Questions tagged [small-sample]

Refers to statistical complications or problems due to having few data. If your question is about a small sample relative to the number of variables, please use the [underdetermined] tag instead.

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19 views

Assessing required $n$ for study: Observational unit and observations

Say we want to use a method that requires $n > 30$. (Whether this refers to number of observational units or total observations is sometimes vague.) We have observations on 10 patients for four ...
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17 views

Sample mean of a geometric distribution

Let $D$ be a distribution with finite mean $\mu$ and finite variance $\sigma^2$. Consider the distribution $S_n$ of the sample mean of $n$ i.i.d. values from $D$. I understand that the Central Limit ...
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29 views

Dealing with Problem of Small Sample Size with Monte Carlo in ARIMA

I am looking for a way one can use Monte-Carlo technology as a way out of small sample size. If I am restricted to a ...
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1answer
22 views

What statistical analysis to run for count data?

I have 10 storages, each has 10000 units. A technical problem has been found in 2 storages, that might leads to an increase in the number of defective units. Basically, I want to compare the number of ...
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1answer
27 views

Paired or not paired t-test in untreated/treated experimental setup

I am analysing the experiment, where the cells isolated from 4 different healthy donors were treated with a certain substance or left untreated (cells from each donor were divided into 2 parts: 1 part ...
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2answers
45 views

Is there a way to increase the number of predictor in a logistic regression when sample size is small?

One of the dependent variables in my dataset is a binomial variable indicating whether an invasive species has been eradicated (with $n_{1}$ = 23) or not (with $n_{0}$ = 75) after the use of a certain ...
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1answer
56 views

Is a beta-distribution GLM appropriate for a skewed bounded continuous dependent variable when sample size is small?

My data contain a bounded continuous variable (score between 0 and 10) representing the efficacy of a given method to control an invasive species. As there are more high scores than low ones, the ...
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1answer
26 views

How to properly split data for machine learning on small data sets

I'm doing a regression task using machine learning on some small data sets (less than 100) with numeric features. Before training the model, I would like to take 20% of the data as a holdout test set ...
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21 views

Regression analysis with small but complete dataset (fully representing reality)?

I have a repeated measures design with about 16 cases and 5-6 points of measuring. Sometimes, 1-4 full cases or some points of measure are missing. (The measures are 20 numerical and categorical data ...
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32 views

How to select and interpret Goodness of fit test for an epidemiological study with small sample size?

I have a study that found an association between exposure to antidepressants and the risk of preeclampsia. The number of women who were exposed and had an outcome (i.e. preeclampsia) was small: 10 ...
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18 views

Forecasting a short time series [duplicate]

I saw a similar type of question in this forum but let me tell you my data point is far less than the data mentioned in that my data points are very less compared to other posts. I have only 20 data ...
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2answers
68 views

Small sample size fails to approach inverse CDF

When sample size $n$ gets large, we know that a sorted set of the $n$ samples approaches the inverse cumulative distribution function (CDF) sampled at $\frac{1}{n}, \frac{2}{n}, \dots, \frac{n}{n}$. ...
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How to choose between Pooled and Satterthwaite methods in t test for 2 small samples with marginally different variances?

I compare means (or medians) of the numeric variable X for two groups composed of 6 and 18 subjects (using SAS). How do I choose between Pooled and Satterthwaite methods if the F-test for Equality of ...
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6 views

Bounding error of percentage estimation on binary data for small populations

Let's say you have a set $X$ with $N$ elements belonging to one of two categories. So, $x \in X$ can be of type A or B (these categories are mutually exclusive). The elements, however, are not ...
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22 views

test whether two samples are from the same high dimensional multinomial distribution

I have two high dimensional vectors (~150 dims), assumed to be sampled from multinomial distributions. How can I test whether the two are from the same multinomial distribution or different ones? (...
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1answer
70 views

Two sample test for exponential distribution with only two observations

Suppose we have two independent random variables $X_1 \sim \exp(\lambda_1)$ and $X_2 \sim \exp(\lambda_2)$ . Now, we are given just one observation each from the two distributions above, say $S_1$ and ...
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13 views

Comparison of property of 5 treatments with just 4 observations each

I have a small dataset with 4 observations per treatment. My plan was to do an ANOVA, so I checked the response variable for normal distribution with Shapiro-Wilk for each treatment and there was one ...
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20 views

What are the solutions for small sample in SEM?

is bootstrap a solution? I use Lisrel 8.8 (the student version) and bootstrap actually does not work in it. Bootstrap S has N/A values.
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11 views

About the Martinez-Iglewicz normality test in R package PoweR

I'm playing around with various normality tests and am currently trying to understand the Martinez-Iglewicz test. I am using its implementation in R with the PoweR package. Since it is supposed to be ...
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8 views

How can I calculate the significance of difference between means and what correlation method should I use?

I’ve collected data from 4 people as a piloting study. Two main parts of my experiment are Auditory and Visual tests. And in each part I have three blocks with 30 trials each. I have calculated the ...
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10 views

How does a smaller sample size affect False Acceptance Rate?

We have a theoretical document describing $x$ amount of audio samples pertaining to a speech recognization project. The document specifies certain ideal targets for FAR and FRR. Specifically: FAR ->...
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1answer
44 views

Ramifications of small + unbalanced group sizes, small number of groups for fixed & random effects models?

I have a variable (call it 'group') that I would like to treat as a random effect in a logistic regression. However, the number of groups is small (9 groups, larger than the recommended absolute ...
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1answer
72 views

Penalized or standard logistic regression?

I am trying to conduct multiple logistic regression. My independent variable has 22 events (yes) and 310(N0) (total sample 332). I am trying to include 20 independent variables (to minimize ...
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1answer
78 views

Hypothesis test for discrete random vector with few samples

Consider a random vector $X \in \mathbb{R}^{d}$ with support $\text{supp}(X) = \{1,2,3,4\}^d$, and let $P_X$ denote its known probability mass function. Note that $\lvert \text{supp}(X) \rvert = 4^d$. ...
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23 views

Small sized training set and results varying based on cross-validation split

I need to try to build a classifier based on around 30 instances. The outcome can also be that the dataset is not large enough for this purpose, however I'm not sure on how can I justify this outcome ...
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79 views

Machine Learning with few observations

Is common to say that Machine Learning techniques represent are purely data driven methods, and them are effective only if we have a large amount of data. I focused here on supervised/predictive ...
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19 views

Can we do a Spearman's corelation between a continuous and an categorical ordered variable (0,1,2,4)?

just a question that may be already answered here, is it possible to perform a Spearman's rank correlation ( to find a correlation) between a continuous variable and a categorical ( ordered) variable ...
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31 views

Do correlation estimates have increased error for small sample data?

When we calculate the correlation between two random variables, we seem confident that the estimated correlation is 100% accurate since I never heard of estimation error being a problem for ...
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32 views

In practice how well does asymptotic normality of the MLE hold?

There is a lot of theory about asymptotic normality of the MLE and many people use the result to generate confidence intervals given finite sample data. But a key question here is how large a sample ...
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15 views

Entropy of large sample $X$ and small sample $Y$ comparison

Distribution $X$ of a real continuous random variable is unimodal and slightly non-normal with $1,000$ observations. Distribution $Y$ has the same characteristics (not perfectly identical in moments ...
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1answer
35 views

Copula from small samples

Which copula estimation approach performs better when the empirical data to be modeled has a small sample size? Parametric copulas (Gaussian, t-, Gumbel, Clayton, etc), or Non-parametric (empirical) ...
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1answer
86 views

How well does GAN (generative adversarial network) perform for small samples?

GAN is an unsupervised learning algorithm that pits a discriminator and generator against one another so that they iteratively compete to enhance the overall model's ability to model/replicate a given ...
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1answer
27 views

Small paired samples comparison: which approach should I prefer?

I have the following small dataset, that consists of scores before and after a certain treatment for 15 individuals: ...
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1answer
55 views

Aggregate-level difference-in-difference analysis

Thank you in advance. I am new to difference-in-difference (DID) analysis. I want to conduct a research project examining an educational policy shock to local school districts. I have aggregated ...
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1answer
23 views

Correlated data series with single repeated value with a few outliers

I'm dealing with about 4,000 stationary time series, most of which I was able to reasonably fit to a distribution based on the KS test. About 200 of the time series, however, were not so well-behaved ...
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17 views

What's the distribution of maximum likelihood estimate on linear regression parameters with small sample size?

$y = k_1x_1 +k_2x_2 + \sigma\epsilon$ $\epsilon \sim D$, wehre $D$ is a known distribution e.g. $N(0,1)$. With $n\rightarrow \infty$, $\frac{1}{\sqrt{n}}((k_1,k_2,\sigma) - (\bar{k_1},\bar{k_2},\bar{\...
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2answers
107 views

Cross Validation in small datasets

I have a really small dataset (124 samples) and I'd like to try out if I get some interesting results with some machine learning algorithms in R. What I've done: I splitted my data set into 75% ...
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135 views

Is bootstrap problematic in small samples?

In "3 Things That Bother Me" (1988), Ed Leamer writes: Bootstrap estimates of standard errors are based on the assumption that the observed sample is the same as the true distribution, ...
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39 views

Sample size vs F1-score, which is more important (small sample size)

I work in a filed were there are many publications based on classifiers trained on small samples sizes (but large amount of features). In most cases the sample size can only be increased by a few ...
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27 views

Adjusting mean for very small population size

I have survey data from 8 respondents out of a population of 10 (very small I know). I know that FPC applies as we have more than 5% of the population in the sample. I can calculate the mean for a 0-...
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19 views

Unexpected behaviour of Anderson Darling test for normality for low sample size

I’m testing the power of the Anderson Darling test to detect deviations from standard normal distributions. I’m calibrating the AD test statistic numerically using python and I noticed an unexpected ...
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1answer
24 views

Using different multiple regression models that each change the available data

So I'm trying to analyse the difference in taxes paid between listed and unlisted companies. However, the sample consists of around 6000 unlisted and only 70 listed companies (there are only 210 in ...
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21 views

Calculate group with highest defective rate

I have data on several types of machines, each with a different rate of failure. I have samples of failures/non-failures for each machine type. The samples are small relative to the population range ...
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9 views

Insufficient n > p for forecasting with an RNN

What is the best approach to handle insufficient sample size when forecasting for multiple sequences simultaneously with an RNN? My training set has n=956 (time points) and p=262 (sequences). I'm ...
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25 views

correcting for small sample sizes

I have been toying with some data relating employment outcomes to choice of college major (which I got from a FiveThirtyEight Git repository). I have included a scatter plot where each point ...
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17 views

Logistic regression with small and differing sample sizes

I asked this question on Stack Overflow and was encouraged to come here for more help regarding methodological limitations. Previous question: I ran the model in SAS and I can't make sense of the ...
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13 views

Logistic GLM: Confidence Interval of response for small sample

I'm trying to find a confidence interval for P (the response) in a logistic regression, for some $X$ values ( $logit(p) = X\beta$ ). Previously I have used the delta method, either in the logit scale ...
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12 views

How much can I get from only one datapoint? [duplicate]

I will be soon ending my bachelors degree and choosing masters major. In my interest is newly opened major and I managed to get information about last years recruitment process, namely how many people ...
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1answer
49 views

Can PCA be used when n = p, where n = 50?

I have a sample size of 50 items with 50 variables (continuous level), and want to minimise the dimension of my data in order to extract the "character" of each item through a small amount ...
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48 views

Linear regression with small N [duplicate]

I was wondering if it makes sense to run a linear regression when my dependent variable only has 20 observations in total (I do have it for 6 years). This is the scenario: 20 observations consists ...

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