm a bit stuck on the general concept and calculations of  iterated expectations. A simple example: $$E[E[Y|X]] = E[Y]$$ I'm not sure how or why this is the case? I have a 3 line proof in my notes using densities and stuff but is there no 'quicker' way. Especially in longer cases like (below) writing everything out is...
Recently, I read an article regarding the association between age and lymph node metastases. The authors stated that: "Because a nonlinear relationship between age and lymph node involvement was expected based on existing literature, lymph node involvement was also regressed on age using nonparametric logist...
The above image represents an article's page views over time. X axis is days with 9 being the most recent day. The y-axis is number of pageviews. I'm looking for a decent, not to complex either physics or statistical calculation that would be able to give me (based on the history of the page views) what the current tr...
Does any know the reference/link where i can find the MATLAB implementation of gap statistics for clustering as mentioned in this paper?
I took some measurements of some data (code run time measurements, for those curious) of which I have no idea what the expected value is. The data is discrete, and I have no idea what type of properties it has or distribution it follows. The only thing that is known is that the values are more or less independent of ea...
I am searching for a good criterion to measure the "goodness of fit" in generalized linear models. To make clear: I am not searching for a criterion which gives me an answer to the question "does overdispersion occur?". What do you think about Nagelkerke's pseudo R-squared? Any thought would be appreciated!
Can anyone tell me the factors that affect the memory requirements of $k$-means clustering with a bit of explanation?
Lets say i want to calculate the information content of a particular message.What apart from the message itself has to be taken into account in doing so, and what data would i need to collect to perform my action?
I've got a question concerning wheter or not to use an offset. Assume a very easy model, where you want to describe the (overall)number of goals in hockey. So you have goals, number of games played and a dummy variable "striker" which is equal to 1 if the player is a striker and 0 otherwise. So which of the following m...
Especially in the computer-science oriented side of the machine learning literature, AUC (area under the receiver operator characteristic curve) is a popular criterion for evaluating classifiers. What are the justifications for using the AUC? E.g. is there a particular loss function for which the optimal decision is ...
TL:DR: Is it ever a good idea to train an ML model on all the data available before shipping it to production? Put another way, is it ever ok to train on all data available and not check if the model overfits, or get a final read of the expected performance of the model? Say I have a family of models parametrized by $...
I'm trying to fit two equations with nls() function in R. The two functions are: $f(x) = c_{1} \exp\left(-\left(\frac{x-\mu}{\sigma_{(x)}}\right)^2\right)$ where $\sigma_{(x)} = \sigma_{11}$ if $x \le \mu$ and $\sigma_{(x)} = \sigma_{12}$ if $x > \mu$ and $f(x) = a K \exp\left(- \frac{a}{b} \exp\left(-b x\right) -...
My current understanding of the notion "confidence interval with confidence level $1 - \alpha$" is that if we tried to calculate the confidence interval many times (each time with a fresh sample), it would contain the correct parameter $1 - \alpha$ of the time. Though I realize that this is not the same as "probabilit...
If there are 0's in the contingency table and we're fitting nested poisson/loglinear models (using R's glm function) for a likelihood ratio test, do we need to adjust the data prior to fitting the glm models (e.g. add 1/2 to all the counts)? Obviously some parameters cannot be estimated without some adjustment, but how...
My research design is as follows: I have these Between Subjects IVs: Experiment Condition - 5 levels Facebook User status - 2 levels (yes/no) My supervisor also wants me to see if there are significant effects of: Gender - 2 levels Relationship Status - 2 levels Relationship Satisfaction - 2 levels And these within...
Context I was talking to a researcher in the following situation. Participants (n = 500) were sampled from schools. Participants came from around 50 different schools. The number of participants per school varied with some schools supplying 20 or 30 participants, but a few schools only supplying 3 or 4 or 5 participan...
One of the data sets I deal with is quite strange. The datawarehouse I downloaded the data from has a lot 999999999 values in one of the variables. Apparently the computer system on which the datawarehouse sits on does not support storing of null values. So they use 999999999 as the "null" value. Now if I just run pret...
I am following a course on Bayesian statistics using BUGS and R. Now, I already know BUGS, it's great but I am not really fond of using a separate program rather than just R. I have read that there are a lot of new Bayesian packages in R. Is there a list or reference on which packages there are for Bayesian statistics ...
I have a set $E_{1}$, with a finite cardinality $n$ of rectangular matrices which contains the useful MFCC coefficients generated from $n$ speech signals. Similary I have a set $E_{2}$ of same cardinality as that of $E_{1}$ which is a collection of vectors of finite dimension containing the LPC of the same set of speec...
I am analyzing scores given by participants attending an experiment. I want to estimate the reliability of my questionnaire which is composed of 6 items aimed at estimating the attitude of the participants towards a product. I computed Cronbach's alpha treating all items as a single scale (alpha was about 0.6) and de...
Does anybody know what the formula for Cook's distance is? The original Cook's distance formula uses studentized residuals, but why is R using std. Pearson residuals when computing the Cook's distance plot for a GLM. I know that studentized residuals are not defined for GLMs, but how does the formula to compute Cook's ...
I am calculating the age of lake sediments at the base of a sediment core by dividing the total sediment mass of the core ($\mathrm{mg} \ \mathrm{cm}^{-2}$) by the sediment accumulation rate ($\mathrm{mg} \ \mathrm{cm}^{-2}\ \mathrm{y}^{-1}$). Both the sediment mass and the accumulation rate have variation associate...
i was wondering what is the differences between Mean Squared Error (MSE) and Mean Absolute Percentage Error (MAPE) in determining the accuracy of a forecast? Which one is better? Thanks
Using Zelig in R I fitted a negative binomial model to my data. The psychology APA standard demands to report the overall R squared, F-Value and p-value for the whole model. I looked at the formula for R square and it is using sum of squares. Since the negative binomial model is not using least square method assuming ...
So our data is structured as follows: We have $M$ participants, each participant can be categorized into 3 groups (G $\in {A,B,C}$), and for each participant we have $N$ samples of a continuous variable. And we are trying to predict values that are either 0 or 1. How would we use matlab to test for an interaction betw...
Choosing to parameterize the gamma distribution $\Gamma(b,c)$ by the pdf $g(x;b,c) = \frac{1}{\Gamma(c)}\frac{x^{c-1}}{b^c}e^{-x/b}$ The Kullback-Leibler divergence between $\Gamma(b_q,c_q)$ and $\Gamma(b_p,c_p)$ is given by [1] as \begin{align} KL_{Ga}(b_q,c_q;b_p,c_p) &= (c_q-1)\Psi(c_q) - \log b_q - c_q - \log\Gamma...
I'm using latent semantic indexing to find similarities between documents (thanks, JMS!) After dimension reduction, I've tried k-means clustering to group the documents into clusters, which works very well. But I'd like to go a bit further, and visualize the documents as a set of nodes, where the distance between any ...
Context This came up recently in a consulting context. A researcher was performing repeated measures t-tests based on experimental data. Some of the analyses involved comparing one condition with another. Other analyses involved performing contrasts comparing one or more conditions with one or more other conditions. Qu...
I am working on understanding various document ranking algorithms like (TF-IDF, LSI, language models, etc) by actually implementing them. I want to understand LDA and using various resources to understand the algorithm. What I don't understand is how we come up with the latent (hidden) variables/topics. Can someone ple...
In my job role I often work with other people's datasets, non-experts bring me clinical data and I help them to summarise it and perform statistical tests. The problem I am having is that the datasets I am brought are almost always riddled with typos, inconsistencies, and all sorts of other problems. I am interested to...
I have two groups (experimental, N=6, and control group, N=20). For each participant I measured a score (let say mean reaction time) 4 times. I would like to check: whether these groups differed in the beginning (Time 1) whether the score changes in time (for control group) compare the change in time for both groups ...
How can I call residuals out from function cv.lm? cv.lm$ss gives me the cross validation sum of squares, but I need individual residuals from each fold. Is it possible to call out?
I am looking to compare individual likert scale items. I measured respondent's level of agreement (in a 5 point-scale) for several items (e.g. from 1 to 5 how much is A competent to treat your condition? how much is B? C? and so on..- 11 items in total). I want to analyse if the scores for each statement are significan...
I am doing a project on sexual selection (male-male competition) in the turquoise killifish Nothobranchius furzeri. There are two morphs of male in the population from which my fish are obtained from- one has a red tail and the other has a yellow tail. My null hypothesis is: Tail colour is not related to dominance/co...
How does a computer algorithm set up to take as input an arbirary bivariate probability density function, generate pairs of numbers from that distribution? I have found a routine called simcontour that is part of LearnBayes in R that performs that operation.
I found a formula for pseudo $R^2$ in the book Extending the Linear Model with R, Julian J. Faraway (p. 59). $$1-\frac{\text{ResidualDeviance}}{\text{NullDeviance}}$$. Is this a common formula for pseudo $R^2$ for GLMs?
I am having trouble understanding the different estimators that can be used in an impact evaluation. I know that the intention-to-treat (ITT) estimator compares differences between eligible individuals without the program, and eligible individuals with the program, regardless of compliance. However, I thought the avera...
I would like to find a reference, preferably free on the internet, where I can read about the theoretical or practical justification for the use of parametric / analytic probability distributions. By parametric distributions I mean the named ones like Normal, Weibull, etc.
I have a nested-case control study that I have been using for analysis. At the end of my work I have deduced a set of variables that I use later to to classify new cases. One example of a simple classifier I am using is a naive Bayes, which will output simply a probability. So here is my question: Could I make my prob...
I'd like to hear your opinions on the following: What parameters would you report when estimating different likelihood based regression? AIC, BIC, Pseudo $R^2$? What is the standard to report? It should be a parameter which answers the question of how good the specified model is.
I have a multitree that represents the lineages of all the fishgroups in a breeding program. It's stored as a double adjacency table with fish_id, sire_id and dam_id. This means a particular fishgroup is only directly aware of its parents (if any) and knows nothing about descendents. I can conveniently output this dat...
There are different methods for prediction of ordinal and categorical variables. What I do not understand, is how this distinction matters. Is there a simple example which can make clear what goes wrong if I drop the order? Under what circumstances does it not matter? For instance, if the independent variables are all ...
I'm reading about the Linear Discriminant Analysis by Fisher and I have a couple of questions about its usage. If you have k>2 classes in a two-dimensional space you find k−1 vectors that you need to use to project the sample data. Is it possible that one sample is closer to different means along different vectors? Su...
How would you know if your (high dimensional) data exhibits enough clustering so that results from kmeans or other clustering algorithm is actually meaningful? For k-means algorithm in particular, how much of a reduction in within-cluster variance should there be for the actual clustering results to be meaningful (and ...
What is power in logistic regression? Is it the ability of the test to reject the null hypothesis when it is actually false? Second, if you're trying to maximize your statistical power when doing a logistic regression, is it better to use predictor values that are only high or low or a range of predictor values?
Can you please suggest me a good model-based learning algorithm to recommend items to the user? Is there any open source implementation available on model based learning algorithm? I am sure Apache Mahout doesn't implemented any model based learning algorithms.
I am trying to use SPSS to build a linear regression on historical data (dependent and independent variables) and then apply this to new data (independent variables only) to generate predicted values and associated prediction intervals. I've looked in detail at the documentation on the REGRESSION procedure within SPSS,...
Assume the following easy example of a glm regression with an offset: numberofdrugs <- rpois(84, 10) healthvalue <- rpois(84,75) age <- rnorm(84,50,5) test <- glm(healthvalue~age, family=poisson, offset=log(numberofdrugs)) summary(test) fitted(test) # How to get one of these values manually? How ...
According to the Wikipedia article on unbiased estimation of standard deviation the sample SD $$s = \sqrt{\frac{1}{n-1} \sum_{i=1}^n (x_i - \overline{x})^2}$$ is a biased estimator of the SD of the population. It states that $E(\sqrt{s^2}) \neq \sqrt{E(s^2)}$. NB. Random variables are independent and each $x_{i} \sim...
I have a large dataset that has many variables. I'm trying to determine which variables correlate strongly with one specific variable. When you look at the entire dataset as a whole, the correlation of different variables is pretty weak. I know, however, that within certain subsets of the data the correlation is stro...
This follows on from my previous question on assessing reliability. I designed a questionnaire (six 5-points Likert items) to evaluate the attitude of a group of users toward a product. I would like to estimate the reliability of the questionnaire for example computing Cronbach's alpha or lambda6. So, I need to check ...
I'm having a hard time understanding what the authors of this paper (pdf) want to tell me with this graph (Fig. 2,3 (shown below) and 4, right): [Caption: A comparison between the standard deviation of the differences (green line) and the standard deviation of all GOMOS (red line) and LIDAR (blue line) ozone profiles....
Consider the following survey question: Q: How would you classify the importance for you of the following 5 items: A B C D E Assign to each item a number in the set {1,2,3,4,5}, with 1 meaning the highest importance and 5 meaning the lowest importance; the number used to an item cannot be used in any other item. H...