# Normalization the data before applying statistical test for large sample size

From my perspective, the reason p-value of a statistical test isn't useful in large sample scenario is because it will change according to the scale.

E.g. let's focus on chi-square test. In a chi-square test, the chi-square score changes linearly w.r.t. the scale of the frequencies (I mean, multiply 10 for each cell in the contingency table, the chi-square will also be 10 times larger). So when the data size is larger, even it has the same ratio/proportion, the p-value becomes smaller.

Thus, in this sense, why don't we just set a standard value, e.g. 1000 or 10000, and do a linear transform to normalize the total sample size to this value before we do the chi-square test. Then I suppose the p-value makes sense again. And scores like Cramer's V or Cohen's h or odds ratio remains the same.

What's wrong with my idea? (I don't know why the number in the table must be counts for chi-square. If this is a problem, maybe think of other tests like ANOVA)

Any idea/thought is appreciated:)

The point is that the sample size is actually informative. If you have the same relative departures from row-column independence, but a 10 times larger sample size, you have much more evidence against the null hypothesis of row-column independence. This is rightly reflected in your $\chi^2$ statistic and corresponding p-value.
Finally, the entries in the contingency table are counts by construction. The fact that you have counts yields an "automatic" assumption that the variance equals the mean, needed to standardize the residuals in the calculation of the $\chi^2$ statistic.