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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23 views

Why does the prediction of a VAR dgp diverge from the test set?

I'm working on a multivariate data set consisting in 44 observations (which have to be splitted: the first 34 observations are in the training set, the remaining ones in the testing set) of 9 ...
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41 views

Appropriate forecasting methods for only 20 observations [duplicate]

I am trying to forecast the regional GDP growth of our region in the next five years, I only have 20 observations in my data which is yearly, what forecasting model is appropriate? I tried ARIMA in r ...
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What is reasonable to do with small -tiny- datasets?. Dealing with rare diseases

I come up from posts like What to do with a small (27) medical dataset? because they are fairly similar. But in a broader context, in rare diseases/studies with a really low sample size -but plenty of ...
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43 views

Number of knots in smoothing splines, residual plots and sample size?

I'm working with a dataset of 56 samples, so I am trying to keep the complexity of the regression model down. However, I have rather complex non linear relationships between some of the predictors and ...
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Minimum number of samples required for an approximately right machine learning algorithm?

I was asked this question in an interview based on the fact that Machine Learning was mentioned in my resume. And this is the question that I was given, Lets say you want to make a prediction with ...
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request reference on the superiority of Gaussian processes in small-data regime

It seems to be widely accepted that Gaussian processes are superior to neural networks in the small data regime. Are there any references (whether books or papers) that make such claims and justify ...
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14 views

Why can't I just compare percentages at face value (with different sample sizes)

I'm having the largest brain fart and I feel like this is actually simple so please give me your thoughts if you have any! I've got these 6 types of claims, that can either be approved or denied. My ...
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1answer
64 views

Survival analysis with only a few time points

I'm investigating the survival of patients with a certain disease, and whether or not they progress to a more severe form of this disease based on several covariates (see EDIT). Currently, I'm ...
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1answer
24 views

Rationale for small sample leads to larger effect sizes

I was recently attending a seminar where the speaker mentioned something on the lines of: Here's a statistical fallacy...smaller sample sizes will lead to larger effect sizes However, the speaker ...
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Confidence interval for mean of a SMALL sample from a Poisson distribution [duplicate]

Let $\lambda > 0$ be a rate parameter and let $P(x; \lambda)$ be the Poisson distribution with rate $\lambda$. Also, let $X_1, ..., X_n$ be a small sample taken from $P(x; \lambda)$. Let $\mu$ be ...
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27 views

Is there any option for small size sample of PCA

I have 73 sample size and 18 variables. Could I have to any way to perform PCA analysis for those data?
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51 views

Best models to use for inference on very small dataset n = 24

I am working on a very small dataset that contains 2 years' worth of monthly data. With a lot of independent variables (approx 50). All of the data are continuous numeric data including the dependent ...
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2answers
22 views

Principal component analysis: low adequacy

I am trying to do a Principal Component Analysis to reduce my data from a test battery. I have a small sample N=58 (It is a selected kind of dog population and due to the Pandemics I am unable to ...
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Every time I run a statistical test, my n-value is doubled

I just finished collecting data for a small study with a within-subject design looking at caching behaviour and how it can be affected by a bird's surroundings. My study had three experimental ...
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Central Limit Theorem: Is the likelihood of obtaining some sample mean exact when n is not infinity?

The central limit theorem states: $$ \lim _{n\to \infty}{\sqrt{n}}{\left({\frac {{\bar {X}}_{n}-\mu }{\sigma }}\right)} \sim \mathcal{N}(0,1) $$ Which means if I ran an infinite number of experiments, ...
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Does machine learning really need data-efficient algorithms?

Deep learning methods are often said to be very data-inefficient, requiring 100-1000 examples per class, where a human needs 1-2 to reach comparable classification accuracy. However, modern datasets ...
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Smaller sample sizes: cut-off for reporting numbers instead of percentages

I have a sample size of 50 and need to report survival at different time points. Is there good practice when I should report percentages instead of numbers? E.g. 25/50 died or 50% died. Googling didn'...
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52 views

Testing for equal proportions when sample sizes are very small

Suppose I observe binary data for two samples (hopefully the notation below is obvious) and I wish to test the hypotheses: $$H_0: p_1 = p_2$$ $$H_A: p_1 \neq p_2$$ I know there is a $z$-test for doing ...
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11 views

How to report F = 0

Can anybody tell me, please, if I need to report in my paper if F = 0 in two-way ANOVA? My samples are quite small: 6 participants in one group and 5 in another. There is also a possibility their ...
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1answer
138 views

Multiple imputation for non-parametric tests on small sample?

I am new to multiple imputation, so apologies if the question is naive. I have been exploring multiple imputation for use on a small data set where there are just a couple of data points. I would like ...
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1answer
84 views

Machine learning in really small dataset

The group that I work with sent me 10 samples, 5 controls and 5 treatment. They asked me to try to use machine learning in this dataset, to see if it could separate the two groups. I believe that this ...
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1answer
43 views

Paradoxical result when computing a confidence interval when population standard deviation is not known

I have been trying to construct a $1-\alpha$ confidence interval for the mean. The distribution from which a sample is drawn is exponential distribution with density: $$p(x) = \frac{1}{\beta}e^{-x/\...
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20 views

Which tests for which $n$ (classification)

in the feedback model I use, I have 3 types of feedback that can be naturally given to a student during a lab. The type of feedback (should) influence the cognitive load (CL) of the student. The CL is ...
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23 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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20 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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2answers
65 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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8 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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14 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
136 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
29 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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20 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
28 views

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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15 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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36 views

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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2answers
78 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
38 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
52 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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38 views

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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61 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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15 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
39 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
19 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
32 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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45 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
82 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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31 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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39 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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