A thought experiment

Imagine two sets of 10 numerals that were specified to code for strength of a positive emotion/opinion versus strength of a negative emotion/opinion, such that "5" coded for "strongly disagree." and "1" coded for "strongly agree."

A: [1,5,2,4,3,1,5,2,4,3]

and

B: [1,5,1,5,1,1,5,1,5,5]

When you sum the numbers that the numerals stand for, the total is 30. There were ten participants. What's the average response?

Stop right there. If this question makes sense to you, go back to bed.

Look at the data!

In A, each of the five responses gets two "votes." That is what a null hypothesis looks like. There is not a consensus opinion. Respondents are just as likely to be neutral as they are to have a strong opinion.

In B, there is strong (dis)agreement.

To mistakenly report a statistic that cannot truly be reported, given the nature of the data, is a crime.

To be continued.