# 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.

444 questions
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### validating model on small binary dataset with balanced outcome

I have a model which is built on a dataset (N=288), and I want to validate it on another extremely small dataset (N=13) and it is only partly similar to the first one. As they really aren't similar I ...
1answer
22 views

### Comparing percentages with unequal sample sizes

I've spent some time collecting participation data on a schools competition. To sum it up: Roughly speaking 1000 schools take part in the initiative every year. Only 10 schools become finalists. ...
0answers
14 views

### Analysing contingency table with small samples

My question is about how to analyse very small samples on contingency tables. I have a contingency table with observation for 2 groups (first variable) answering questions with multiple choices (...
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96 views

### Leave-one-out cross validation in regression: R squared cannot be used - how else may model performance on unseen data be evaluated?

I have a regression problem with very few datapoints, therefore I want to use leave-one-out cross validation (effectively N-fold cross validation with N being the number of datapoints) to determine ...
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### What is the best hypothesis test method for a small sample size?

i am somewhat confused on how to proceed with the hypothesis testing, i have 1 sample with a total of 31 inputs divided into 2 groups of different conditions, 1 sample has 16 inputs, the other has 15. ...
1answer
42 views

### Calculating required sample size for estimate lower bound on 95% of the population

I'm interested into sampling from a population, with a long time to get a sample (O(1), usually 1/2 mins), with lots of candidate populations to sample from (running a metaheuristic optimization). I ...
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14 views

### What statistical property is absent in 2-sample hypothesis tests of 5 measurements?

Suppose we observe a random sample of five measurements: 10, 13, 15, 15, 17, from a normal distribution with unknown mean $\mu_1$ and unknown variance $\sigma_1^2$. A second random sample from another ...
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### Is a single count data point significantly different from a set of reference count data

I have counted the number of occurrences of protein domains in the proteomes of 16 different insect species, 1 focal vs 15 reference species. For each of the ~4700 protein domains in my data, I have a ...
1answer
32 views

### Linear Forecasting with a small dataset

I am trying to get some forecast (5 years more) from a small dataset that is as follows: ...
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### Small N Small T Panel Data - options?

I have Panel data for 21 counties over 11 years. Most literature seems based on either small T and large N or small N and large T. I tried applying a fixed effects model (one-way, individual) to the ...
1answer
70 views

### Is a cross-validation list needed when there are no hyperparameters

Original problem formulation - 12/04/2019: I have a data set of 14 observations with six features each and an output variable of two classes. I applied a logistic regression model with the following ...
2answers
47 views

### 10% rule for sample sizes

In an introductory stats book by Nicole Radziwell "Statistics the easy way with R" , an assumption used for nearly every statistical test (e.g.t-tets, anova, etc) is that the sample size should not ...
2answers
129 views

### What “nice” property of a confidence set is being violated

Suppose that I have $X_{i} \overset{i.i.d.}{\sim} P$ with $E[X_{i}]=\mu$ and $V[X_{i}^{2}] = \sigma^{2}<\infty$. Then by the central limit theorem I know that: \begin{align} \sqrt{n} (\bar{X}_{n} ...
1answer
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### Sample size for rare diseases

Disease X has an prevalence of approximately 1% of a very large population. I need to calculate the sample size for a 2-arm RCT for the patients with X. power: 80%, significance level=0.05, expected ...
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### Minimum Sample Size with the Panel Data; Firms and Obeservations

I'm working on the panel analysis with the data of 20 firms in two nations (10 for each nation). It is an annual data which covers the time period from 1980 to 2015. As it is my first time to deal ...
1answer
21 views

### Validity Small Sample Size

A fellow working student of mine is doing her bachelor's thesis right now. She's looking into the effect that a brands presence in ski resorts has on customer perception of that brand. Since she is ...
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### What are recommended practices to avoid overestimation of size/dispersion from small samples of negative-binomially distributed data?

I want to estimate mu and size/dispersion accurately for a large number of small samples (n = 6-8 is typical). When I try to do maximum-likelihood inference (or related, Bayesian inference with ...
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### Minimum Sample Size for M&A Event Study

as statistics beginner I was hoping you could help me with regards to the following problem: I wanna conduct an event study (analysing abnormal returns of share prices) to derive performance effects ...
1answer
66 views

### Significance Tests - Why Would a Low Sample Size Cause Problems?

Okay, on my AP Statistics test on the chapter on significance tests, the following free response question appeared: When the manufacturing process is working properly, NeverREady batteries have ...
2answers
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### Sample size question (small vs large)

I have a question about sample sizes. I have a data set in which I have following conditions: 1) Day 1: Total=3500, Fail=200;Fail%=6 2) Day 2: Total=6700, Fail=340, Fail%=5 3) Day 3: Total=1100, ...
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23 views

### What are the values of a student's distribution (k, µ and σ) when x1 = 10, x2 = 10 and x3 = 10? [duplicate]

I have a sample that contains only 3 values that are x1 = 10 x2 = 10 x3 = 13 Remark: I know that x3 value is not what is written in title I will calculate the ...
0answers
28 views

### Characterization of risk factors for a very rare condition

I am looking at a cohort of patients including 13000 patients, out of which only 160 have condition A. Out of these patients, only 6 have condition B. I would like to be able to characterize those ...
2answers
69 views

### Can one make statistical inferences from 6 patients?

Is it conceptually correct to make statistical inferences from a very small number of patients (even when using exact methods like Fisher's test, etc)? What do I have to look out for: power or p-value?...
0answers
12 views

### Retrospective risk factor analysis in small samples

I am looking for risk factors for an specific outcome (death at a certain time) in a retrospective cohort of a disease. I have 40 observations and lots of variables (30+), mostly cathegorical. Have ...
0answers
26 views

### dummy variables and interaction terms: when the number of observations matters

Some authors conducted a univariate cross-section regression using 26 observations: $$Y_i = a + b \cdot X_i + e_i$$ Some others did the same regression and added another one where $X$ is split ...
1answer
47 views

### How to approach a classification problem when the sample size is only about 50

I was given a data consists of 53 people and I was asked to come up with a general classification rule based on biomarkers that can be used to classify each person under one of the three possible ...
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7 views

### How to account for low sample size when computing performance?

I am interested in analyzing user performance at a per user level. Users have the opportunity to engage with an app by answering trivia questions and can choose how many questions they want to answer. ...
0answers
20 views

### Sample size calculation for parametric test, with large effect expected, small numbers. Should I use parametric or non parametric tests?

I am trying to figure out what would be the best way to analyze data from a randomized double blind trial we conducted. We sought to find if two dosages of a drug were effective for a severe symptom ...
2answers
69 views

### Inference based on a single observation

Imagine we use machine A to perform a task, we repeat it 1000 times and it always takes more then 30 min to finish the task. We buy a new machine (machine B) and in the first run it takes 29 min to ...
1answer
31 views

### How do I determine the likelihood of a single measurement coming from a known distribution? [duplicate]

I have a set of 2000 numbers that form an approximately normal distribution, with a mean of about 0.24, and an SD of 0.06. These form an estimate of the population. I now have a single sample ...
1answer
38 views

### Index accuracy based on sample size out of population size

Suppose I have people who work at different companies and I am interested in seeing their view on some topic. In order to do this, I decide to conduct interviews on people from each of the different ...
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52 views

### Assess statistical significance with before & after binomial data from few participants

For the quantitative analysis of a pedagogical approach, I applied a series of (equivalent) tests prior and after lessons. I want to evaluate the reading (proper identification of sounds from written ...
2answers
63 views

### How can I analyze small sample?

I want to use multivariate OLS on a sample size of 33, but I read somewhere that the rule of thumb is that there should be at least 30 observations to fit one covariate. I want to add around 5 ...
2answers
185 views

### MANOVA with variables from different datasets

I conducted several experiments where I have one underlying independent variable (tree species, IV). Each of these experiments gave me one dependent variable (DV), like bark pH, rugosity or the water-...
1answer
36 views

### 95% limits of a normally distributed parameter

How do I find the 95% limits of the population distribution of a normally distributed parameter? I've taken the mean and SD from 10 different readings of the parameter. Will the 95% limits be mean +/-...
0answers
22 views

### Alternative test to paired t-test? [duplicate]

I need to compare data from paired groups, but my distributions are non-normal, and my sample size is small. Are there any tests I could apply? I've been looking into non-parametric alternatives like ...
0answers
41 views

### Estimate unknown sum of iid random variables

Let $X_1, X_2, \dots$ be a sequence of independent and identically distributed discrete random variables with common mass function $f_X(x)$ defined for when $x \in \{0,1,\dots,N\}$ and $N$ is known. ...
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25 views

### Sample Size Adjusted Metric for Calibration Curve

I'm creating a model that provides a predicted probability of an event happening. I am using calibration curves that plot predicted probability (x-axis) versus the actual event frequency (y-axis). I ...
1answer
36 views

### What if you don't reach the optimal sample size?

I have used a binomial sample calculation to conclude that we need a sample size of 150, which for a response rate of 80% there is 80% power that the confidence limits between 71% and 89% cover our ...
1answer
105 views

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### What is the minimum number of observations required for percentile calculation?

Here it is stated, but not justified, that percentile calculation requires at least three observations. However, in this book the authors say that it depends on the percentile value (e.g., for the ...
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14 views

### Method of calculating an average from statistically insignificant sample

I am collecting weather data from a region that has a 10 weather stations placed around it. The stations collect data such as temperature highs and lows, amount of precipitation, etc. Some of these ...
1answer
107 views

### Build a statistical model based on small sample size

I hope my question is not too wide and that this is the right place to ask it. I'm working in the field of spectroscopy and chemometrics. I'm building a statistical model to predict pollution levels ...
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77 views

### algorithms for high dimensional data in a small sample size

I am trying to analysis high-dimensional data in a small sample size and I meet a problem: First,I divided all samples into two sets: training set and test set. Second, in the training set The Y is ...
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24 views

### Conducting a Pilot Study without Large Sample

I want to obtain preliminary evidence that some experimental manipulations I would like to use in research have a good chance of being successful (i.e., successfully manipulating the intended ...
0answers
17 views

### Weak Sample Size & Low Statistical Power

I have a problem of sample size for my research paper approval. I could only ran the statistics on 5 subjects for both plantar pressure and temperature measurements but the statistical power seems to ...
0answers
131 views

### Model Validation Firth Logistic Regression r

I am modeling Neilsen Ratings based on an AnAttr using Firth Logistic Regression using R using the logistf Library. Typically I use Pearson's Hosmer and Lemeshow in SAS to test model fit. I am ...
1answer
26 views

### checking the equality of variances when we have very small data sets

I have two groups with very small sample sizes. Each group has around 6 observations. I was wondering which test I can use in order to check the quality of variances? Is there any cutoff value in ...