Descriptive statistic >> Statistical inference > Value of interval estimates | Nonparametric methods

The width of the confidence interval for both sample means and sample proportions can be partially manipulated by varying the value of two control elements. Firstly, it is possible to increase or decrease the confidence level (error probability) and secondly, it is possible to expand or constrict the interval by forming samples of different size.
The connection between the width of the interval and the confidence level lies in the fact that the width of the interval is increased with the increase in the confidence level (i.e., error probability decreases as wider intervals have higher chances of including population value). Thus, the researchers themselves determine the alpha level or acceptable error probability (tolerance probability) (alpha is usually taken as 0.05 or lower). This applies to all methods of statistical conclusion.
Sample size is inversely related to the width of the interval. With the increase in the sample size the width of the interval decreases (at constant alpha level), i.e. larger samples provide more accurate estimates.
If we speak of statistical hypothesis testing, the probability of the null hypothesis deviation depends on four independent factors:

The latter connection emphasizes the most significant constraint in statistical hypothesis testing. The mere fact that the differences are statistically significant does not make them important in any other sense. For instance, with very large sample sizes (e.g., if N is greater than 1000) even relatively small differences are statistically significant. However, statistical significance and theoretical or practical relevance is not the same thing. Significance in itself does not provide relevance, whose identification presupposes substantive analysis, comparison with research hypotheses, and the use of more sensitive statistical methods.
Let us imagine that on the basis of a large sample (n > 1000) we detected the statistically significant difference between men (X mean = 1.4 hours per day) and women (X mean = 1.3 hours per day) in the amount of time spent on the Internet. This raises the question whether this difference between men and women is essential enough (0.1 hour or 6 minutes) to include it in the final report.