# UNDERSTANDING THE Z-SCORE IN GENERAL AND AS A REQUIREMENT OF ISO17025, LABORATORY MANAGEMENT SYSTEM

In this article detail of Z –Score discussed keeping in view:- Use of Z-score in general and
- Use of Z-score in proficiency Test (PT) as part of one of the requirement of ISO/IEC 17025

**WHAT IS Z-SCORE?**To understand Z –score first we understand difference between Normal distribution and Standard Normal Distribution. Z-score is also known as standard score and it measures how many standard deviations is a Z-score from mean. More specifically, it measures how many standard deviations above or below a population mean is.

**FORMULA FOR Z-Score CALCULATION:**

**So, we will start with,**

**Use of Z-score in general**

**EXAMPLE:**A student, Vartika got 475 marks in exam and mean of all marks of students is 460 and standard deviation is 20. We have an assumption that exam marks found to be normally distributed. Total no of students appeared for exam is 25. We can see that, Vartika’ s mark is more than mean by 15 (= 475-460). Now we have to see, how well Vartika perform as compare to other 25 students? For this we will use Z-score. Z scores are used to assist evaluation of performance, here in this case performance of students.

*Z score is based on the distribution of results around the mean.*Formula for Z – Score is as below: Here, X = the score, µ = Mean and σ = Standard Deviation To simplify, we will arrange our numbers in tabulated format as below,

Exam | Score (X) | µ ( Mean) | σ ( Standard Deviation) |

Marks | 475 | 460 | 20 |

*The probability of a score can be found out when frequency distribution is normally distributed. In this case standard normal distribution convert the data in frequency distribution with mean is 0 and standard deviation is 1.*To calculate probability, we have to take help of standard normal distribution table or excel.

**A.Probability of score lower than “Vartika”**NORMSDIST (z) = NORMSDIST(0.75) = 0.7734 That is, 77.34 % of students having marks lower than “Vartika” This can be found using Cumulative Standard Normal Distribution Table

**B.Probability of students having marks better than “Vartika”**= 100-77.34 = 22.66% i.e. 0.2266 This can be found using Standard Normal Distribution Table.

**C.Probability of marks lower than “Vartika” but above mean**= 0.50 – 0.2266 = 0.2734 i.e. 27.34 % NOTE: The above is the case, when values more than mean is better. Z score is more useful when we want to calculate, at what minimum marks student came in top 10 %. As our mean is 460, we can conclude that marks will be more than mean. Marks above 10 % is 100-10 = 90 or 1-0.1 = 0.9 Calculate Z score with use of excel formula, =NORMSINV(0.9) =1.281552 =1.282

Exam | Score (X) | µ ( Mean) | σ ( Standard Deviation) | Z-score |

Marks | ? | 460 | 20 | 1.282 |

**Use of Z-score in proficiency Test (PT) as part of one of the requirement of ISO/IEC 17025**

**EXAMPLE:**

**Keeping same value as in above example of marks obtained in exam, this will help to understand Z-Score.**NOTE: In this case, value closed to mean is better. To understand this we will take example of mechanical testing of steel sample, where sample are tested to check Ultimate Tensile Strength (UTS) , Yield Strength (YS) and percentage elongation of steel. To make this easy,

- We will only consider value of UTS.
- To understand difference between two examples (i.e. of score in exam and UTS value) all the numbers in both examples are kept as it is.

**Here, in PT test Interpretation of Z- Score is carried out on below criteria,**

**|z-score| 2 — Satisfactory performance 2 < |z-score| < 3 — Questionable performance |z-score| > 3 — Unsatisfactory performance**

Test | Score (X) | µ ( Mean) | σ ( Standard Deviation) |

UTS | 475 | 460 | 20 |

**Next, if we want to compare two labs test results first is “Lab VAS” and another is “Lab AVS”.**

Test for “Lab AVS” | Score (X) | µ ( Mean) | σ ( Standard Deviation) |

UTS, Mpa | 500 | 460 | 20 |

**Besides Z-score, the other two evaluation criteria in PT are**

**Percent difference, D**

**2. En numbers**This is use in measurement of comparison scheme. Here, X- is participating lab result Xref – is assigned value Ulab – is uncertainity of participating lab result. Uref – is uncertainity of reference laboratory’s assigned value.

**En number evaluation criteria is as below,**|En| 1—- Satisfactory performance |En| 1—- Unsatisfactory performance Hope this article may useful to understand Z-score.

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By aloksmishra, April 30, 2019 @ 5:47 am

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By ViVEK SHROUTY, May 16, 2019 @ 6:56 am

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