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Suppose that $w_1,w_2,\ldots,w_n$ and $x_1,x_2,...,x_n$ are each drawn i.i.d. from some distributions, with $w_i$ independent of $x_i$. The $w_i$ are strictly positive. You observe all the $w_i$, but not the $x_i$; rather you observe $\sum_i x_i w_i$. I am interested in estimating $\operatorname{E}\left[x\right]$ from ...
Assume there are 2000 students, $m$ boys and the rest are girl. Now we take a sample of 5 students which contains only 1 boy. We claim that there are more girls than boys in the population. So what we want to do is to check the maximum likelihood under $H_1$ $H_0$, but the problem is I don't know how to get the maximum...
Say I have a number of time series, e.g. a number of temperature records from various stations in a region. I want to get a single temperature record for the whole region with which I could describe aspects of the regional climate. The intuitive approach might be to simply take the average of all stations at each times...
This is also a question that relates very much to Python as a statistics workbench and excel as a statistics workbench. I know there is a huge discussion about Ruby versus Python but this is not the point on this question. I thought that Ruby being faster than Python and having a very natural syntax could benefit me to...
How does using 1 - correlation as the distance influence the determination of the number of clusters when doing kmeans? Is it still valid to use the classical indices (Dunn, Davies-Bouldin...)?
Is this formula right? $$\renewcommand{\Pr}{\mathbb P}\Pr[\cap_{i=1}^n A_i] = \sum_{i=1}^d (-1)^{i-1} \sum_{|K|=k} \Pr[\cup_{k\in K} A_k],$$ with $K$ a subset (without repetition) of $\{1, ..., n\}$. I have found a similar formula that expresses $\Pr[\cup_{i=1}^n A_i]$ in terms of $\Pr[\cap_{k\in K} A_k]$, and I'd lik...
I want to estimate a multivariate variance function in R. That is, I want to allow the variance (as well as the mean) to vary according to some set of independent variables. In this particular case, I want to estimate the effects of a set of typical demographic covariates (age, race, education) on the variance of lo...
Let $X_1,X_2,...,X_n$ be a fixed number of Bernoulli random variables. My problem is to find a distribution for $Y$ such that for some function $f$, we have $Y=f(X_1,X_2,...,X_n)$. There are two candidate functions to use, $max$ or $avg$. I have no idea if an average function would work here or not but I think it'd giv...
I have a large data set (400k rows X 60 columns) that I'm trying to use to build a knn model. I'm using the caret package version of knn and the forward.search method from the FSelector package to eliminate variables via cross-validation. My problem is that once I use more than 20k lines of data I get a message about...
Suppose we have two samples and we wish to determine if they are drawn from the same distribution, the samples A,B being composed of some integers say. If we test this using a two-sample permutation test, specifically by looking at permutations where the differences in the means of the samples are as extreme as the dif...
My data is a panel of countries by year. Suppose my main RHS variable is a country's GDP and my main LHS variable classifies countries by whether the country is a democracy. Is it desirably to weight each observation by the country's population in a particular year? Since the world population has generally increased ...
I am obtaining confidence intervals using different bootstrap methods. When comparing them, what is does it mean to use Monte Carlo variation to look at how much the upper and lower limits vary for each bootstrap?
I'm using support vector regression to model some fairly skewed data (with high kurtosis). I've tried modeling the data directly but I'm getting erroneous predictions I think mainly due to the distribution of the data, which is right skewed with very fat tails. I'm pretty sure a few outliers (which are legitimate data ...
I am analyzing weather data from 2 sites, and trying to determine if they are correlated. For the most part, I am able to run linear regressions and Pearson's correlations since the data are relatively normal. However, when looking at relative humidity, it obviously has an upper limit in place (100%; it would have a lo...
I'm trying to write my own Python code to compute t-statistics and p-values for one and two tailed independent t tests. I can use the normal approximation, but for the moment I am trying to just use the t-distribution. I've been unsuccessful in matching the results of SciPy's stats library on my test data. I could use ...
An investigator wishes to produce a combined analysis of several datasets. In some datasets there are paired observations for treatment A and B. In others there are unpaired A and/or B data. I am looking for a reference for an adaptation of the t-test, or for a likelihood ratio test, for such partially paired data. ...
This is a fairly basic question: If a number of regression models are being evaluated for fit to a dataset, and each model has 3 variables, will AIC and R-square rank the models similarly? I'm assuming the answer is yes, because the penalty aspect of AIC for added variables would be a non-issue. But, I'm unclear if thi...
Essentially, I have two collinear variables which could be seen as either random or as fixed effects, a dependent variable I'm fitting the model to, and a variable that's assuredly a random effect. Dependent var: Number of neuron spikes (FiringRate) in a specific region of mousebrain Fixed effects: 1) Time at which dat...
I have two sets of data representing stars parameters: an observed one and a modeled one. With these sets I create what is called a two-color-diagram (TCD). A sample can be seen here: A being the observed data and B the data extracted from the model (never mind the black lines, the dots represent the data) I have only...
I'm going through the videos in Andrew Ng's free online machine learning course at Stanford. He discusses Gradient Descent as an algorithm to solve linear regression and writing functions in Octave to perform it. Presumably I could rewrite those functions in R, but my question is doesn't the lm() function already giv...
If I have some fixed non-recurrent (DAG) topology (fixed set of nodes and edges, but the learning algorithm can vary the weight on the edges) of sigmoid neurons with $n$ input neurons which can only take strings in $\{-1,1\}^n$ as input and lead to one output (that outputs a real value that we round up to 1 or down to...
I have a list of (x,y) pairs that form a cluster of points. I was able to find the mean of the cluster, but I'd like to be able to find the standard deviation of the cluster. How can I define the standard deviation? I defined the mean as the point (mean of x values, mean of y values). What type of standard deviation v...
What formula is used in the standard deviation function sd in R?
Let $X=\min(U,V)$ and $Y=\max(U,V)$ for independent uniform(0,1) variables $U$ and $V$. What's the covariance of $X$ and $Y$? Could you develop some calculations, especially regarding the computation of $\mathbb{E}XY$?
How does one calculate the distribution of a random variable $Z = X + Y$, where $X$ is Poisson distributed and $Y$ is normally distributed and independent of $X$? How to do that in general case? Do you know any textbook about this topic? It's really hard for me to seach on this topic, because I don't know what to call ...
For what distribution $F$ is $X_1 + \dots + X_N$ most nearly exponential, $X_i$ i.i.d. ~ $F$, for $N$ = 2, 4, 8, 16 ? How would one go about solving problems of this kind numerically ? ("Most nearly" means some metric on distributions, of which there seem to be many; $\mathbb{E}( X - Y )^2$ ?)
Consider a multinomial $2\times 2$ table $\begin{pmatrix} x_{11} & x_{12} \\ x_{21} & x_{22} \end{pmatrix}$ with theoretical probabilities: $$\begin{pmatrix} \theta_{11} & \theta_{12} \\ \theta_{21} & \theta_{22} \end{pmatrix}.$$ The conditional distribution of $x_{11}$ given $x_{11}+x_{12}=n$ is binomial with size $...
My data mydata consists of columns of x1,x2,..,x100,y in R. But I am thinking a linear model with second order terms such as y ~ x1^2 + x2^2 + x1*x2 + ... how do I achieve that within formula or in any other way in R? When I tried above, my model pls ignored all second order terms. Do I have to manually create those co...
Which type of test is most appropriate for this comparative-descriptive study? I have two groups of subjects (250 in each). My goal is to determine if the two subject groups are different and if so, how. I'm using an online survey of 50 statements (embedded are 5 statements about 10 different possible factors). Subjec...
My first post in this useful community. Ive been trying to use GLS methods in non-linear mixed effects models and have found this post, Prediction with GLS extremely informative and helpful. Some of my questions are probably more of a follow up to the above post which discusses the predictive capability of GLS. Below ...
An assumption of the ordinal logistic regression is the proportional odds assumption. Using R and the 2 packages mentioned I have 2 ways to check that but I have questions in each one. 1) Using the rms package Given the next commands library(rms) ddist <- datadist(Ki67,Cyclin_E) options(datadist='ddist') f <- lrm(grade...
In finance, two procedures are sometimes used to help evaluate the likelihood that positive results were obtained strictly due to data mining: White's Reality Check (WRC), described in White's (2000) Econometrica paper titled "A Reality Check for Data Snooping", Monte Carlo Permutation (pair matching of historica...
Suppose you take 3 samples and report a 99% confidence interval for each dataset. How would you go about calculating the probability that all the datasets contain the true population mean? No other statistics are provided.
I have a 2 by 2 design with 12 subjects. The two factors are within-subjects variables. For each cell, 24 responses were collected from each subject. My question is whether I need to aggregate every 24 responses into a mean and then use the mean in lmer as the dependent variable. This webpage http://talklab.psy.gla...
I was chasing down a citation about the incidence of postoperative wound infection in diabetic patients, and I found this 1998 abstract by Pomposelli with the following statement: "In patients with hyperglycemia (> 220 mg/dL) on POD 1, the infection rate was 2.7 times that observed (31.3% vs 11.5%) in diabetic patient...
I am working on implementing a Fisher Exact Test for some unemployment and wage data. The idea is to describe two populations (one receiving an assistance program (the "treatment") and one not receiving it) via a summary statistic. The first statistic that I am using is the difference in average wage-level post-treatme...
I've fit a Linear Mixed Effects model to some "accuracy" scores for a study with rats. The fixed effects are TrialNumber and Age, and the random effect is the individual rat (Rat). Age is included because the trials span a number of months (and Age is measured in days; not all rats were the same age at the start of the...
We typically educate clients on the potential bias of one mode over another (online versus paper surveys for example) and the bias a scale can have when designing questionnaires. A client recently asks me how we could test for this bias and I am looking for ideas?
When trying to estimate the parameters of a known distribution, it might occur that the maximum likelihood estimator and the method of moment estimator don't work well when there's only one observation. What are some good non-Bayesian alternatives to maximum likelihood estimators and method of moment estimators if ther...
I'm having a look at x-ray waiting times in an emergency department and how these relate to the day of the week and the time of day that requests are ordered. (Want to know if patients have to wait longer for their x-rays on weekends and at night compared with day shifts). The waiting times have a significant right ske...
I want to make a logistic model from my survey data. It is a small survey of four residential colonies in which only 154 respondents were interviewed. My dependent variable is "satisfactory transition to work". I found that, of the 154 respondents, 73 said that they have satisfactorily transitioned to work, while the r...
Recently I have been playing with linear regression for classification. For the binary case, it is straightforward. For the multiple case, I know there are issues with using this approach (like masking). However, I cannot fully understand how this masking arises. As understand in the multiple case one has to compute a ...
Are the RSS examinations worth doing as a way to learn more statistics? I have been working a physicist for most of my life so I'm a little bit loathed to pay to learn maths as I can usually get my head around new statistical methods as and when I need them. The problem I have is that I only use what I know about and o...
On an attempt to solve this problem I've managed to reduce it to finding the expected number of white balls picked until one black ball is observed (let's call that value $v$). Except that, unlike the geometric distribution, this needs to be done without replacement. Hypergeometric distribution doesn't come to the resc...
This is a basic question on Box-Jenkins MA models. As I understand, an MA model is basically a linear regression of time-series values $Y$ against previous error terms $e_t,..., e_{t-n}$. That is, the observation $Y$ is first regressed against its previous values $Y_{t-1}, ..., Y_{t-n}$ and then one or more $Y - \hat{Y...
My understanding is 'no', a stationary process does not imply a normal distribution of the data. However I haven't found a clear indication in my library or online. I am interested in other resources comparing stationary and heteroscedastic processes to data distributions. I understand a stationary process joint probab...
I am interested in the Bayes risk of some distribution $\pi$ $$ r(\pi) = \mathbb{E}_{\pi(x)}[ \mathbb{E}_{\Pr(y|d,x)}[L(x,\hat x(y|d))]], $$ where $L$ is some loss function and $\hat x$ is the posterior mean (here: Bayes estimator). Here $d$ is some experimental design parameter. If $L(x,\hat x) = |x-\hat x|^2$ (sq...
I have a CFA with four factors - they are all intercorrelated except for two. Is this a problem for the model to have two factors uncorrelated?
I am trying to come up with an easier algorithm than usual nonlinear optimization algorithms for linear support vector classifier. My idea is Once classifier is determined, it's easy to decide support vectors (data misclassified + data near the discriminant plane) Provided that support vectors are fixed, it's straig...
Suppose we have $\newcommand{\E}{\mathrm{Exp}} X \sim \E(\lambda)$, $Y \sim \E(\mu)$, and $W = \min(X,Y)$. I know that $W \sim \E(\lambda+\mu)$. I know how to derive it. But, I tried this alternate derivation that gave me a different distribution for $W$, and I still can't figure out what's wrong with it. I started wi...
I am trying to see if there is a statistical significant difference between the amount of bycatch in 5 different types of gear used by fishermen. For each gear I have varying number of replicates as there are higher number of fishermen using certains types of gears compared to others. I have converted my raw data into ...
I have a data set with 3 continuous variables and 3 categorical variables. I know that I have to create dummy variables for categorical variables but I am wondering if it is a must to do that for all 3 categorical variables in this case?
I'm trying to calculate the upper percentage points for the 0.99 percentile for samples drawn from a normal distribution, with a sample size of 500. How can I calculate the expected values for skewness, kurtosis, studentized range, which would be expected for a drawing of 500 values?
I have a streaming data set, examples are available one at a time. I would need to do multi class classification on them. As soon as I fed a training example to the learning process, I have to discard the example. Concurrently, I'm also using the latest model to perform prediction on unlabelled data. As far as I know, ...
I am a software developer (mostly .NET and Python about 5 years experience). What can I do to help me get a job in the machine learning field or really anything that will get me started in that field? Is post-graduate degree a hard requirement?
for (i in 1:160) { situps[i] ~ dnorm(mu[i],prec[gender[i]+1]); mu[i] <- b0+b1[gender[i]]+b2[health[i]]+b1b2[health[i],gender[i]]; } b0 ~ dnorm(0,.001); for (i in 1:4) { b2[i] ~ dnorm(0,.001); } for (j in 1:2) { b1[j] ~ dnorm(0,.001); prec[j] <- pow(sigma[j],-2); sigma[j] ~ dunif(0,10); } for (i ...
When using NNs for estimation purpose, we have three layers: input, output and hidden layer, and we must choose the number of nodes for every layer. Is there a method or rule of thumb to choose the correct number of nodes?
Whenever I see people using ngrams - I often see them looking for higher chains like 4-grams, 5-grams and so on. However, I'm wondering why I never see any mention of "nested ngrams" (I'm not sure what the real name is). For example, suppose you tracked the bigram "to follow" followed by the bigram "after dark" instead...
I am very new to functional data analysis (FDA). I am reading: Ramsay, James O., and Silverman, Bernard W. (2006), Functional Data Analysis, 2nd ed., Springer, New York. However, I am still not very clear where/when to use FDA? Could someone please give me an example especially in medical studies? I really don't k...
I have a simple document classification problem where i need to classify some documents to a definite set of classes. I need to perform a feature selection (where I will select the most important words from each class). Currently I am calculating the tf-idf scores. Is there a better way to do that ? I heard about chi-...
I have 60 apps. For each app, I look at 10 review of that app, and count how many of the reviews say the app is unreliable. Let $X_i$ denote the number of such reviews, for the $i$th app. I want to check whether the reviews seem to be pretty consistent for each app. For instance, if one review says the app is unrel...
I have an implementation of an MCMC algorithm (Metropolis-Hastings and Adaptive Metropolis-Hastings) that I want to modify to suit my needs (it's pyMC, if anyone is interested on the details). My problem is that the parameter space for my model is very high (10-20 parameters), so the burn-in period is crucial for each...
Any arbitrary distribution of a multivariate binary variable can be represented as a log-linear model. That is, for $X = (X_1,\dots,X_d)$ a $d$ dimensional binary rv, the distribution can be written as $\log(\text{p}(x)) = \sum\limits_{A\subseteq V} \beta_A (\prod\limits_{i \in A} x_i)$ where $V={1,\dots,d}$. E.g. for ...
The Swiss Public-Use Sample of the national census is a 5% sample drawn from the entire census survey. According to the documentation, the persons are sampled uniformly without replacement. Persons are the "primary sampling unit", the selection probability and person weights are all equal: $\pi = 0.05, w = 1/\pi = 20$....
I have compared two regression models using ANCOVA by following this tutorial but using my own data. Here is a snippet of my data: X MC CC RC FM AT HS 1 0.874375 NA NA NA NA grab 1 2 0.451250 0.41948802 0.44885230 0.45113...
I'm trying to compare 5 different gears used by fishermen and the amount of bycatch found in each. The values have a unit of "% of time encountered" and range between 0% (ie: never have bycatch) and 100% (ie: encounter bycatch every time they go out). I chose this as not all the fishermen fished the same amount of time...
I often find myself asking questions like, "I know this variable $x$ lies in $(0,1)$ and most of the mass lies in $(0,.20)$ and then declines continuously towards 1. What distribution can I use to model it?" In practice, I wind up using the same few distributions over and over again simply because I know them. Inste...
Motivation I am interested on using R to do data analysis on a considerable amount of data. Having to plot each time I want to observe if it fits any particular distribution by eyeball (which can be misleading), and recall in memory how the shape looks like (or compare, say, on a book). As a programmer, I would like t...
Definitions Open Source Project: In short (and roughly described, only to the purpose of clarification) open source projects allow me to have access to the code of a certain 'program'. Motivation and Background (so I can understand your answer) I have a undergoing majors in CS, expect a very high level course in sta...
I've been under the impression that the mid-$p$ values generally control the Type I error, and consequently confidence intervals based on mid-$p$ values control the coverage. However I have checked that this is not true with the binom.midp() function of the binomSamSize package (see below). Is it a problem with binom....
The following is question 8 of chapter 8 in Wasserman's All of Statistics: Let $T_n = \overline{X}_n^2$, $\mu = \mathbb{E}(X_1)$, $\alpha_k = \int|x - \mu|^kdF(x)$, and $\hat{\alpha}_k = n^{-1}\sum_{i=1}^n|X_i - \overline{X}_n|^k$. Show that $$v_{\mathrm{boot}} = \frac{4\overline{X}_n^2\hat{\alpha}_2}{n} + \frac{4\o...
If i do a modelLookup('glmnet') it says TRUE for probModel (and in fact, I'd expect it to be usable as a model to predict probabilities in a binary outcome prediction problem as glmnet has a 'binomial' family argument). However, following the instructions from the caret package I say: trainControl = trainControl(classP...
Suppose you are using the factorization theorem to find a sufficient statistic. Let us say that we have a negative sign in front of $T(x)$. How do you know whether or not to "absorb" a negative sign into a sufficient statistic or any other sign? So instead of $T(x)$ we could have $$\widetilde T(x):=−T(x) \>.$$ For exa...
I recently used bootstrapping to estimate confidence intervals for a project. Someone who doesn't know much about statistics recently asked me to explain why bootstrapping works, i.e., why is it that resampling the same sample over and over gives good results. I realized that although I'd spent a lot of time understand...
I have been doing some fitting using the fairly standard expression, $$\chi^2 = \sum_i \frac{(y_{i} - F(x_{i}, \theta))^2}{\sigma_{i}^{2}}$$ where y is my measured data, $\sigma$ is the experimental uncertainty and $\theta$ is the parameter I'm estimating. I know that in reality my data are not independent and that I c...
If we have the following histogram: And, want to describe it based on one of the following options, which one do you think is correct? Why? positively skewed symmetric none of the above negatively skewed My initial suggestion would be "3. none of the above". What do you think? Thanks.
I'm trying to aggregate $T$ local image descriptors (i.e. histograms) into a vector, namely, the Fisher Vector as described in this paper by H. Jégou et al., Aggregating local image descriptors into compact codes, to perform image classification. As a first step, the algorithm calls for running K-means to assign each l...
While studying about probability distributions I found that distributions such as $\chi^2$ only would be able to tell if there is or there is not relation between a variable, but not how strong it is. Later, it is pointed out that it is possible to observe how strong this relation holds using a method particular to th...
Consider estimating the variance of a RV $X$, we start with the sample variance: $$ \begin{array}{ll} V_1 & = \frac{1}{N-1} \sum_{i=1}^N (X_i - \bar{X})^2\\ & = \frac{1}{N-1} \left(\sum_{i=1}^N X_i^2 - 2\bar{X}\sum_{i=1}^N X_i + N\bar{X}^2 \right)\\ &= \frac{1}{N-1} \left(\sum_{i=1}^N X_i^2 - N\bar{X}^2\right) ...
I have some items described by 43 categories like this: Dataset Item Category1 Category2... Category43 D1 Item1 1 0 0 ... 1 ... D1 Item3 1 0 0 ... 1 ... D2 Item4 1 0 0 ... 1 ... .. What I did was to create a freq...
I am building a model in R using support vector machine (SVM) with KBF kernel. The model seems to work quite well. I would like to assess the relative importance of predictor variables. Can anyone tell me how this can done. Does there exist an R script for that?
I am implementing random forest in my code, I find that when I build one tree, the oob error(mean square error since I do regression) is close to zero, while more tree is build, the oob error stablized, this is counter-intuitive, since the textbook teaches me that the oob error should decline as more trees builds, I co...
How does Adaboost select best features from the sample data (or a unit feature vector)? It would be nice if someone can explain if the above statement is true or not. I've seen the term features and classifiers being used in place of each other in the documentation that's available of Adaboost (that's what I thought). ...
I have a question: Does a sufficient statistic have to be one to one? For example, can $T(x) = x^2$ or $T(x) = |x|$ be sufficient statistics? I know that one to one functions of sufficient statistics are sufficient.
For each minute of an hour, I have a minimum and maximum observed value. for example: time min max 00:00 12.13 15.10 00:01 14.23 17.02 00:02 11.12 12.10 ... 00:59 09.11 09.89 We can assume that, during that minute, the observed values were uniformly distributed between the minimum and the maximum values. ...
A covariance matrix of multivariate random variable can be constructed given a time-series random variables. Eg. If you observe a student's performance in different objects (Math, English, Physics, etc) for a period of time; then you can construct the covariance matrix for those objects for that specific student. Howe...
I'm pretty sure that I'm missing something obvious here, but I'm rather confused with different terms in the time series field. If I understand it correctly, serially autocorrelated errors are a problem in regression models (see for example here). My question is now what exactly defines an autocorrelated error? I know ...
I have a set of numbers which are assumed to be coming from a Poisson distribution. The set has some outliers also and because of that, maximum likelihood estimates are badly affected. I heard that robust estimation procedures can help in such a situation. Can any one explain how to do this? I am not a statistics stude...
I am looking at pre and post test depression scores in a 2x3 design with treatment and genotype as the IVs and depression score as the DV. However, I have to use one depression test for younger people and a different depression test for older people, because I would like to covary out age. I think I need a repeated m...
I am using the strucchange package to detect structural changes in my data. The plot of my Fstats shows several peaks, yet if I use breakpoints one additional breakpoint is found. My F statistic at that point suggested by breakpoints is even below the threshold. Why does it find more?
I am doing a research on 20 participants where 10 will be from computers background and rest will be from non computing background. Each participants will attend a lab session and the performance of the participants will be evaluated based on a rubric. Each row of the rubric is evaluated on scale of 1 to 4. The researc...
In most of the examples I've seen so far of neural networks, the network is used for classification and the nodes are transformed with a sigmoid function . However, I would like to use a neural network to output a continuous real value (realistically the output would usually be in the range of -5 to +5). My question...
I am doing research on 20 participants and the participants will work on a lab module. There will be a pretest before the lab module and post test after the lab module on concepts related to flowchart, pseudo code , etc., The possible outcomes for the question is Yes/No. Which statistical method should i use to analyz...
So the description I read is: It is important to note that the formulas for calculating the variance and the standard deviation differ depending on whether you are working with a distribution of scores taken from a sample or from a population. The reason these two formulas are different is quite complex and r...
I'm developing a tool to conduct expert elicitations of scientists. As answers to questions are speculative, we like experts to help us understand the range of answers they find plausible, to get some idea of uncertainty. For one type of question, we have them input a lower-bound, upper-bound, 25th percentile, 50th per...
I'm currently working with a data set that consists of a monthly case count for several sites, along with a number of site-specific covariates. We're trying to estimate the effect of one of them on the case-load (either in terms of numbers or a percent). At the moment, I've been using Peng and Dominici's Statistical Me...
I am using 10 independent variables in building logistic regression model. I am sure that some of these variable are correlated. Can anybody tell me how to check for multicollinearity among independent variables in this case. Thanks!
So, I am new here. I need to perform a sample size calculation for a clinical trial. The study sample will be select according to criteria of person's height. Persons within the particular height range (female, 1.6m to 1.7m) will be invited to participate in trial. We know the expected sample standard deviation from pr...
I've been asked to analyze some data for an experiment that's already been done. 15 rats were raised in 5 groups of 3 No treatment Saline treatment (control drug is delivered via saline) Drug treatment Saline shock (high dose) Drug shock (high dose) Due to budget constraints, groups 2~5 were physically pooled (i.e. t...
In 50 individuals we measure the presence of 2 SNP's ("single nucleotide polymorphisms") and 1 trait. We assume that both SNP's and the trait are binary. We assume the model $Y_{ijk} = \text{Bernoulli}(p_{ij})$, where $$Y_{ijk} = 1\text{ if person }k\text{ with SNP 1 }= i \text{ and SNP 2 }= j\quad (i,j\in \{0,1\})\tex...