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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21 views

What is a good location equivalence test for comparison of small and large samples?

I have two one-dimensional samples, one is small (like 2 values) and another of a larger size (several dozens). I want to estimate the probability that the two samples are drawn from different ...
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13 views

How to analyze small dataset? [closed]

I have a small dataset with continues variables , dependent variable is normally distributed and linearly associated with the independent variable. I tried doing linear regression but the model doesn'...
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19 views

How to analyze country specific data with 40 data points?

I have country specific aggregated data with 40 data points. My independent variable is the availability of health care facilities and dependent variable is infant mortality rate. I tried using linear ...
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19 views

Non-asymptotic estimation error bound of quantile regression

If we have $w_j$ observations $y_i^j$ at points $\vec{x}_j$, $j=1,\cdots,N$, we can conduct quantile regression to get $$ y = \vec{k} \cdot \vec{x} $$ and use $$\vec{k} \cdot \vec{x}_0$$ to predict ...
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29 views

Chi Square Test on small sample size

I have the following dataset and I am trying to run a Chi-square test between the control and pilot. The only issue is that, for a Chi-Square test to return proper results, the sample size need to be ...
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5 views

How can get rid of the small sample-adjustment in ivreg in R

I am currently attempting to replicate the results of a Stata Code. The original code uses the stata command: ...
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6 views

Independent samples t test for following up missing data - inadequate sample size

I'm running a missing data analysis in SPSS on a data set that examines correlations between an IV and five DVs (all continuous variables). Seven of the participants were inadequately sampled, so I'm ...
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1answer
16 views

Significant difference/ANOVA test when some values occure only once

I have fake dataframe with neighbrhood codes and prices of houses in those neighbrhoods, with this amount of values for each negihborhood: ...
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1answer
61 views

How to construct a confidence interval of the mean, when the distribution is unknown and the sample is small?

I'm looking for the preferred approach to construct a finite sized confidence interval for the population mean, assuming: The distribution of the population is unknown The sample size is low The ...
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1answer
25 views

Multiple roots of the likelihood equations vs. consistency

I'm trying to understand the implications of the Huzurbazar-Chanda theorem in finite samples. The result basically says that of all roots of the likelihood equations, one and only one tends in ...
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18 views

Inclusion of missing data with adapted Winsorizing approach for small sample?

We have a dataset of patients with a rare condition (n=~10 for each of 2 groups). The participants completed a battery of standardized tests that use a mean of 100 and a standard deviation of 15. In ...
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1answer
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Flow cytometry on a couple of samples yields millions of cells so p numbers are tiny (even when sampling few individuals) - is this valid?

I recently did flow cytometry to quantify cell numbers on 4 similar samples from one group and 4 from another different group (n=4). The samples each contained millions of cells and I wanted to ...
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11 views

Statistical test for assessing trends (one-sample)

I'm interested in looking at annual trends. The numbers represent the total number of a particular animal species that have been counted in that year. We see a decreasing trend, and I would like to ...
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Binomial Data, uneven sample sizes, how do analyze this data?

I work with nonhuman primates, and have had them (4 total) perform a series of 3 tasks. Each of the three tasks are 2 choice categorization tasks. So the data is correct/incorrect for each trial. ...
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34 views

Can I use inferential statistics in a non-probabilistic sample?

Can I use inferential statistics (eg, binomial test, One-Sample Chi-Square Test etc) in a non-probabilistic sample (convenience sample)? The sample size (n) = 45. Is there any reference to support the ...
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1answer
30 views

Can we say there is High Bias if we have high training error due to small training data size?

If for a very small dataset we have a high training error, can we say that we are underfitting or have a high bias because of the low amount of training data? Or do we use these terms (underfitting  ...
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1answer
49 views

Can these two situations be efficiently distinguished? [closed]

We have N+1 dice, one two-sided and N 6-sided ones. The marginal probability density functions are such that each die is fair, i.e. each face shows up with probability $1/6$. We want to distinguish ...
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Small sample OLS regression: how to conduct inference?

Consider a linear data generating process (DGP) $$ y=X\beta+\varepsilon, \quad \varepsilon\sim i.i.D(0,\sigma^2) $$ with some unknown distribution $D$ with zero mean and finite variance $\sigma^2$ (...
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60 views

How to compare groups when some participants could not complete the tasks?

Main question: What analysis could best capture group comparison when a portion of participants could not complete selected tasks due to insufficient skills? Details: The dataset has two groups and ...
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11 views

How to analyze treatment efficacy for small dataset

I have baseline and post-treatment questionnaire data on behavioural treatment and control groups. Each group has less than 10 participants. I have missing data both on baseline and posttreatment ...
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2answers
37 views

Error in the fraction estimated from a finite sample?

This seems like a basic statistics question, but I (a non-statistician) have been unable to find a definitive answer in online searches, possibly because I'm not using the right search terms. Given a ...
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8 views

Sentiment on Social Media Data - what to do with only 600 training examples

I'm working on a sentiment analysis-adjacent problem. I'm trying to map a huge amount of features (in the thousands) to a 100 feature output. However, due to the data limitations, I only have 600 ...
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1answer
18 views

Significane versus null hypothesis for small number of data

I have a model that correctly identifies something seven times out of the finite number of 8 data points as true. I was wondering how can I calculate a significance statistics given the very low ...
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1answer
13 views

Can I test interrater reliability between 2 groups of unequal sample size

Two groups (expert and semi-expert) rate items in an online survey using a 4 point Likert scale. Members of each group are asked to rate (i) the importance of problems and (ii) how useful each ...
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25 views

Comparison of Coefficients of Variation (CVs)

I have to compare the variability of measures between 2 groups (geographical regions). Each group consists of a limited number of elements (i.e., the number of districts of each region); hence, a ...
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1answer
46 views

Probability on different time scales

I just finished reading "Fooled by Randomness" by Nassim Taleb. He, inter alia, gives the following example to prove one of his points: A 15% return with 10% volatility per annum translates ...
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1answer
23 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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22 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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33 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
28 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
70 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
51 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
66 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
32 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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22 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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34 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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19 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
72 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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155 views

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
125 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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0answers
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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21 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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14 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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11 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
65 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
75 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
104 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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