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

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32 views

Non normal and nonlinear data

I'm working with pilot study data (n=70) that has two continuous response variables and a number of categorical and continuous predictors. Naturally my data does not follow a normal distribution nor ...
2
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2answers
32 views

How to empirically show that a certain quantity approximately follows a normal distribution?

To motivate some theoretical work, I need to show that two certain variables (say $X$ and $Y$) approximately follow a normal distribution in actual datasets. I have one large dataset with about $300$ ...
3
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1answer
52 views

About the central limit theorem and statistical testing

Wikipedia states that In probability theory, the central limit theorem (CLT) states that, given certain conditions, the arithmetic mean of a sufficiently large number of iterates of independent ...
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8 views

Statistical significance in a small peer group

I am looking at the gross profit margins in a industry where there are 10 companies. The company I am interested in has a gross profit margin of 28% and the mean gross margin across all 10 companies ...
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0answers
20 views

Small sample difference-in-difference analysis with 2x2 experimental design

For my master's thesis I ran a small-scale experiment with a 2x2 design (42 participants, ~10 per treatment). Initially the sample was supposed to be larger, and therefore a regression analysis would ...
2
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1answer
48 views

Non-parametric, repeated measures two-sample test with small sample size

My data consists in two samples relative to the expression of a given gene, with 4 replications in both samples. I am interested in testing whether the two samples come from the same population, ...
4
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1answer
32 views

Comparison of groups with low N

Recently, I have seen a study that was comparing three groups of subjects. Each of these groups had N=3 participants. The author was claiming very strong conclusions from the mean-differences of ...
0
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1answer
38 views

Poisson goodness-of-fit of small sample

Please note that I have no background in statistics - this is for personal interest. The post is inspired by a question at work. We were given data by another department asserting that for a ...
0
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1answer
35 views

Pairwise non-parametric test for small sample sizes

I was asked to check a small dataset (3 replicates for 5 treatments, each) for significant outcome differences. I give an example: The variance within replicates in the data cannot be assumed ...
29
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3answers
3k views

What can we say about population mean from a sample size of 1?

I am wondering what we can say, if anything, about the population mean, $\mu$ when all I have is one measurement, $y_1$ (sample size of 1). Obviously, we'd love to have more measurements, but we ...
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0answers
14 views

What is the correct measure of significance to use on a small non-normal mixed data set?

I'm trying to run statistics on a small data set that does not have a normal distribution (possibly due to size of sample). I'm trying to work out if the sample group has any effect on the result ...
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0answers
17 views

Which test for paired data with small sample size?

I have four paired samples (subjects tested once, then again under different conditions), and am unsure which test to use to calculate significance with such a small sample size. It was suggested to ...
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0answers
7 views

Figure out geographical distribution of ecommerce buyers

I am a total noob at this kind of thing. Will appreciate detail and links to tools to hold my hand through this. (Or even a consulting service that can help.) Context: I need to figure out a flat ...
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1answer
27 views

Aggregate ts data with few observations

I am looking to predict the outcome of a business process (inherently complex). I have four years of data across 15 companies. I am trying to: (1) understand key drivers in this process (what ...
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1answer
98 views

Model selection and performance evaluation with different sample sizes

Suppose there are K experimental units. Each unit is associated with its own dataset consisting of 400 observations. For each unit, we set up a two-sample test, 200 vs 200. Because of a large sample ...
0
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0answers
17 views

Independence test for two small, exhaustive, categorical variables

I've got a categorical variable $var$ and a binary variable $critere$, from a pretty small (n = 300) but exhaustive dataset (i.e., the dataset contains the whole population that I want to study). I ...
3
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1answer
41 views

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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0answers
41 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-$e^{-\lambda_{1}}$)}\\ ...
2
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0answers
50 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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0answers
11 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 ...
3
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1answer
76 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 ...
1
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0answers
31 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 ...
0
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0answers
23 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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0answers
29 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 ...
2
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0answers
65 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 ...
2
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0answers
70 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 ...
0
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1answer
22 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). ...
3
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0answers
19 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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37 views
0
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0answers
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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0answers
26 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 ...
6
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0answers
102 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 ...
2
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0answers
28 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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165 views
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5answers
1k 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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0answers
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, ...
2
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1answer
103 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! ...
2
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0answers
25 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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0answers
48 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 ...
2
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1answer
54 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 ...
3
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1answer
78 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 ...
4
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2answers
40 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 ...
1
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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 ...
0
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0answers
63 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 ...
0
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0answers
39 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 ...
1
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1answer
313 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 ...
2
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1answer
54 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 ...
1
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1answer
60 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 ...
0
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0answers
26 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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21 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 ...