Is that margin gap real or just a wider spread?

Fourteen advisory engagements against sixteen managed-service engagements, on gross margin. Advisory looks 3.3 points better and the Welch test says that gap cannot be told from noise, because advisory spread is five times wider.

Words on this sheet

  • Standard deviation: How far a typical reading sits from the average, in the same units as the readings.

Finance Intermediate Statistics free

After you install, this is the model to open.

Do Our Two Service Lines Earn the Same Margin?

  1. In your spreadsheet, click the Sortia icon in the strip of icons down the right-hand edge. No strip? Click the arrow at the bottom-right to open it. You can also use Extensions, then Sortia, then Open Sortia.
  2. Click Start from a template and put that name in the search box.
  3. Pick the card with that name and click Load this template. It arrives on a new tab with real numbers already in it.

The answer

Advisory ahead by
3.3 margin points, 45.3% against 41.9%
p (two-tail)
0.45 chance makes this gap half the time
Spread, advisory
15.8 points of standard deviation
Spread, managed
3.2 points: predictable, not worse

Fourteen advisory engagements and sixteen managed-service engagements, each with its gross margin. Advisory averages 45.29% and managed averages 41.94%, so advisory is 3.35 points ahead and the partner who runs it says so in every meeting. Click Run: t comes back at 0.78 with a two-tail p-value of 0.4476. A gap this size would turn up by chance nearly half the time if the two lines earned identically, so on this evidence there is no difference to act on.

What makes the result rather than just deflating it is the two spread figures in the summary block beside the data. Advisory margins have a standard deviation of 15.75 points and managed margins have 3.17, a five-fold difference, and the Welch test spends its degrees of freedom accordingly, reporting 13.92 rather than the 28 an equal-variances test would have claimed.

Advisory ranges from 22% to 71%; managed ranges from 36% to 47%. So the honest summary of this practice is not that one line is better, it is that one line is predictable and the other is a lottery with a slightly higher expected payout, and those two facts point at completely different decisions about cash, about which partner covers holiday, and about what you promise a bank.

Run the equal-variances version on the same two ranges to see what taking the default would have bought you: a two-tail p-value of 0.4119 instead of 0.4476, on 28 degrees of freedom instead of 13.92. Same verdict here, but on 28 degrees of freedom that sixteen wildly variable engagements never earned, and on data where the gap was larger that difference decides the answer.

The two lines have different counts on purpose, because a real practice does not run the same number of each, and this test does not require it. What the test cannot tell you is whether the advisory spread is fixable. If the worst engagements share a cause, this is a scoping problem dressed as a statistics one. To use your own practice, paste one line into each pair of columns and widen both ranges.

The model

It arrives on a tab called Template: Two Service Lines, One Margin, carrying these columns:

  • Advisory engagement
  • Gross margin
  • Managed engagement
  • Gross margin

with the model computed beside the data:

Advisory average0.4529
Managed average0.4194
Advisory spread (standard deviation)0.1575
Managed spread (standard deviation)0.03172
Worst advisory engagement0.22
Worst managed engagement0.36

Once it is in your sheet

  1. The model arrives with real numbers in it and runs as it stands, so you can press the button first and understand it second.
  2. Change the numbers to yours. The sheet marks which cells are inputs and which hold formulas, and most labels carry a note explaining the row.
  3. Press the run button at the bottom of the panel. It is labeled for the tool you are in, and the result lands on its own tab, with a written reading of it beside the figures.

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