How do you know if an insignificant P value is because of chance error or because the sample size of the data is too small? I have always thought that an insignificant P value is the product of chance causing variation in the data. However when I was watching a talk on a study, the presenter mentioned how the insignificant P value meant that the sample size of the data was too small to make any conclusions rather the being the product of chance error. How can you tell if an insignificant P value is caused chance error or small sample size then?


The presenter mentioned how the insignificant P value meant that the sample size of the data was too small

This is very wrong.

*

*The p-value does not indicate whether the sample size was too small.


*It is the estimate of the error/deviation in the measured effects that indicates this.
(Along with a relative comparison of the size of that error and the size of the suspected effect that one hoped to be able to measure. The error should be smaller than the effect that you hope to measure.)
What this presenter is saying is presumptive. An insignificant p-value can occur when the sample is too small. But... it can also occur because there is no effect. It sounds like this presenter presupposes the presence of an effect and bases the story of the discussion and conclusion around this
It is also a bit silly to state this as a conclusion. It is a bit like saying 'the experiment failed' while hiding that it already failed before it started because the sample is too small (instead it looks like the presentation makes the 'too small sample' is a discovery). In order to know that the sample is too small you do not need to observe an insignificant p-value. You can already determine beforehand whether a sample is going to be too small to be able to detect a certain magnitude of effect. The only situation when this is not the case is when there is no reasonable a priori estimate of the variance that might be expected on the measurements. But even then, one should not say that the insignificant p-value means that the sample is too small.
