Case 1
- What you have
- Raw score, mean and SD
- Raw score
- 75
- Norm-group mean
- 60
- Norm-group standard deviation
- 10
- z-score
- 1.5
65.0
Open with these valuesT-Score Calculator
65.0
Result: 65.0A T-score is a z-score moved onto a scale with mean 50 and standard deviation 10, so the numbers stay positive and whole. It carries no more information than the z-score it came from. This is not the T-score from a bone-density scan, which is a different measure.
Worked examples
Case 2
- What you have
- Raw score, mean and SD
- Raw score
- 42
- Norm-group mean
- 60
- Norm-group standard deviation
- 12
- z-score
- 1.5
35.0
Open with these valuesCase 3
- What you have
- A z-score
- Raw score
- 75
- Norm-group mean
- 60
- Norm-group standard deviation
- 10
- z-score
- 2.33
73.3
Open with these valuesHow it's calculated
T = 50 + 10 · z
- StepSay whether you have a raw score or a z-score.
- StepFor a raw score, add the norm group's mean and standard deviation.
- ResultRead the T-score.
What this number means
A T-score answers one question: how far from average does this result sit, counted in standard deviations, written on a scale that is easy to read. The quantity underneath is the z-score, which counts exactly that distance from the mean of a norm group. T places it on a scale centred at 50 where one standard deviation is worth ten points, so T = 50 + 10 · z. The two modes are two ways in. Given a z-score, the calculator applies the shift and stops: a z of 2.33 becomes 73.3, a z of −2 becomes 30. Given a raw score, it works out z first — subtract the norm-group mean, divide by the norm-group standard deviation — and then shifts. A raw score of 75 against a mean of 60 and a deviation of 10 sits one and a half deviations above average, so 50 + 15 = 65. A 42 against a mean of 60 and a deviation of 12 sits one and a half deviations below, giving 35. A 100 against a mean of 80 and a deviation of 8 is 2.5 deviations up, giving 75. Note what the raw mode leans on: the mean and the deviation describe the comparison group, not your result. Change them and the answer moves while the raw score stands still.
Not the T-score from a bone-density scan
That is a different measure that happens to share the name. This one places a score on a scale with mean 50 and standard deviation 10.
Nothing is gained in the move
A T-score carries exactly what the z-score it came from carries. The shift only removes negative numbers and decimal places.
Ten points is one standard deviation
A T of 50 is exactly average for the norm group, which is a z of zero. Every ten points away from 50 is one standard deviation.
Mean and deviation belong to the norm group
In raw mode the answer depends on the norm group's mean and standard deviation, not on the raw score alone. A raw score of 75 gives a T of 65 with mean 60 and deviation 10.
Commonly misread
A T-score of 60 means 60 percent.
It means one standard deviation above the norm-group mean. About 84 percent of the norm group score lower.
A T-score tells you more than the z-score it came from.
It tells you the same thing on a different scale. T is 50 plus ten times z, and nothing is gained or lost in the move.
A score well below average has to come out negative.
The scale exists to avoid that. A z of −2 becomes a T of 30, which is easier to read on a report than a minus sign.
The two modes answer different questions.
They are two ways into the same number. A raw score of 75 with mean 60 and deviation 10 gives 65, and so does entering its z directly.
Reference table
| T-score | z-score | Roughly |
|---|---|---|
| 30 | −2.0 | About 2 % score lower |
| 40 | −1.0 | About 16 % score lower |
| 50 | 0 | Exactly average for the norm group |
| 60 | +1.0 | About 84 % score lower |
| 70 | +2.0 | About 98 % score lower |
Questions
What is a T score?
A z-score shifted onto a scale with a mean of 50 and a standard deviation of 10. T equals 50 plus ten times z, and nothing is gained or lost in the move.
Why use it instead of a z-score?
To avoid negative numbers and decimals. A z of −2 becomes a T of 30, which is easier to read on a report than a minus sign.
What do the two modes do?
Raw takes a score, a mean and a standard deviation and computes z itself. The z mode skips that step and takes the z-score directly — a raw score of 75 with mean 60 and deviation 10 gives 65 either way.
What does a T of 50 mean?
Exactly average: a z of zero. Every ten points away from 50 is one standard deviation.
Sources and last check
Information, not professional advice.