BMJ Surgery Authors guidelines include a sentence saying that if the sample size is less than 30 then report with the numbers, not percentage. What is the reason behind this?
If the sample size is less than 30, the confidence should be less than 5%.
So yes it is necessary.
It is always advisable to report sample size as well as confidence interval. It is because sample size show the degree of freedom to generalize findings, In small sample it is always possible that a high confidence level may result in the acceptance or rejection of the null hypothesis incorrectly.that is a type I and type II error. If sample is large enough, there is less chance of this. One can test it by increasing size of sample and find out change in confidence interval of the parameter (s).
In my personal opinion, reporting research findings by percentage even when the sample size is less than 30 is necessary because doing so provides a relevant information- PROPORTION (multiplied by 100) which expresses a better comparative value than the frequency count.
If the sample size is less than 30, the confidence should be less than 5%.
So yes it is necessary.
Presenting frequency as percentage is ideal. However, if the sample size is small, presenting as percentage can be misleading. Let’s say your sample size is 30 and you classified your observations into 3 classes. Ideally you would have 10 observations in each class. However, in biological data it would rarely happen. Frequently; one of the classes can have larger or smaller observations. Let’s say the frequencies are 14, 13, 3 (46.67%, 43.33% and 10%). Another one: 14, 14, 2 (46.67%, 46.67%, and 6.67%). 1 change in the frequency of small class resulted in more than 3% change in percentage. If the sample size was 300 and frequencies were 140, 130, and 30 and in the 2nd scenario 140, 131, and 29, the change in the small class would be much smaller as percentage (the figure would be 9.67%, instead of 6.67%).
The reason is the sample size is too small to yield a meaningful or reliable percentage.
Be sure to calculate the sample size by many well-defined formula according to your study design, and in well-controlled experiment less than 30 each group could still get precise results.
There is not much reason behind this. If the sample is small, an observed proportion has a large standard error, so a confidence region will be large. Publish the proportion by all means, as long as you also report the standard error.
Even with tiny sample sizes one can validly compute signifance levels, confidence regions. Of course if effects are small, noise is large, and sample size is small, you will discover that your sample has told you almost nothing. But if the effect is large and the noise is small then even a small sample will be able to confirm these facts.
I suspect the reason behind the recommendation is that if one had computed confidence intervals and significance levels one would have found out that the sample indeed told us nothing hence the value in doing the experiment and publishing the paper is close to nihil. And if all such papers were not published the journal would no longer be viable.
Jast I like to report ODDS: y1/y0. For the sake of future possibilities of reanalisis & meta-analisis!
It is just good report absolute number when you have small sample size. For example, if you take 10 sample female patients in a cancer hospital of which 5 have breast cancer. Then, we cannot say 50 % patient have breast cancer in a cancer hospital . Like wise if you take another 10 sample, all of them breast cancer. then we say 100% women have breast cancer in the same hospital. Now evaluate your self. Thus, one have to be very careful while reporting percentage. First researcher needs to clear on it , then to CI.
The press like to report the most-sensational-appearing numbers and these are often the percentages. A professional scientific report should include all the results so that the reader can draw their own conclusion. Hence, report the frequency, the percentage, the mean, SD, and where the population result was inferred from a sample, the appropriate confidence limits are expected.
It depends on what the percentages are used for. If you try to generate a population estimate from a 30 participants sample, this does not make any sense. However, if the percentages are reported in describing the sample, this is acceptable and frequently done.
It would be handy to have a link to the BMJ guidance that is being referred to here so that the exact wording can be verified in context. As a standalone general piece of advice, the advice you have presented from the BMJ is unsound.
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