TESTS OF SIGNIFICANCE

It is a test to compare the results of the method with those accepted method.

HOW TO INDICATE THAT WHETHER THERE IS A SIGNIFICANT DIFFERENCE??

By using: The T test

The T test Is used to determine if 2 sets of measurements are statistically different. The comparison between 2 set of measurements which made by 2 method, one will be test method and the other one will be accepted method. By using T test, we can determine whether these two method are significant difference.

A statistical T value is calculated and compared with the tabulated T value. If the calculated T value > the tabulated T value Then there is a significant difference between the results by the two methods at that confidence level.

There are 3 ways can be used in a T test. If accepted value of μ is available, the result is statistically equal to μ at a given confidence level. If accepted value of μ is not available, then we need to replicated analyses on a single sample by 2 method, or a series of analyses on a different sample by 2 method but one of the method should be accepted method.

1. T Test when an Accepted Value is Known

Calculated T value = 2.9 Tabulated T value = calculated T value > tabulated T value There is a significant difference between the reference value and the measured value.

Comparison of the Means of Two Samples When t test is applied to two sets of data,µ is replaced by the mean of the second set. Reciprocal of the standard deviation of the mean( √N/s) replace by the difference between the two. Sp is pooled standard deviation of the individual measurements of two sets:

The pooled standard deviation sometimes used to obtain an improved estimate of the precision of the method. Calculating the precision of the two sets of data in a paired t test. Preferable to perform several sets of analyses examples on different samples with slightly different compositions.

If indeterminate error is assumed to be the same for each set, then the data of the different set can be pooled.

The pooled standard deviation, s p is given by: x => values in each set N => num. of measurements x =>means of each of k sets of analyses N – k => degree of freedom from (N 1 -1) + (N 2 -2) + … + (N k -1)

EXAMPLE : A new gravimetric method is developed for iron (III) in which the iron is precipitated in crystalline form with organocarbon “cage” compound. The accuracy of the method is checked by analyzing the iron in an ore sample and comparing with the results using the standard precipitation with ammonia and weighing of Fe 2 O 3.

The results, reported as % Fe for each analysis, were as follows Test MethodReference Method 20.20%18.89% X₁=19.65% X₂=19.24% Is there a significant difference between the two methods?

Solution

Paired t Test t value is calculated in a slightly different form difference between each of the paired measurements on each sample is computed

Average difference D is calculated and individual deviations of each from D are used to compute a standard deviation, s d t value is calculated from :

Example You are developing a new analytical method for the determination of blood urea nitrogen (BUN). You want to determine whether you method differs significantly from a standard one for analyzing a range of sample concentrations expected to be found in the routine laboratory. It has been ascertained that the two methods have comparable precisions. Following are two sets of results for a number of individual samples.

95% confidence level is considered significant 99% level is highly significant Smaller the calculated t value, more confident that there is no significant difference between the two method

Too low confidence level (e.g. 80%), likely to conclude erroneously that there is a significant difference between two methods (type I error) On the other hand, too high confidence level will require too large a difference to detect (type II error) If a calculated t value is near tabular value at the 95% confidence level, more tests should be run to ascertain definitely whether the two methods are significantly different

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