How much that is hidden may still reside in a person, or how much may still reside hidden! How inventive is hidden inwardness in hiding itself and in deceiving or evading others, the hidden inwardness that preferred that no one would suspect its existence, modestly afraid of being seen and mortally afraid of being entirely disclosed! Is it not so that the one person never completely understands the other? But if he does not understand him completely, then of course it is always possible that the most indisputable thing could still have a completely different explanation that would, note well, be the true explanation, since an assumption can indeed explain a great number of instances very well and thereby confirm its truth and yet show itself to be untrue as soon as the instance comes along that it cannot explain-and it would indeed be possible that this instance or this somewhat more precise specification could come even at the last moment. Therefore all calm and, in the intellectual sense, dispassionate observers, who eminently know how to delve searchingly and penetratingly into the inner being, these very people judge with such infinite caution or refrain from it entirely because, enriched by observation, they have a developed conception of the enigmatic world of the hidden, and because as observers they have learned to rule over their passions. Only superficial, impetuous passionate people, who do not understand themselves and for that reason naturally are unaware that they do not know others, judge precipitously. Those with insight, those who know never do this. Soren Kierkegaard, Works of Love, (1847) Hong 1995 p. 228-229

There are two tests that you can run that are applicable when the assumption of homogeneity of variances has been violated: (1) Welch or (2) Brown and Forsythe test. Alternatively, you could run a Kruskal-Wallis H Test. For most situations it has been shown that the Welch test is best. Both the Welch and Brown and Forsythe tests are available in SPSS Statistics (see our One-way ANOVA using SPSS Statistics guide).

This, of course, leaves us none the wiser as to how to model velocity, as the equation of exchange is nothing more than an identity. MV=PQ just says that the money flow of expenditures is equal to the market value of what those expenditures buy, which is true by definition. The left and right sides are two ways of saying the same thing; it’s a form of double-entry accounting where each transaction is simultaneously recorded on both sides of the equation. Whether an effect should be recorded in M, V, P, or Q is, ultimately, arbitrary. To transform the identity into a tool with predictive potency, we need to make a series of assumptions about each of the variables. For example, monetarists assume M is determined exogenously, V is constant, and Q is independent of M and use the equation to demonstrate how increases in the money supply increase P (i.e. cause inflation).

Unfortunately, many focus on skills rather than literacies.

Little consideration is given to the diversity of how these supposed “digital natives” experience technology

Golden Age economics ended. Golden Age assumptions did not. For 30 wonderful years, we had been unusually flush, and we got used to it, re-designing our institutions to assume unending increases in subsidized demand. This did not happen. The year it started not happening was 1975.