-value, when used in statistical testing contexts, ought not to be taken as a definitive source of truth. In fact, it was not meant to be when conceived. See the brilliant Nature article on this for an extensive comment on the topic.
The error margin
If you have a statistic to be used to describe the quantity of interest, say for instance (and typically) the sample mean of a series of measurements, to compute an error margin against if you'd
First, choose the desired confidence level, usual choices are 90%, 95% or 99%
Check whether the population standard deviation
is known or not: if it is, compute a z score; if it isn't, compute a t score
The margin of error will be given by
is known you'd use
, otherwise you'd use
(the sample mean) and
. It will then, and quite intuitively, depend on how many data points you've got. The result is meant to be interpreted as you are, at the chosen confidence level CL, CL% confident that the estimate of your variable lies within the error margin.
An application: the minimum sample size in the binomial parameter
The binomial parameter is
is the number of successes and
the number of trials. How good is this parameter (which is computed on a sample of size
) as an estimate of the real population parameter? Translated: how big does
have to be for
to be reliable?
Intro: the De Moivre-Laplace theorem and how we use it
Statement: the binomial distribution is approximated by a gaussian distribution when