Standard Score Calculator

[PLEASE READ FIRST] This app does not judge anyone's chances at any school, and it holds no list of school or university scores. It works out a T-score from the numbers you type. The "top X%" figure is a guide that assumes the marks follow a normal distribution. ────────── 🔢 Standard Score Calculator — a T-score is not the height of a mark Eighty marks. On its own that settles nothing. Mean 60, standard deviation 15　→　T-score 63.3 Mean 70, standard deviation 5 　→　T-score 70 The same 80, two different answers. A T-score reads where a mark sits inside its group, not how high it is. That is why this app asks for three numbers. ■ A test taken by two people always gives 60 and 40 As long as the standard deviation is the population one — half the gap (÷ n). A hundred and a zero, fifty-one and fifty: the same answer. The mean sits halfway between the marks, so the higher is one deviation above and the lower one below. With the sample deviation (n−1, Excel's STDEV) the same two come out at 57.1 and 42.9. Nothing shows more quickly that a T-score reads position and nothing else. ■ One Japanese word, two numbers z-score　(mark − mean) ÷ SD　　0 at the mean, 1 one deviation above T-score　50 + 10 × z　　　　　 50 at the mean, 60 one deviation above T-score (50 + 10z) is used in Japan for exam scores, and in psychological testing elsewhere. The Japanese word for "standard score" covers both numbers, while in English it normally means the z-score — easy to mix up: one deviation above the mean is "1" on one scale, "60" on the other. This app never asks you to pick one. It shows both at once. ■ Three topics ▪ Find the T-score … mark, mean and SD give the T-score and the z-score ▪ Mark needed … target T-score, mean and SD give the mark and the gap ▪ Top % … a T-score gives the top per cent and the rank out of 100 ■ No ceiling and no floor A T-score can go above 100 and below 0. If one person in a group of n stands right out on their own, and the deviation is the population one (dividing by n), the highest they can reach is 50 + 10√(n−1). 2 people　　　 60 10 people　　　80 100 people　 149.5 1000 people　366.1 With the sample deviation (n−1) the highest out of a hundred is 149.0 instead. If one person out of a hundred gets full marks and the other ninety-nine score the same, that person is at 149.5 and the rest at 49. That is why the mark for a target T-score can come out above full marks; this app does not know what they are. ■ Top per cent T-score 30　97.72% T-score 40　84.13% T-score 50　50% T-score 60　15.87% T-score 70　2.28% T-score 80　0.13% An eleven-row chart in steps of five sits on the same screen, with the rank out of a hundred beside it. These figures assume a normal distribution, which real marks never quite follow, so treat them as a rough guide — furthest off when the group is small. ■ When the standard deviation is zero If everyone scored the same there is no T-score: you would be dividing by zero. Type a zero and the app stops and says why. The other way round: the smaller the deviation, the further one mark moves it. With a mean of 60 and a deviation of 2, 62 is already a T-score of 60. ■ What this app does not do ▪ It does not estimate anyone's chances at a school ▪ It holds no list of school or university scores ▪ It keeps no record of results over time ▪ It does not work out a mean and SD from a list of marks ▪ It does not distinguish sample and population deviation; it uses what you type ▪ It draws no bell curve. Numbers only No account is needed. The calculation happens on your device, and nothing you type is sent out. ■ What the screen holds ▪ One to three input fields. No settings screen ▪ Common values are one tap away ▪ The last five entries stay in the history; results copy out in one tap ▪ A quick chart on the top-per-cent topic, and six short notes ▪ Japanese and English, chosen by your device language ────────── For when a result lands and you want to know where the number came from. NISAKE GAME