How is standard error affected by multiplication? If I have some measure, suppose the difference of two means, and then I multiply it by 100; how will the standard errors be affected? Will they be multiplied too? or will they be completely different?
 A: The standard error of the difference between means is multiplied by the same factor as the data.
There are at least three ways to see this:

*

*Try it out in your favourite software with a simple example.


*Generally, the standard error has the same units of measurement and dimensions as the quantity being estimated. So multiplying by a factor is just like changing the units, say working in terms of cm rather than m.


*Specifically, if you look at the precise formula, you will get a more detailed analysis that boils down to #2.
For other measures, the standard error may well be unchanged. For example, the units you use have no bearing on Pearson correlation; that is much of the point of Pearson correlation; it quantifies how far relationships are linear and you should (and do) get the same answer regardless of units. You wouldn't want the correlation between height and weight to depend capriciously on use of metres, feet, kg or pounds or whatever else. (Conversely, that is a limitation of covariance.)
