People make conclusions off of tinier sample sizes. There are plenty of scientific studies with just 50 or 100 people, but you need to keep the small numbers in mind.
As long as sampling was done correctly, then small sample size won't matter much !!
Most studies are worthless due to small sample sizes and confounding variables, and most “conclusions” are based on cherry-picked outliers. The fact that it’s common to do this doesn’t make it responsible or correct.
There's 15 documented adverse events, but we don't really know how many adverse events there were in total. If we simply study those 15 adverse events, then your population study is only those 15 events (with a hell-of-a-lot of selection bias).
----------
But I'm mostly thinking about how one person I know thinks: "Did you hear about these 15 cases and even one of them died! Clearly J&J is unsafe to take!!!!"
For that kind of conclusion, its like they've focused their mind entirely on 15 cases, as if their "population of study" was 15. Its obviously bad logic, but maybe I wasn't very clear in my original post that I was referencing some bad logic there.
---------
But there's plenty of 50-person or 200-person studies that ARE properly done, and the science is solid. Especially when we're looking at say Phase 1 / Phase 2 style trials of safety and/or efficacy (the earlier stage trials before a Phase 3 trial is conducted).
Its not a big enough sample to be "certain" of the results, but its a big enough sample to "provide evidence", possibly in conjuction with other studies.
----------
In many cases: having 5 or 6 studies with 50-random people each and performing a meta-study across them (especially if all 5 of those studies were of high quality sampling) would lead to a more robust conclusion than just one 1000-person study done slightly incorrectly (ex: the 1000-person "study" is a voluntary telephone survey or some other low-quality study)
This study referenced up above had the ~285 or whatever people who answered the survey, not that much info. ~285/350 is not that much data.
Anecdotally and based on my own experience I'd agree that the burnout is high, probably over 50%.
That is the value of a study of this size. The ability to quickly determine if there is any "there" there. The headline is sensationalistic but such is the nature of publish or perish science today.
Not even close to accurate.
If the election count is say, 48% for A and 50% for B and 2% other, that's that. You don't have error bars, you don't have student-t tests, you don't have random varaibles, you don't have "confidence intervals". You assume you have the ground truth. You have a precise number assumed to be without error.
Its actually a fundamentally different kind of math than what is typically taught in statistic classes (standard error vs standard deviation. R-values, random variables, etc. etc.)
When it comes to "total population" style information gathering, the questions of reliability are about whether-or-not you in fact, grabbed the total population... and nothing really "mathematical" (such as what are my 95% confidence interval?)
---------
When people say 600,000 died of COVID19 in the USA, there's no error bar, standard deviation, or random variable on that number. It is what it is: the ground truth according to a particular source.
And when you have a 2nd source of information with slightly different numbers (ex: State databases vs US level databases), you have a non-mathematical problem for how to resolve the apparent contradiction.
There's no "metastudy" over other surveys. There's no "resample again", there's no reproducibility. These statistical concepts and tests simply do not apply. If you do in fact decide to conduct a 2nd census, you will find that the numbers will differ in practice (ex: recounting the same set of ballots a 2nd time). But there's no underlying mathematical model for why this happens, as is the case in typical population statistics (student t-test assumes a standard error over a standard deviation of a hypothetical sample, etc. etc.)
In the case of J&J blood clots, there's billions of additional people who could take the J&J vaccine. 15/21 million people who took he J&J vaccine got blood clots. But if you want to know what percentage of "people who take the J&J vaccine get blood clots" that's not the same thing. The population includes an infinite number of people.
The converse also needs to be held in mind as well. Very large studies are more likely to display statistically significant findings. Your p-value is really just a test of your sample size, so as the study grows your p-value tends to shrink. Get a large enough sample and you'll almost always find statistical significance. Just referencing a p-value isn't enough, it needs to be read in the context of the study size (whether large or small).
Edit: For those downvoting, here is a much better and eloquent explanation:
https://twitter.com/daniela_witten/status/131218095960997478...
> If you’re testing whether mean=0 and actually the truth is that mean=0.000000001, and if you have a large enough sample size, then YOU WILL GET A TINY P-VALUE.
Think about this for a second. Does it make sense that the results of my statistical test would change if I measured in terragrams vs. micrograms? No, it doesn't, because it's not the numerical difference between null hypothesis and sample mean, it's the difference relative to standard deviation.
If the effect size is 0.000000001 and the standard deviation is 0.0000000000000001 then this is an enormous, important effect. If the standard deviation is 0.1, then this is a really small and unimportant effect. It can still be observed correctly with a sufficient sample size though because you've stated it's a real effect to begin with.
You will absolutely not get a tiny p value just because your sample size is large. That is wrong. You will be able to detect very small effects, but if there is no difference, you are more likely to draw the correct conclusion with 1,000,000 samples than with 100 samples.
The point the author here is trying to convey but is not getting clearly, is that a large sample size can detect an effect that is practically useless and call it significant. p-values tell you if it seems probable, given your data, if there is a difference between the two datasets. They make no claims about whether the difference is material.
Example python code to do prove p values are not likelier to be smaller just due to large sample sizes, given no actual difference:
import random
from scipy.stats import ttest_ind
num_tests = 10000
res = []
for test in range(num_tests):
n = 100
a = [random.random() for _ in range(n)]
b = [random.random() for _ in range(n)]
res = res + [ttest_ind(a,b)[1] <= 0.05]
print(f"10,000 tests with n=200 {sum(res)/ num_tests}")
num_tests = 1000
res = []
for test in range(num_tests):
n = 100000
a = [random.random() for _ in range(n)]
b = [random.random() for _ in range(n)]
res = res + [ttest_ind(a,b)[1] <= 0.05]
print(f"10,000 tests with n=20,000 {sum(res)/ num_tests}")>You will be able to detect very small effects, but if there is no difference, you are more likely to draw the correct conclusion with 1,000,000 samples than with 100 samples.
I believe that this is to the tweet author's point where they stated that in the real-world a null hypothesis never exactly holds true. So you can detect even the tiniest of variance with a large enough sample.
>given no actual difference
I think the error here is that there is a priori knowledge of no difference, where the author is stating that in real-life scenarios there will always be some differences even if being too minute to be of practical significance. We can fabricate "no difference" in simulations but in real experimental design there will almost always be variance, even if it's just an artifact of the measurement process rather than being causal from the independent variable(s). Whether or not the differences statistically significant depends on the experiment design, to include sample size.
So while I understand your valid point I think the author's claim was more about the practical application of statistics rather than the mathematical precision as it relates with simulated examples. But I could be misinterpreting.
Of far greater problem is False Discovery Rate related things. Where you test 20 different things at once, and by chance identify one of them as significant even though the true effect size is 0. This is another area where increasing your sample size can help avoid problems, but even still you need to acknowledge your tools are imperfect.
I'm assuming you mean within the confines of the experiment, correct? I agree. The tweet author was eluding to the fact that "IRL" the null hypothesis is almost never true at the population level. Meaning if you grab a large enough sample you will detect very, very small differences. (This was her Lucky Charms ~ blood type example in the tweet). I also agree with that. I don't think the two claims are mutually exclusive and the fact they can coexist is (I believe) precisely her point about sample size.
Lucky Charms does probably relate to blood type in some impossibly small way. It makes sense that a biological trait has some relation to dietary consumption. I don't think any sort of non-garbage tier journal with peer review would publish it, but good on p-values for helping us detect them though. Not bad on sample size for making it possible to discern this effect size with a high degree of confidence.
It's worth noting that we also have many other tools to help us. For example you can test, given an expected effect size and a sample size, what the probability is of getting a statistically significant result, or a non-significant result, or a significant result that erroneously goes in the wrong direction. Or what the range of likely true mean effect size is given a significant sample difference.
We want large samples. They enhance confidence in findings. The author's premise seems to be it's better not to know that small rocks exist if we're only looking for big rocks. But fails to mention that the tools to find small rocks also help us identify big rocks with more clarity.