## Training and consultancy for testing laboratories. ### Calculating standard uncertainties for each uncertainty contribution

In evaluating the combined uncertainty of a testing method from various sources of uncertainty, we need to ensure that we work on a platform of standard uncertainties expressed as standard deviations throughout, because in addition to the standard uncertainty (u) values obtained by our own evaluation (Type A uncertainty), we may also encounter the so-called Type B uncertainty contributions which are uncertainty (U) values given by a third party or from experience and other information in different forms.   Read on … How to calculate standard uncertainties for each source of uncertainty

### Basic discussion on measurement uncertainty evaluation Currently many measurement uncertainty (MU) courses and workshops for test laboratories in this region are run by metrology experts instead of practicing chemists. Some laboratory analysts and quality control personnel have found the outcome after attending the two- or three-day presentations rather disillusion, leaving the classroom with their minds even more uncertain. This is because they cannot see how to apply in their routine works as there are no practical worked examples demonstrated to satisfy their needs…..  Read on  Measurement uncertainty – the very basic

### Std additions in instrumental calibration When there is a significant difference between the working calibration standard solutions for instrumental analysis and the sample matrix, its matrix background interference whilst using the calibration curve prepared by ‘pure’ standard solutions cannot be overlooked.  Using the standard additions method for instrumental calibration is a good option.  Read on …..

### Hypothesis testing – comparison of two means

One of the most important properties of an analytical method is that it should be free from bias.  That is to say that the test result it gives for the amount of analyte is accurate, close to the true value.  This property can be verified by applying the method to a certified reference material or spiked standard solution with known amount of analyte.  We also can verify this by carrying out two parallel experiments to compare their means….

Hypothesis testing – comparison of two experimental means

### 7 practical steps of hypothesis testing

This is a follow-up of the last blog.  Read on ……

7 Steps of hypothesis testing

### Revisiting Hypothesis Testing

Few course participants had expressed their opinions that the subject of hypothesis testing was quite abstract and they have found it hard to grasp its concept and application.  I thought otherwise. Perhaps let’s go through its basics again.

We know the study of statistics can be broadly divided into descriptive statistics and inferential or analytical statistics.   Descriptive statistical techniques (like frequency distributions, mean, standard deviation, variance, central tendency, etc.) are useful for summarizing data obtained from samples, but they also provide tools for more advanced data analysis related to a broader picture on population where the samples are drawn from, through the application of probability theories in sampling distributions and confidential intervals.  We use the analysis of sample data variation collected to infer what the situation of its population parameter is to be.

A hypothesis is an educated guess about something around us, as long as we can put it to test either by experiment or just observations. So, hypothesis testing is a statistical method that is used in making statistical decisions using experimental data.  It is basically an assumption that we make about the population parameter. In the nutshell, we want to:

• make a statement about something
• collect sample data relating to the statement
• if given that the statement is true and the sample outcome is unlikely, we shall realize that the statement probably is not true.

In short, we have to make decisions about the hypothesis. The decisions are to decide if we should accept the null hypothesis or if we should reject the null hypothesis with certain level of significance.  Therefore, every test in hypothesis testing produces a significance value for that particular test.  In hypothesis testing, if the significance value of the test is greater than the predetermined significance level, then we accept the null hypothesis.  If the significance value is less than the predetermined value, then we should reject the null hypothesis.

Let us have a simple illustration.

Assume we want to know if a particular coin is fair.  We can give a statistical statement (null hypothesis, Ho) that it is a fair coin.  The alternative hypothesis, H1 or Ha, of course, is that the coin is not a fair coin.

If we were to toss the coin, say 30 times and got heads 25 times.   We take this as an unlikely outcome given it is a fair coin, we can reject the null hypothesis saying that it is a fair coin.

In the next article, we shall discuss the steps to be taken in carrying out such hypothesis testing with a set of laboratory data.