Linked Questions

85
votes
10answers
324k views

Is there a minimum sample size required for the t-test to be valid?

I'm currently working on a quasi-experimental research paper. I only have a sample size of 15 due to low population within the chosen area and that only 15 fit my criteria. Is 15 the minimum sample ...
46
votes
5answers
8k 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 can'...
22
votes
4answers
2k views

What to say to a client that thinks confidence intervals are too wide to be useful?

Suppose I am a consultant and I want to explain to my client the usefulness of confidence interval. The client says to me that my intervals are too wide to be useful and he would prefer to use ones ...
5
votes
3answers
6k views

Can you do statistics with 4 data points?

I was just involved in a Q/A were a poor guy was requested to run a statistical test to prove that algorithm A is better than two other algorithms. However, he has only 4 data points. Does it really ...
13
votes
2answers
8k views

When data has a gaussian distribution, how many samples will characterise it?

Gaussian data distributed in a single dimension requires two parameters to characterise it (mean, variance), and rumour has it that around 30 randomly-selected samples is usually sufficient to ...
3
votes
4answers
4k views

Is it ever appropriate to fit a regression on 3 points?

Lets assume we only have 2 variables, x and y, and our model (in R code) is lm(y~x). Given ...
6
votes
3answers
819 views

Which statistical test to use when there's no data of SD but just know the mean?

In our lab, we work with the retina which yields very little sample. Although we have a reasonable sample size of six animals in each group, I don't understand which test to be used to test for ...
1
vote
1answer
8k views

t-test using a sample less than 30 [duplicate]

When I do the two tailed t-test using a sample less than 30, can I use this result? This is because I do also still see the t-test table which has degrees of freedom far less than 30. How further ...
1
vote
0answers
6k views

Minimum sample size for t-test [duplicate]

Can you do a t-test or ANOVA between 2 or 3 groups respectively if one of those groups has a sample size of 2? Are the results interpretable in the same way as with larger sample sizes(n=4,5,6?). If ...
2
votes
1answer
1k views

sample size to get 99.6% confidence on a one-tailed test

If I have a normally distributed population of 3.5 million elements, and I want to sample enough of them to make a statement with 99.6% confidence on a 1-tailed test, what should my sample size be? ...
1
vote
1answer
1k views

Testing statistical significance in two conditions

I am measuring two unpaired variables $x$ and $y$ in two different conditions ($x$ and $y$ are magnitudes of some special magnetic signals). In the first condition, my hypothesis is that $\bar{x} > ...
9
votes
2answers
352 views

Dynamic calculation of number of samples required to estimate the mean

I am trying to estimate the mean of a more-or-less Gaussian distribution via sampling. I have no prior knowledge about its mean or its variance. Each sample is expensive to obtain. How do I ...
2
votes
1answer
324 views

How to compare means among groups with a single value?

My aim is to compare means among different groups, but I only have one single value (mean) for each group. I also have the total number of individuals per group. I don't have data for all individuals ...
2
votes
2answers
290 views

$p$-value when standard deviation is zero

What test can be used to indicate a $p$-value when both sets of data in a comparison have standard deviation of 0? For example, Set 1 has values of 1, 1, 1 and Set 2 has values of 5, 5, 5. Or is it ...
3
votes
0answers
588 views

What are the characteristics for a problem to be statistical?

Today, I read a post Computing and Sustainability: What Can Be Done?. And I found that the author of this post can easily find statistical problems in other fields, such as computer science. Since as ...
5
votes
1answer
74 views

Can t test be used for comparing groups with a sample size of 3?

I'm wondering if t test maybe used for a really small sample size. I have a set of data with only 3 entries for each group and I need to compare whether the two groups are significantly different.
3
votes
1answer
87 views

How to analyze if only N and means are available?

I have data on following experiment: Sample taken from each of 5 normals and 5 patients All normal samples are pooled and mixed together. Similarly all patient samples are also mixed ...
8
votes
0answers
135 views

Statistical test for one paired observation [duplicate]

In this question, @whuber writes in his reply that If you were willing to assume something about that common distribution (such as it is some Normal distribution--but without knowing or assuming ...
0
votes
1answer
80 views

Posterior predictive of Gaussian

Given is a Gaussian $\mathcal{N}(\mu,\sigma^2)$ with unknown $\mu$ and known $\sigma^2$. There is only one data point $x$. What is the parameter for the mean of the posterior distribution, i.e. what ...
3
votes
1answer
87 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 ...
0
votes
0answers
102 views

correct way to calculate sample size in behavioral experiment

This question was asked many times before, but the typical answer is usually 'do a power sample calculations'. The problem that I can't grasp is that in most well-known papers the samples that they ...
1
vote
0answers
70 views

What are examples where only a single sample is needed?

Consider the following setup: Let $\Omega$ be a finite (but humongous) state space and $\pi:\Omega\to[0,1]$ be a probability mass function. It seems to me that when people want to "sample" in this ...
1
vote
0answers
39 views

How should I calculate sample size when Cohen's $d$ effect size is $> 5.6$?

I am working in R. I am doing some simulations of sample sizes by drawing random samples from two normal distributions. I am calculating Cohen's $d$ effect size with: ...
0
votes
0answers
17 views

Significance for low sample sizes

The question is - formally speaking, what should the minimum sample size be in order to trust statistical metrics like p-value and power? Let's say we have population A and B each having values ...