Keep a decade-year only when it differs from the overall-mean

How the yearly changes were measured

Yearly index changes were measured from January and December monthly averages of a broad U.S. stock composite. There was a 1957 break between an earlier compiled series and later published index levels.

The decennial-profile used those yearly changes from January 1890 through December 1990 and was shown as a cumulative path across a typical ten-year calendar.

How each decade-year was compared

Each decade-year mean was plotted with a dispersion-band, the individual yearly observations, and a comparison against the full-sample mean. The dispersion-band is a one-standard-deviation interval around that decade-year mean and shows how wide the yearly outcomes are.

The formal test treated p less than 0.05 as the significance-cutoff for calling a decade-year mean different from the overall-mean.

Which decade-years met the significance-cutoff

In the 101-year sample, only the fifth and eighth decade-years met that cutoff relative to an overall-mean change of 5.4 percent with a standard deviation of 18.7 percent.

What a sample-extension did to those two slots

Adding earlier nineteenth-century observations left the fifth year below the cutoff at 0.037, while the eighth year rose to 0.097 and no longer qualified. The longer-sample overall-mean annual change was 4.6 percent with a standard deviation of 19.0 percent.

The leftover decade-years and a naive seasonal-overlay

After fifth- and eighth-year observations were removed, the remaining decade-years averaged 2.3 percent with a standard deviation of 18.1 percent, and none stood out from the others.

A naive calendar that concentrates exposure in visually strong years and stands aside in the seventh and zeroth years does not survive the same year-by-year significance filter.