Archive for the ‘Basic statistics’ Category
Data analysis allows us to answer questions about the data or about the population that the sample data describes.
When we ask questions like “is the alcohol level in the suspect’s blood sample significantly greater than 50 mg/100 ml?” or “does my newly developed TEST method give the same results as the standard method?”, we need to determine the probability of finding the test data given the truth of a stated hypothesis (e.g. no significant difference) – hence “hypothesis testing” or also known as “significance testing”.
A hypothesis, therefore, is an assumptive statement which might, or might not, be true. We test the truth of a hypothesis, which is known as a null hypothesis, Ho, with parameter estimation (such as mean, µ or standard deviation, s) and a calculated probability for making a decision about whether the hypothesis is to be accepted (high p -value) or rejected (lower p -value) based on a pre-set confidence level, such as p = 0.05 for 95% confidence.
Whilst making a null hypothesis, we must also be prepared for an alternative hypothesis, H1, to fall back in case the Ho is rejected after a statistic test, such as F-test or Student’s t-test. The H1 hypothesis can be one of the following statements:
H1: sa ≠ sb (2-sided or 2-tailed)
H1: sa > sb (1- right sided or 1- right tailed)
H1: sa < sb (1- left sided or 1- left tailed)
Generally a simple hypothesis test is one that determines whether or not the difference between two values is significant. These values can be means, standard deviations, or variances. So, for this case, we actually put forward the null hypothesis Ho that there is no real difference between the two s’s, and the observed difference arises from random effects only. If the probability that the data are consistent with the null hypothesis falling below a pre-determined low value (e.g. p = 0.05 or 0.01), then the hypothesis is rejected at that probability.
For an illustration, let’s say we have obtained a t observed value after the Student’s t-statistic testing. If the p-value calculated is small, then the observed t-value is higher than the t-critical value at the pre-determined p-value. So, we do not believe in the null hypothesis and reject it. If, on the other hand, the p -value is large, then the observed value of t is quite likely acceptable, being below the critical t-value based on the degrees of freedom at a set confidence level, so we cannot reject the null hypothesis.
We can use the MS Excel built-in functions to find the critical values of F– and t-tests at prescribed probability level, instead of checking them from their respective tables.
In the F-test for p=0.05 and degrees of freedom v = 7 and 6, the following critical one-tail inverse values are found to be the same (4.207) under all the old and new versions of the MS Excel spreadsheet since 2010:
But, for the t-test, the old Excel function “=TINV” for the one-tail significance testing has been found to be a bit awkward, because this function giving the t-value has assumed that it is a two-tail probability in its algorithm.
To get a one-tail inverse value, we need to double the probability value, in the form of “=TINV(0.05*2, v)”. This make explanation to someone with lesser knowledge of statistics difficult to apprehend.
For example, if we want to find a t-value at p=0.05 with v = 5 degrees of freedom, we can have the following options:
So, it looks like better to use the new function “=T.INV(0.95,5)” or absolute value of “=T.INV(0.05,5)” for the one-tail test at 95% confidence.
The following thus summarizes the use of T.INV for one- or two-tail hypothesis testing:
- To find the t-value for a right-sided or greater than H1 test, use =T.INV(0.95, v)
- To find the t-value for a left-sided or less than H1 test, use =T.INV(0.05, v)
- To find the t-value for a two-sided H1 test, use =T.INV.2T(0.05, v)
ISO FDIS 17025:2017 – Impacts on accredited laboratories
As noted in my previous article on the final draft international standard FDIS 17025:2017 (https://consultglp.com/2017/10/30/iso-fdis-170252017-sampling-sampling-uncertainty/ ), the current ISO/IEC 17025:2005 version widely used by accredited laboratories around the world will soon be replaced by this new standard, expected to be published very soon.
The ILAC (International Laboratory Accreditation Cooperation), a formal cooperation to promote establishing an international arrangement between member accreditation bodies based on peer evaluation and mutual acceptance with a view to develop and harmonize laboratory and inspection body accreditation practices, has recommended a 3-year transition to fully implement this new standard from the date of its publication. At the end of the transition period, laboratories not accredited to the ISO/IEC 17025:2017 will not be allowed to issue endorsed test or calibration reports and will not be recognized under the ILAC MRA terms.
Today, there are over 90 member accreditation bodies from over 80 economies have signed the ILAC Mutual Recognition Arrangement (ILAC MRA). This new ISO standard therefore has a tremendous impact on all accredited calibration and testing laboratories of which their national accreditation bodies are signatory members of the ILAC MRA.
Each national accreditation body is expected to work out its own transition plan with actions to be taken to help the laboratories under its charge to smoothly migrate to the new practices. These actions might include, but not limit to, effective communication, scheduled seminars/training courses for laboratory managers and technical assessors, and mapping out a time table and policies to achieve the ultimate goal.
In the nutshell, the new standard has standardized and aligned its structure and contents with other recently revised ISO standards, and the ISO 9001:2015, in particular. It reinforces a process-based model and focuses on outcomes rather than prescriptive requirements such as the absence of familiar terms like quality manual, quality manager, etc. and giving less description on other documentation. It will allow more flexibility for laboratory operation as long as the laboratory’s technical competence can be assessed and recognized by the standard.
The following notes highlight major significant changes in the new revision as compared with those in the 2005 version:
- Standard format
Many requirements under the 2005 version remain unchanged but appear in different places of the document, under headlines like general requirements (Clause 4), structural requirements (Clause 5), resource requirements (Clause 6), process requirements (Clause 7) and management system requirements (Clause 8). Also, there are certain language updates to reflect the current standard practices and technologies.
- Laboratory activities
Under Clause 3 on Terms and Definitions, the term “laboratory activities” in sub-clause 3.6 has included “sampling, associated with subsequent testing or calibration” in addition to the existing “testing” and “calibration” activities. This is a major scope expansion of the laboratory activity for accreditation and will be a challenge for most testing laboratories which are engaged in field sampling. Sub-sampling of test sample in a laboratory prior to analysis is considered to be part of the test procedure.
- Risk-based thinking
The revision has incorporated a new “risk-based thinking” which requires the laboratory to plan and implement actions to address possible risks and opportunities associated with the laboratory activities. The laboratory is responsible for deciding which risks and opportunities need to be addressed. The aims are to:
a) give assurance that the management system achieves its intended results;
b) enhance opportunities to achieve the purpose and objectives of the laboratory;
c) prevent, or minimize, undesired elements
The word of ‘risk’ can be found in the following requirements:
Clause 4.1.4: Identifying risk to impartiality
Clause 220.127.116.11: “When a statement of conformity to a specification or standard is provided, the laboratory shall document the decision rule employed, taking into account the level of risk (such as false accept and false reject and statistical assumptions) associated with the decision rule employed and apply the decision rule.”
Clause 7.10: Actions taken for nonconforming work based upon risk levels established by the laboratory
Clause 8.5: Actions to address risks and opportunities
Clause 8.7: Updated risk and opportunities when corrective action is taken
Clause 8.9: Management review agenda to include results of risk identification
The new standard has stressed on the laboratory’s impartiality. Under Clause 4 General Requirements, the Sub-clause 4.1 requires the laboratory to identify risks to its impartiality on an on-going basis and if a risk to impartiality is identified, the laboratory shall be able to demonstrate how it will eliminate or minimize such risk.
- Decision rule
The term “decision rule” is new to this ISO standard. It first appears in Clause 3.7 under Terms and Definitions which states that “rule that describes how measurement uncertainty is accounted for when stating conformity with a specified requirement”. This is in relation to Sub-clause 7.8.6 on providing “Reporting statements of conformity”.
Before the laboratory provides any statement of conformity to a specification, it is required to first assess the level of risk (such as false acceptance, false rejection and statistical assumptions) involved in the decision rule employed which has to be documented. See Sub-clause 18.104.22.168.
- External provided products and services
The new standard combines current Sub-contracting, Supplies and External Services which affect laboratory’s activities under a new headline with requirements, controls and communication guidance given under Sub-clause 6.6
- Evaluation of measurement uncertainty (MU)
Clause 7.6.1 requires laboratories to identify the contributions to measurement uncertainty. When evaluating MU, all contributions which are of significance, including those arising from sampling, shall be taken into account using appropriate methods of analysis.
The standard in its Clause 7.6.3 Note 3 states that “For further information, see ISO/IEC Guide 98-3, ISO 5725 and ISO 21748”. It is inferred that the laboratory has a choice in the MU evaluation methods, i.e. using either the conventional GUM (bottom up) or the holistic method performance (top down) approaches can be applied in the MU evaluation.
- Options in management system requirements
The new standard allows the laboratory to implement a management system in accordance with Option A or Option B after meeting the requirements of Sub-clauses 4 to 7.
Option A asks the laboratory to address all its sub-clauses 8.2 to 8.9 as the minimum requirements, and Option B is for a laboratory which has already established and is maintaining a management system in accordance with the requirements of ISO 9001, and which is capable of supporting and demonstrating the consistent fulfillment of the requirement of Clauses 4 to 7, whilst fulfilling at least the intent of the management system requirements specified in Sub-clauses 8.2 to 8.9.
In conclusion, in addition to aligning with the other current international standards in its structural forms and wordings, the new version of ISO 17025 to be implemented introduces new laboratory activity scope on sampling and new requirements such as risks and opportunities, decision rule, sampling uncertainty and two management system options.
Laboratories will need to acquire new skills in carrying out risk assessment, making decision rule, evaluating sampling uncertainty and learning how to incorporate this uncertainty into the overall measurement uncertainty evaluation.
Now, accredited laboratories await for their respective national accreditation body to provide new laboratory accreditation guidelines and directives in this significant migration of ISO/IEC 17025 standards from the existing 2005 version to the latest one during this 3-year transition period.