Refers to any statistical complication or problem due to having few data.

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References for tiny sample statistics

There are multiple fascinating problems and approaches connected to really small samples. It is possible to estimate confidence intervals using a single point, or there are well known problems such as ...
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34 views

Confidence interval for function of the parameter - small sample size

I am trying to come up with a solution for this problem. Consider the following set of random variables: \begin{align*} X_{11},...,X_{1n_{1}}\quad &\text{i.i.d. Bernoulli(1-$e^{-\lambda_{1}}$)}\\ ...
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28 views

Proper test for comparing two means from different distributions? (with limited data)

I have some data on frog weights for a small sample ($n \approx 30$). I need to compare the mean frog weight from this sample $\mu_s$ to the mean of another, much larger sample of frog weights $\mu_r$ ...
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7 views

Average-to-average comparison with non normal response variable and dependent explanatory variable

I would like to compare the average expression of a gene in three different brain regions of a mammal (see the table below). Unfortunately, I had only 11 mammals to calculate each average. Moreover ...
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1answer
66 views

What is the name for this unintuitive result with OLS on a very “asymmetric” regressand, and how should it be addressed?

Say our sample consists of about a hundred Belgian (x = 0) and Swiss (x = 1) chocolate bars. We test them to see if they have safe (y = 1) or lethal (y = 0) levels of arsenic. As it turn out, 90% are ...
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22 views

Testing interactions with non-normal ordinal data

I am testing a hypothesis in which my scale DV (PSS) is predicted by an interaction between an Ordinal DV and a scale IV. The ordinal IV is TF (Total Freq) The scale IV is and PQM (Practice ...
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14 views

Confidence interval odds-ratio matched case control

Consider having a list of pairs of binary data denoting observations from a matched case control study. The list may be used to set up a contingency table and an odds-ratio can be calculated by ...
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24 views

Which exact test should I use for my data?

I'm very new to statistical analysis, and I am wondering if I am paying too much attention to unimportant questions. My data consists of about 40 cases involving a particular kind of lawsuit. After ...
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60 views

What methods can I use to aid in modeling a smaller data set when I have a significantly larger data set with fewer variables?

I currently have a data set with about 4,000 rows. The current model I have established for it is not very good, and I am going to receive more data for about 150 of these points, and I'm hoping that ...
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33 views

Johansen's cointegration test in small sample under non-normality

I am looking for references regarding the behaviour of Johansen's cointegration test (trace test, perhaps also eigenvalue test) in small samples with non-normal innovations. I wonder how robust the ...
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1answer
20 views

Can I conduct t-test for this study [duplicate]

In my study there are only 15 subjects in the intervention group and 15 in the control group. Can I use the relevant t-test to analyze each inter group and intra group differences(pre & post). ...
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16 views

Regression: Should I use the prediction interval obtained given n=9 and an outlier (Cook's D= 0.558) present?

The data I'm working with has 9 observations. I'm using only one predictor variable. Using SAS, I fit the model and checked the residuals. The typical model assumptions appear to be met, but there ...
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28 views
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2 views

Comparing change in lateral root densities between treatments for different genotypes

I have been growing 4 genotypes of the same plant and been recording their lateral root density under both control conditions and a salt treatment. I have calculated the decrease in lateral root ...
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18 views

feature selection in a small sample size

I need an advice. I have a dataset consisting of 108 observations (27 subjects * 4 time points) and ~10000 features. The data represents intensity values (comes from continuous domain). When I run ...
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76 views

ANOVA: testing assumption of normality for many groups with few samples per group

Assume the following situation: we have a large number (e.g. 20) with small group sized (e.g. n = 3). I noticed that if I generate values from the uniform distribution, the residuals will look ...
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24 views

Can I reuse the dataset set aside for performing t-test based on the following condition?

I have a small number of samples and large number features. For doing the feature selection I'm going to divide my total set into a feature selection set and a test set.I run the t-test on the former ...
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108 views
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5answers
790 views

Best method for short time-series

I have a question related to modeling short time-series. It is not a question if to model them, but how. What method would you recommend for modeling (very) short time-series (say of length $T \leq ...
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10 views

How to test correlation of two variables from four repeated measures of each one among four groups

I have four plots from where I took a measure of two indicators of population abundance (as continuous variables) throughout four surveys (say, at spring 2010, fall 2010, spring 2011, fall 2011). So, ...
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1answer
89 views

The best model of an AICc-based model selection on a very small sample has an high number of predictors: does it make any sense?

I'm working with a very small sample size (N=14) and I'm using AICc to identify the most parsimonious model using a large number of possible predictors. Unexpectedly the best model has six predictors! ...
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0answers
22 views

How to analyse the ratio of two continuous variables sampled repeatedly over time

I am measuring reproductive hormones in dolphins over time to look at seasonal changes. The sample type (respiratory vapour) that I am using suffers from variable water dilution that cannot easily be ...
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42 views

Rare event sampling [closed]

Suppose $A$ is a very small subset of $\{0,\dots,n\}^3$ and I am trying to find an element of $A$. I first inspect maybe 50 random triples $(x_i,y_i,z_i), 1\le i\le 50$, and find that none of them are ...
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1answer
41 views

Estimate normal distribution from small sample with rankings

If I have n samples from an $N(\mu,\sigma)$ distribution, how can I estimate the distribution from a subset of m of these n samples where the order within those n is known. For example, if n = 100 ...
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1answer
65 views

Paired samples or independent sample hypothesis test for two time periods

I want to know if employees in an organization are surveyed in 2013 and again in 2014 if the samples from the two time periods are considered related and dependent or independent if they are asked the ...
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2answers
36 views

Do any statistical tests compare distributions when one has far fewer observations?

I've been researching different methods to compare two distributions for equality, or inequality rather. I want to compare actual user performance against projected performance, after a particular ...
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1answer
23 views

Using a measure of productivity which is determined by reviewers

Apologies for the ambigious title - I wasn't sure how a problem like this is expressed. I have a small sample of 20 individuals, of which the dependent variable (of interest) is binary with 5 ...
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50 views

OLS with dummy and few observations (12 mean values from 2.5k observations)

I have a dataset of 12 markets, in total ~2.5k trades happened over all markets. I now calculated 6 different measures for the each markets performance (my 12 observations per measure I want to use as ...
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32 views

Calibrated Probabilities for Outlier Detection Algorithm

I am currently developping a 2 class classification algorithm. However, as the dataset is at the moment really small (<50 observations) and imbalanced (~1/10 ratio), I decided to rather first ...
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1answer
224 views

Increasing sample size with bootstrap sampling

I'm trying to perform some classification analyses with a relatively small dataset (201 observations, 32 predictors). There are 8 classes in my data with unequal sample sizes ranging from 10 in the ...
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1answer
44 views

Size multilevel logit model

I want to estimate a multilevel logit model. But I'm confused about the minimum number of groups and observations per group. What would be the minimum number of observations per group? My case: I ...
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1answer
56 views

Using nonparametric tests with small samples even when data are normaly distrubuted

Is it appropriate to use a nonparametric test with a small sample (e.g., less than 65 people) even when data are normally distributed? For example, using the Spearman correlation? Actually my data is ...
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23 views

Small sample size : dealing with bootstraping for linear or nonlinear multiple regression

I am wondering to heal my ignorance from your experiences or your modeling knowledge. I have many matrices of quantitative variables, let me start with three matrices of proportions.To express ...
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18 views

Problem Approach: uncertainty about sample size

I have a time series of events (weekly aggregate date) Each event is information on contracts closed by a sales representatives during working weeks. The goal is to calculate what is the expected ...
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1answer
70 views

ANOVA-type test but with known population variance of each group

I have a set of $N$ samples $s_{i}$, each one sampled from a normal distribution with standard deviations $\sigma_i$, which are known. I would like to know if the distributions have the same mean. I ...
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1answer
77 views

MANOVA when sample size is smaller than the number of DVs

I need to compare $16$ quantitative variables, measured for two groups, A and B. I thought of applying MANOVA. However, there are only $4$ and $9$ cases for groups A and B respectively. I looked for ...
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11 views

Selecting the right DV in study of treatment effect on a small sample?

I want to run a simple experiment at work to see if making a single change F on a product, has any significant adverse effect on the performance. I need help to ...
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13 views

Optimizing selection from varying sets

On pages of website(s) I have a set of potential messages to choose from and only one or two slots to show them in. (think 'this product is on sale' or 'this product is new'). On each page the set ...
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38 views

Few-clusters bias correction for cluster robust covariance matrix in random effects model

I'm currently working on some experimental data. Subjects are randomly assigned to one of two treatments. For each treatment I ran three sessions with 20 subjects each. In each session, participants ...
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1answer
17 views

Cross validation and small samples

I have a sample of 415 observations. With a sample with this size, it's possible to use cross validation?
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88 views

Is my sample suitable for elastic net? What are the assumptions?

I was hoping to use multiple regression to identify significant predictors but I have a tiny sample size (group 1 n=9, group 2 n=37) so I'll be unable to do this. I have read that regularisation ...
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14 views

Model Specification tips for increasing the power of a GLM model with small sample size? (SAS)

I am working on a model that uses a wide variety of categorical predictors vs. a continuous dependent variable. Unfortunately, my usable n ends up being 28. I am having difficulty getting significance ...
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1answer
934 views

Regression with very small sample size

I want to run a regression with 4 to 5 explanatory variables, but I have only 15 observations. Not being able to assume these variables are normally distributed, is there a non-parametric or any other ...
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2answers
84 views

If one group has 23 participants and the second group has 117 participants in it, can we rely on the result of t-test? [duplicate]

I was evaluating a research paper in which the authors have 23 male participants and 117 female participants. They have applied t-test to calculate Gender differences and have even concluded on ...
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1answer
22 views

Increasing statistical power by having a highly sensitive outcome measure

Is it logical to say that you can increase statistical power by having a highly sensitive outcome measure? I say this because a highly sensitive test has low Type II error, and low Type II error leads ...
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106 views

Rule of Thumb for minimum length of time series for Autocorrection estimation

I had a related question answered here: Rule of Thumb for minimum length of time series for AR(1) estimation However the answer gives rise to a new question. I want to be able to estimate the Auto ...
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1answer
116 views

Rule of Thumb for minimum length of time series for AR(1) estimation

I have a data set of 350 points, I want to estimate the lag 1 auto correlation for different sub-sets of the data. More precisely I want to take non overlapping windows of length 1,2,3....n and ...
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33 views

regression analysis for dataset with few predictors and few samples

I have a small pilot dataset containing experimental measurements for 12 samples, 4 numeric predictors and 1 numeric outcome variable. The goal is to obtain a first rough estimate on the extent to ...
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62 views

Validating Bootstrapped Probability of Survival Results From Small Sample Size Data

Quite often in industry, due to cost and schedule constraints, decisions must be made on small sample size data. I have 4 cycles-to-failure values resulting from running samples to failure in a ...
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1answer
67 views

parametric bootstrap for low sample sizes

I believe that this question is sufficiently different from previous related ones to warrant a new post. (I apologize if it has been answered already) I need to decide between various resampling ...