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Reinforcement the test in the meaning of difference

The story on this page is not statistics, but it is a point when doing Hypothesis Testing in practice.

The test for the difference in the mean value is the easiest to understand, so the subject is the Hypothesis Testing for Diffrence of Average, but the idea can be applied to other tests as well.

What is the "meaning of difference"?

When testing is used in practice, it is common to say, "There was a significant difference, so it is effective." or "There is no significant difference, so it is ineffective." That's the case when you're just talking.

The test uses the word "significant" only in statistical terms. In Strength and Weakness of Big Data, there is a story that "the conventional test to judge whether the p-value is significant is strange". That's it, there's something to think about.

When testing the difference in mean values, what is reinforcing is the realistic meaning.

Types of realistic meanings

The realistic meaning of the difference is not one kind.

Significant figures and resolution

Significant Figures and Resolution are, for example, "This measurement cannot measure a size finer than 0.1."

You can also find it on the Statistics with minimum confidence interval (Impossibility of statistics) page with a minimum confidence interval, but considering the significant figures and resolution, we can say that there is no difference from a non-statistical point of view.

However, there seems to be an objection to this idea. Some people seem to think, "If the number of samples is very large and the average value is calculated, even with a measurement system that is limited to 0.1 increments, it is possible to accurately measure even fine digits such as 0.54667."

Common differences

Suppose that the difference in the average value before and after the measure is 0.5. Suppose that not only the results of the test, but also the histogram showed a clear division.

If the person who analyzes the data is not usually involved in the data, "There was a difference! It becomes, For those who are usually involved in that data, it can be like, "That kind of difference happens often." Changes that seem to occur slowly over a long period of time may remain as experiences and memories, but it may be difficult to verify them later. From the point of view of experience and memory, it is sometimes useful to confirm whether it is really the result of the countermeasures.

Economically meaningful differences

Even if the difference is statistically significant, it is another matter whether it makes economic sense or not.

For example, if the labor and effort required to process defective products is a burden, but the labor does not change even if 150 defective products occur or 200 defective products occur, It makes no economic sense. In this case, it is only when the number of defective products can be reduced to 0 that the difference is meaningful.