What it means
Raw figures are hard to compare. A $150,000 sales month means one thing for a team that averages $120,000 and something very different for a team that averages $400,000.
Converting results to z-scores puts everything on the same scale, so you can see how unusual a result is. A z-score is calculated by subtracting the average from the value and dividing by the standard deviation.
A score of 1 means the value is one standard deviation above average, and a score of -2 means two standard deviations below. In data that follows a roughly bell-shaped pattern, most values fall between -2 and 2.
Analysts use z-scores to spot outliers, such as an expense claim far above normal or a transaction that might signal fraud. They also use them to compare different measures on one scale, for example ranking funds by return and risk.
Because the scores are unit-free, a figure in dollars and a figure in percentages can be put side by side. The Altman Z-score is a separate but related use of the letter.
It combines several financial ratios into a single number that is used to assess the likelihood that a company will struggle financially. Lenders and credit analysts treat it as a screening tool rather than a prediction, and it works better for some types of company than others.
In day-to-day finance work, z-scores are easy to produce in a spreadsheet. A standard deviation function and an average function are all that is needed, and the results can then be sorted to bring the most unusual items to the top.
This makes the method popular with auditors, controllers and anyone reviewing a long list of transactions. Z-scores come with assumptions.
They work best with reasonably symmetrical data, and a handful of extreme values can distort the average and the standard deviation. Context still matters, because an unusual result is not always a bad one.
In practice
Real-world examples.
Example
A finance team reviews expense claims and calculates a z-score for each one. A claim of $4,500 with a z-score of 4 stands out against an average of $600, so it is checked first. It turns out to be a legitimate conference fee.
Example
A fund researcher converts the one-year returns of 50 funds into z-scores. A fund scoring 1.5 outperformed most of its peers, and one scoring -2 lagged far behind. The firm uses the ranking as a starting point for further research. Analysts then look at fees, strategy and risk before making any recommendation.
Example
A credit analyst at a bank calculates the Altman Z-score for a manufacturing client before renewing a facility. The score sits in the cautious range, so the bank asks for more detailed cash flow forecasts. The decision is made on the full picture, not the score alone.
Formula
Calculation
Z = (Value - Mean) / Standard deviation
Worked example: a sales team has an average monthly result of $120,000 with a standard deviation of $15,000. One salesperson closes $150,000 in a month.
Difference from the mean = $150,000 - $120,000 = $30,000.
z = $30,000 / $15,000 = 2.
A z-score of 2 means the result is two standard deviations above average, which is unusually strong. A salesperson who closed $105,000 would have a z-score of ($105,000 - $120,000) / $15,000 = -1.Case study
Seen in the real world.
This is an illustrative story about a fictional business. Northgate Components is an invented parts supplier whose accounts team checks daily payments for errors. Payments average $8,000 with a standard deviation of $2,000.
One day, a payment of $20,000 appears. Its z-score is ($20,000 - $8,000) / $2,000 = 6, which is far outside the normal range. The team investigates before releasing the funds and finds that a clerk had keyed in an extra zero on a $2,000 invoice.
The error is corrected, and the company saves a large overpayment that would have taken weeks to recover. Northgate then adds a z-score alert to its payment approval process. The illustrative lesson is that a simple statistical test can catch costly mistakes. The team also agrees to review the alert threshold every quarter, so that it stays useful as payment patterns change.
Watch out
Common mistakes.
- Treating every high z-score as a problem. It only says a value is unusual, and the cause may be perfectly legitimate.
- Using z-scores on very small or heavily skewed data. The average and standard deviation become unreliable, so the scores can mislead.
- Confusing the statistical z-score with the Altman Z-score. They share a letter but measure different things and use different calculations.
Questions
People also ask.
What is a good z-score?
It depends on the purpose. For performance, a high score may be good, and for error checking, a very high or low score is a warning.
What z-score is considered an outlier?
A common rule of thumb is a score above 3 or below -3, though teams choose thresholds that suit their data.
Is the Altman Z-score reliable?
It is a useful screening tool, but it is a simplification. It should be combined with cash flow analysis and other information.
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