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We have a data set with two covariates and a categorical grouping variable and want to know if there are significant differences between the slope or intercept among the covariates associated with the different grouping variables. We've used anova() and lm() to compare the fits of three different models: 1) with a sin...
Suppose we have 2 kernel functions $K_1(x,y)$ and $K_2(x,y)$. We know, that the dataset ($(x_1,y_1),\ldots,(x_l,y_l),$ $y_i \in \{-1,1\}$ ) is separated with the first one (that is, there are $w,$ $w_0$: $$y_i(K_1(w,x_i)-w_0)>0 $$ for all $i=1,\ldots,l$ ), and not separated with the second kernel function. What we can ...
In their textbook, Graphical Models, Exponential Families and Variational Inference, M. Jordan and M. Wainwright discuss the connection between Exponential families and Markov Random Fields (undirected graphical models). I am trying to understand better the relationship between them with the following questions: Are a...
In my current regression model, one of the explanatory variables I need is "capital" (K). The country under consideration here is Côte d'Ivoire (West Africa) and, as you may already know, finding data for small open economies is very often an extremely difficult task. I was able to find the data for "capital formation"...
Possible Duplicate: Machine Learning: Linear classifier Suppose we have 2 kernel functions $K_1(x,y)$ and $K_2(x,y)$. We know, that the dataset ($(x_1,y_1),\ldots,(x_l,y_l),$ $y_i \in \{-1,1\}$ ) is separated with the first one (that is, there are $w,$ $w_0$: $$y_i(K_1(w,x_i)-w_0)>0 $$ for all $i=1,\ldots,l$ ), and ...
I'm trying to derive covariance from "embedded" random variable (r.v.). Say we have two Gaussian r.v.'s $$ X_1 \sim N(\mu_1, \sigma^2_1)$$ $$ X_2 \sim N(\mu_2, \sigma^2_2)$$ where $\mu_1$ and $\mu_2$ are also Gaussian r.v, $$\mu_1 \sim N(\theta_1, \delta^2_1)$$ $$\mu_2 \sim N(\theta_2, \delta^2_2)$$ with covariance $\d...
I have conducted a study in which I have gathered 3 sentences per participant. These sentences were then classified and the words per sentence were counted. I want to test if there are significant differences in the word count means for the different categories of the classification. However, because the sentences are...
Usually $r$ is transformed into Fisher $z$ to test difference between two $r$ values. But, when a meta-analysis is to be performed, why we should take such a step? Does it correct for measurement error or non-sampling error and why should we assume that $r$ is an imperfect estimate of population correlation?
I asked survey respondents about two points in time, and asked participants the degree to which they "agree", a typical Likert-style question. For example, as if I had asked "Before Obama became president, life was good" and a separate question, "After Obama became President, life has been good". Normally, one would as...
I must make a critical appraisal of a cancer survival paper. I hope someone here can give some hints. The paper investigates person-level markers of socio-economic status as exposure and looks for association of these with survival and also comorbidities, disease/prognostic factors and treatment using Cox proportional ...
Consider SMV with the polynomial kernel $k(x_1,x_2)=(\langle x_1, x_2\rangle + 1)^d,$ where $d > 1.$ Is it true that if the dataset is separated with a hyperplane then the SVM (with the kernel $k$) always separates the dataset with a hyperplane (without any errors in the dataset)?
I'm normalizing (or standardizing or feature scaling) my neural network training inputs and training targets. I just doing linear scaling and the formula I'm using is: I = Imin + (Imax-Imin)*(D-Dmin)/(Dmax-Dmin) where I is the scaled input value, Imin and Imax are the desired min and max range of the scaled values, D ...
Hello after struggling with using R for the last couple of days I was hoping someone could help me with a statistical analysis I am completing for an environmental science honours project. Using R statistics is not something we have been taught and I am worried that I may have bitten of more then I can chew, however my...
I have been set the following question as part of homework: Design and implement a simulation study to examine the performance of the bootstrap for obtaining 95% confidence intervals on the mean of a univariate sample of data. Your implementation can be in R or SAS. Aspects of performance you may want to look at are c...
I have a dataset that includes one independent variable with 3 levels (group 1, group 2, and group 3) and a repeated dependant variable (pre test score, post test score). I am using the statistics package SPSS and when I took the method I thought I would use "repeated measures anova" there didn't seem to be a way of sp...
I am trying to replicate an extension of Random Forests introduced in a recent research publication for my project. For instance, for the binary split of data at each node, instead of randomly assigning all example from each class a binary label, they suggest using an SVM to learn a binary split of data. Furthermore, ...
If X is a random variable with a normal distribution, then Y = exp(X) has a log-normal distribution. Likewise if X is a random variable with a binomial distribution, then Y = exp(X) has a log-binomial distribution. My questionIn case of the log-normal distribution mean and variance are well known, for the log-binomial ...
I am very glad that I have found this community and I wanted, beforehand, to thank anyone reading my post. I appreciate that very much! I am estimating the ruin probability for Weibull (in the light tail case) distributed claims. For this purpose I need to calculate the adjustment coefficient. The CDF is given by: $$ ...
I can't understand how this works: $e$ is the error term and $x$ is the explanatory variable. $$Var(e|x) = E(e^2|x) - [E(e|x)]^2$$ I know that $[E(e|x)]^2$ = 0 because $E(e|x) = 0$, and squaring 0 is still 0. So that leaves $Var(e|x) = E(e^2|x)$ I am confused on this part. This may be a clearer idea of what I am after:...
I've been involved in a machine learning project recently and am now in the process of writing the project up for a paper submission. We used the naive bayes classifier on the project and developed a method for adjusting the classification of datapoints depending on how exactly we want the classifier to perform, ie. in...
Can you tell me some procedures in R, which are able to find differentially expressed genes for a given microarray data? Moreover,If you can give some ideas related to clustering of significant genes for microarray data, it will be quite helpful for me.
I am trying to do a priori sample size calculation based on published results. However, I am unable to obtain a reasonable estimate of the published effect size (which is not reported) as I am unable to obtain an estimate of the pooled standard deviation or the standard deviation of the difference. The problem resides ...
I want to use Lasso or ridge regression for a model with more than 50,000 variables. I want do so using software package in R. How can I estimate the shrinkage parameter ($\lambda$)? Edits: Here is the point I got up to: set.seed (123) Y <- runif (1000) Xv <- sample(c(1,0), size= 1000*1000, replace = T) X <- matrix(X...
I am carrying out an evaluation for an intervention using secondary data. Unfortunately the design of the study is weak as participants cannot be randomised. I am looking to see whether the intervention has had any impact on patients quality of life? A measure of QoL has been taken before and after the intervention, i ...
I am trying to do a logistic regression to look at the relationship between the number of cigarettes smoked by subjects in a sample (0-60 per day) and a yes/no outcome. As a lot of people in the sample are non-smokers, there are lot of zeros for the continuous covariate. I have a few questions about this: Is this co...
"Bootstrap validation"/"resampling cross-validation" is new to me, but was discussed by the answer to this question. I gather it involves 2 types of data: the real data and simulated data, where a given set of simulated data is generated from the real data by resampling-with-replacement until the simulated data has the...
This is just an example that I have come across several times, so I don't have any sample data. Running a linear regression model in R: a.lm = lm(Y ~ x1 + x2) x1 is a continuous variable. x2 is categorical and has three values e.g. "Low", "Medium" and "High". However the output given by R would be something like: summ...
Is there a package that performs three-level nested logit in R? I've looked at the mlogit package, but didn't see a three-level example.
Given we have a large database of texts (e.g. product descriptions) and we want to extract multiple types of information (e.g. brand, release date, features, price, etc.) what's a good library to use? I have found many general purpose HMM libraries (such as HMM in R, GHMM, Jahmm, etc.) but I wonder which is the best ...
What is the ‘correct’ way to compare the effect of a drug in different conditions? For example, if I have conditions a, b, c and d, where there are different numbers of ‘control’ and ‘drug’ cells in each condition and a single parameter has been measured in control and drug-treated cell (different cells). Of course I c...
I'm working on an open health survey application, planned to be used in developing country. The basic idea is that survey interviews are crowdsourced - they are performed by unorganized volunteers who submit forms data of the interviews they performed by using their mobile devices, and each survey is accompanied by th...
So I have data elements such as rent price, late payments, unit type and location. I haven't done statistical analysis since my university time where I majored in industrial engineering 2 years ago Anyways my approach is to look for different metrics to look at such as avg rent price, occupancy rate (look at when a un...
Below I show two equivalent ways to write a mixed model in R and SAS. The two R models as well as the two SAS models yield the same estimates of the random and fixed effects and the same standard errors of the estimates of the fixed effects. But the two SAS models do not give the same confidence intervals of the fixed ...
I have a data set that includes a primary dichotomous independent variable (e.g., smoking), a primary dichotomous dependent variable (e.g., chronic back pain), and several covariates (e.g., diagnosis of several mental disorders, age, sex). I have calculated propensity scores for smoking using the covariates of interest...
Suppose you are analyzing a huge data set at the tune of billions of observations per day, where each observation has a couple thousand sparse and possibly redundant numerical and categorial variables. Let's say there is one regression problem, one unbalanced binary classification problem, and one task of "find out whi...
I am performing a cluster analysis in SAS and some of the variables that I am trying to cluster contain outliers. I've tried to transform the data (log and/or standardize them) but didn't quite work out. So, for example, let's say I came down to 9 clusters, then one or two clusters will have just one value in them. De...
I have a graph and there are two points that could be two potential outliers. I'm trying to create a polynomial line of best fit with undefined order. I believe I could use a >2 standard deviations exclusion rule, but I'm sure how exactly this is applied. Do I determine the qualifiying standard deviation by using all t...
This may be a lame question, but I got stuck and can't get my head around it. I am running a gene expression analysis, comparing $\sim 10,000$ genes between two groups, $n=6$ samples per group. My pipeline goes like this: I check whether the two groups have equal variances using Levene's test for each gene. For those ...
I would like to understand how to generate prediction intervals for logistic regression estimates. I was advised to follow the procedures in Collett's Modelling Binary Data, 2nd Ed p.98-99. After implementing this procedure and comparing it to R's predict.glm, I actually think this book is showing the procedure for co...
I am running a probit regression with glm. I got a non-significant value (p~0.98) for an interaction that other statistical methods suggested should be significant. Looking into it, I think it's because 1 of the cells had zero positive ("YES") outcomes. When I artificially change a data point so that there's one pos...
This question is about Bayesian Networks. I want to calculate the probability for certain events to be in a certain state knowing all conditional probabilities. Consider that I am totally new to Bayesian Networks. The problem Consider a Bayesian Network. For all variables $A_i,B_i \dots Z_i$ in the network I know the p...
I am trying to test whether or not there is a significant difference between maximum likelihood estimates of two genetic parameters (selection and dominance) across two environments with genotype data from a cross. There are three genotype classes, C11, C12, and C22, and I am looking to maximize the likelihood below: l...
I have a csv data set like this. Levels, Trial, Fail 1,100,1 2,200,3 3,300,4 How do I test if the probability of fail or success is the same across all the levels?
Thru this site I've recently discovered Sankey Diagrams, a great way to visualize what is happening in a traditional flow chart. Here is a good example of a Sankey Diagram by George M. Whitesides and George W. Crabtree, Source; Don't Forget Long-Term Fundamental Research in Energy, Science 9 February 2007:Vol. 315. no...
I am reading a manuscript that provides the "maximum posterior probability" in a Bayesian context as a statistical summary of a parameter. Is the term "maximum posterior probability" equivalent to (i.e., "exchangeable" with) "posterior mode"?
I am working with two sets of data and would like to determine if they come from the same distribution -- hence the two population KS-test. At this point, I have binned both sets of data, counting the number of entries in each bin, to create relative frequency histograms. These binned arrays look like: dis1 = [0.0, 4....
I have six dependent variables (count data) and several independent variables, I see that in a MMR the script goes like this: my.model <- lm(cbind(DV1,DV2,DV3,DV4,DV5,DV6) ~ IV1 + IV2 + ... + IVn) But, since my data are counts, I want to use a generalized linear model and I tried this: my.model <- glm(cbind(DV1,DV2,DV...
Suppose I have survival data coming from a cohort study. The outcome of interest is death and a subject can die either because of cancer or because of other causes. The two outcomes under study are therefore mutually exclusive. Now, suppose that I'm interested in assessing whether the magnitude of the associations betw...
I am testing many (500,000) genetic variants, and the tests are FDR corrected and give me a q-value. Normally I would just call everything with q < .05 significant. But in this case I am testing those same genetic variants in two other related experiments (not using exactly the same individuals, but the samples may ove...
I am carrying out an evaluation for an intervention using secondary data. Unfortunately the design of the study is weak as participants cannot be randomised. I am looking to see whether the intervention has had any impact on patients quality of life? A measure of QoL has been taken before and after the intervention, i ...
does anyone know if there exists some binary dataset that i can freely download? If possible, i prefer dataset in textual format and inspired by some real phenomenon. Thank you in advance,
I want to sample from a distribution which has fixed to a given values mean(=0), standard deviation(=1), skewness(=0) and kurtosis. I also want this distribution to be as general as possible, i.e. to have Kullback-Leibler divergence from uniform distribution as small as possible (this condition is equivalent to princip...
@whuber has demonstrated how to simulate multivariate outcomes ($y_1$, $y_2$, and $y_3$) for one time point. As we know, longitudinal data often occur in medical studies. My question is how to simulate repeated measures multivariate outcomes in R? For example, we repeatedly measure $y_1$, $y_2$, and $y_3$ at 5 various ...
Given the sample mean $\bar{x}$ and the sample variance $s^2$ of a random variable $X$, is it possible to estimate the shape $\sigma^2$ and log-scale $\mu$ of the log-normal distribution, with probability density function $$f_X(x;\mu,\sigma^2) =\frac{1}{x \sqrt{2 \pi \sigma^2}}\, \mathrm{exp}\left( {-\frac{(\ln x - \mu...
I'm an ecology PhD student, but unfortunately not a very mathematically sophisticated one. I am interested in ways to compare two non-linear models. I was really impressed with this answer, which covers part of my question, about looking at the absolute area between the curves. Thinking about it further, it seems to m...
I have a question regarding the use of a grouping variable in a non-linear model. Since the nls() function does not allow for factor variables, I have been struggling to figure out if one can test the effect of a factor on the model fit. I have included an example below where I want to fit a "seasonalized von Bertalanf...
I want to analyse the data from an experiment. The participants get different acoustic signals and judge them. The score is a high number, if they feel comfortable with the signal in the other case it is a lower number. I have 5 different signals and 15 participants. The experiment was performed 5 times for each subje...
Continuing on from this question and this question re BIC and its approximation to the Bayes factor with a unit information prior (Kass & Wasserman, 1995), I'm trying to quantify this relationship as a stepping stone into Bayesian stats. So far, my calculation of the BIC approximation of the Bayes factor (based upon my...
My question is to create an index to measure a manager's earnings forecast ability. I use earnings forecast accuracy (dollars difference) and the earnings forecast horizon (days difference) to capture the ability. However, those two variables condition on each other. How should I weight them and create index? The small...
First of all, I apologize for my half-forgotten understanding of statistics. I hope I can accurately describe what kind of test I'm after in a way that doesn't sound confused. I have one sample and one population. I would like to know the probability that my sample is part of that population. But I also want to know...
I need to calculate the pooled odds ratio and associated 95% confidence interval for meta-analysis of 2 studies about the risk of bleeding. The only information I have is the odds ratios and 95% confidence intervals. They are 2.7 (1.8 – 4.0) in the first, and 1.3 (0.5 – 3.4) in the second study. I computed the standard...
I have seen a few times the technique of using the Gaussian PDF for continuous features in Naive Bayes. here and here. Illustrated in the first link: How is this possible? I always learnt that the PDF is not a probability -- as the probability of any exact value of x is zero.
Just throwing out a general question. What do people think of applying feature selection methods when using SVMs to build predictive models? I understand that SVM have built in regularization with how they're trained, but I've heard for certain cases (e.g. features >> examples) feature selection is still useful. I'm ma...
In biological sciences, ($CI$) stands for the Combination Index which is a conventional method for dose-response assessment and drug interaction analysis. It can be defined as: $$CI = \frac{\bar{D}_{1} \hat{\beta}_{1}}{ln(\bar{SF}_{1}) - \hat\alpha_{1}} + \frac{\bar{SF}_{1} - \hat{\alpha}_{2}}{{0.5} - \hat\alpha_{...
Is there any clustering algorithms that: does not assume the number of clusters to be known, and processes the data in only one pass by considering it as a continuously arriving data stream (and we do not know the data set size beforehand)?
I am calculating a certain statistic(relative entropy) of a certain sequence alignment over DNA sequences. The statistic has a certain distribution in the entire genome of which I only have 1000 sequences of length 1000. I want to test the significance of a certain value of the statistic but I obviously do not know the...
I have two matrices A and B of the same dimensions. Each cell a(i,j) represents some parameter I'm interested in, and b(i,j) represents the corresponding value in the other matrix. The cells are not interrelated. What's the best way to represent how close these two matrices are? The entries in these matrices are t...
Sample of 102 broken into two groups based on a factor of interest Group 1, $n=77$ Group 2, $n=25$ Trying to figure out how to test if the demographic (age, race/ethnicity, gender, education level, have kids, etc) break down is significantly different between groups. I've calculated proportions and it seems like most ...
I have two observational variables, $\text{C}_{\text{obs}}$ and $R$, both subject to measurement error. I believe that a model of the form $$\text{C}_{\text{mod}} = a_0 + a_1R + a_2R^2 + a_3R^3$$ would be a reasonable representation of the relationship between $\text{C}_{\text{obs}}$ and $R$. I want to determine the c...
I have a time series of anomalies in some data, with 69 observations in total. I want to statistically test if the number of anomalies in the time series have increased over time? Can I use a t-test for the purpose, possibly by dividing my data into 2 or 3 groups, and then comparing these groups? In case, I'm completel...
Estimate Std. Error t value Pr(>|t|) (Intercept) 10.2758 0.5185 19.817 < 2e-16 *** rprice2 -1.8581 0.5139 -3.616 0.000696 *** I would like to use the Std. Error of rprice2 to make other calculations. I know to reference any of the objects in the model, I use the syntax model$object, bu...
I have large dataset (around 2 million records and 300 features) with a lot of missing data. Most of the independent variables are categorical (some of these variables have more than 40 valid values). The outcome is either Y or N. The Y outcome is a rare event: around 98% of outcomes are N. I'm supposed to fit a logis...
I did the multiple linear regression on a dataset of 412 observations, with one response variable (Y) and 25 explanatory variables(X1-X25). Y and most of Xs are not normally distributed. Besides, there are some correlation between several Xs. The plot show that the residuals strongly correlated with Y positively and we...
I have carried out a simulation experiment where $n$ out of $N$ items $x_i$ were drawn with replacement with unequal probabilities $z_i$ from a finite population. (If it matters: $z_i = 1/(Nx_i)$ in my case, but perhaps there are more general results.) Then, I estimated the population totals of the indicators $$ y_i :...
Suppose I have an algorithm that classifies things into two categories. I can measure the accuracy of the algorithm on say 1000 test things -- suppose 80% of the things are classified correctly. Lets suppose I modify the algorithm somehow so that 81% of things are classified correctly. Can statistics tell me anything a...
I am running a multi-level model on data which is set out with one row per individual survey return, each with Individual ID and Organisational ID as columns. There are variables which can be aggregated in to group, but I first have to justify this aggregation, and believe I have to use ICC(1), ICC(2) and Rwg. Although...
This is a discrete problem concerning integers. If there are $n$ independent random variables $X_1,...,X_n$ that each take on a value from $\{1,...,x\}$ uniformly at random ($x$ distinct values), what is the probability that the minimum (call it $l$) is unique? The following are approaches I've taken: Lower Bound: Tre...
I want to "blow up" a sample, taken with replacement, for which I know the overall sampling probability $\pi_i$ for each item $i$. Is it valid to use bootstrapping and apply inverse probability weighting during the selection (as in the Horvitz-Thompson estimator: weight each item with $1/\pi_i$), or are there any pitfa...
I wanted to ask whether it was possible to use the auto.arima function to identify subset ARIMA models rather than those of pure lags? I have identified a model in Stata in subset lags that performs well and wanted to cross check this with the auto.arima() function but I can't seem to figure out if subset lags are supp...
I am a computer scientist performing research, which includes calculating the Spearman rank correlation of two lists, one ranked by a human, another by a computer program. I have the following questions: I was reading this post and have become concerned with how large my sample size has to be to have a significant con...
While I know that there are a series of functions for generating heat maps in R, the problem is that I'm unable to produce visually appealing maps. For example, the images below are good examples of heat maps I want to avoid. The first clearly lacks detail, while the other one (based on the same points) is too detailed...
I am using Rasmussen's GPML code in Matlab R2011a_student. I have training data (2560x29707) w/ labels (6 classes), and test data (640x29707). To prep the data I have converted from sparse to full, binarized the classes (ie. All classes that = 1 are 1, everything else is -1). I planned on running this 6 times to ac...
I am estimating a multivariate logit model. I have included a square term on my main independent variable, IDV and IDV:IDV. And of course a set of control variables. The results indicate an inverted U shaped relationship; IDV is positive, while IDV:IDV is negative. I have graphed the probabilities using -postgr3-: post...
Short version: is there any statistical method that can be used to develop estimates of abundance, spatial distribution, and/or rate of spread of a species when my dataset only includes presence data and not absence? I am not dealing with fossils in the strict sense, but I speculate that if such a method exists it migh...
I would like to setup up an algorithm for detecting an anomaly in time series, and I plan to use clustering for that. Why should I use a distance matrix for clustering and not the raw time series data?, For the detection of the anomaly, I will use density-based clustering, an algorithm as DBscan, so would that work ...
So I have two related questions. I am performing a logistic regression model and want to know how to enter these variables. 1) For one survey I have questions and the responses are Yes, Don't know, and No. Can I just create a dummy variable for Yes (1) with Don't know and No coded as 0 or do I need to exclude the Don...
I am helping a friend with a data project. He's interested in building a canary-in-the-coal-mine alert system for his website which tells him when the number of users dips below some critical lower bound. The number of users varies by time of day, and day of the week. I have 550 days of by-the-minute data, though we ca...
I am looking for a reference to the paper where k-fold cross-validation was introduced (rather than just a good academic reference for the subject). Perhaps it is too far back in the mists of time to unambiguously identify the very first paper, so any early papers where the idea was used would be of interest. The earl...
Good variable names are: a) short / easy to type, b) easy to remember, c) understandable / communicative. Am I forgetting anything? Consistency is something to look for. The way I would put it is that consistent naming conventions contribute to the qualities above. Consistency contributes to (b) ease of recall a...
I would like to somehow use the standard deviation of the following set of numbers to categorize values into five different groups. How would I do this? Do I take the max value of the set and divide by four, to get five equal parts? Set of numbers 1 1 1 15 22 9 99 100 240 3 7 Standard Deviation 75 Divided by 4...
I'm working on a Bayesian inference package and I have a function that finds the maximum a posteriori point. Right now I'm using scipy's implementation of BFGS to find that minimum of the log posterior, but I've had some trouble with handling large negatives and -infinities. I'd like to see if there's a better algorith...
I have a couple of questions for prediction and tolerance intervals. Let's agree on the definition of the tolerance intervals first: We are given a confidence level, say 90%, the percentage of the population to capture, say 99%, and a sample size, say 20. The probability distribution is known, say normal for convenienc...
I am running a project which compares citation counts across datasets per year, and then wants to plot the general change in the frequency in which a given source is cited. Here are two example datasets: 1999 - SOURCE A {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 23, 70, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 25, 0, 3, 13, 0, 1, 0, ...
I am trying to test if one algorithm is statistically significantly faster than another using the One-sample t-test These are the results I have and I am trying to prove Algo2 is significantly faster than Algo1 Mean (ms) Variance Algo1 5171 782 Algo2 3753 1920 with a sample size of 78,869...
http://en.wikipedia.org/wiki/Cyclostationary_process What are the methods in modelling and forecasting such time series? It is mentioned in the link above that there is a deterministic approach to treat such a time series. Can anyone explain what does it mean?
How can I express multiple response variables for linear model? For example, I can do this with single response variable lm(Y1 ~ X1+X2+X3, data=somedata) But if I want to use Y1-Y100 response variable in the model, how can I do that? UPDATE: I am hasty. I just found an answer from http://www.mail-archive.com/r-help@r...
I am confused on one issue of topic modeling analysis. When we perform the topic modeling analysis over a collection of documents, do we need to provide a set of topic candidate list as the input for the analysis? Or the resulting topics are just extracted from the input documents themselves?
I have data on patients attendance of a series of sessions of counseling. At each session, a patient could be A, S or D. Each patient has data for 12 sessions, and there are ~100 patients. I am interested in how the variables are 'autocorrelate'. I could just make 3x3 tables of (e.g.) time 1 vs. time 2, time 1 vs. 3, t...
Possible Duplicate: What is the probability of n people from a list of m people being in a random selection of x people from a list of y people? Let's say we have 5 kinds of marbles, 1000 of each, mixed up in a giant tub. I want to know how many I have to draw out (without replacement) before I can be 50/70/90% sure...
Suppose you have character values as the x values. Suppose you want to draw a histogram. How do you convert the character values into numerical values?