ERT 207 ANALYTICAL CHEMISTRY

ALINA RAHAYU MOHAMED

PUSAT PENGAJIAN KEJURUTERAAN BIOPROSESUNIVERSITI MALAYSIA PERLIS

• Lecture

• 18th July 2008

TOPICS TO BE COVERED:

3.0 UTILIZATION OF STATISTICS IN DATA ANALYSIS:

3.1 SIGNIFICANT TESTING

3.2 THE STUDENT T -TEST

3.3 THE Q TEST: REJECTION OF A RESULT

4.0 CALIBRATION CURVE

4.1 SLOPE,INTERCEPT AND COEFFICENT OF

DETERMINATION

4.2 DETECTION LIMIT

3.1 SIGNIFICANT TESTING

• Why we do testing to our experimental data?

• 1. to compare data among friends with the intention of gaining some confidence that the data observed could be accepted or rejected.

• 2. to decide whether there is a difference between the results obtained using two different methods. All these can be confirmed by doing some significant tests.

t test is used to decide whether there is a significant difference in the means for two

sets of data.

1.True or accepted value and confidence limit known.

2. Comparing mean for two sets of data.

3.2 THE STUDENT T -TEST

The calculated t value is compared with the t value from the table (Table 3.1 from Gary D.Christian) for the sets of data and at a required level of confidence.

Select a confidence level (95% is good) for the number of samples analyzed (= degrees of freedom +1).

Confidence limit = x ± ts/√N.

It depends on the precision, s, and the confidence level you select.

Select a confidence level (95% is good) for the number of samples analyzed (= degrees of freedom +1).

Confidence limit = x ± ts/√N.

It depends on the precision, s, and the confidence level you select.

(a) True or accepted value and confidence limit known.

The calculated t value (ItI) is then compared to the t value from the table (Table 3.1).

If t calculated > ttable, then there is a significant difference in the results of the two methods used at a certain level of confidence.

If tcalculated < ttable, then there is no significant difference in the results of the two methods used at a certain level of confidence.

Example 1: The true value (μ) for Cl- in a standard sample is 34.63 %. After three analysis, it is found that the mean is 34.71 % and s equals to 0.04 %. From the result, is there any determinate error that occurs in the method used?

Solution:

For the three analysis or N-1 =2(Table 3.1)

t calculated > ttable for 90 % confidence

levels, and

t calculated < ttable for 95% confidence

level and more.

Therefore there is no significant difference for confidence level greater than 95 % and we can conclude that there is no determinate error for confidence level greater than 95 %.

Example 2: You are developing a procedure for determining traces of copper in biological materials using a wet digestion followed by measurement by atomic absorption spectrophotometry. In order to test the validity of the method, you obtain an NIST orchard leaves standard reference material and analyze this material. Five replicas are sampled and analyzed, and the mean of the results is found to be 10.8 ppm with a standard deviation of ±0.7 ppm. The listed value is 11.7 ppm. Does your method give a statistically correct value at the 95% confidence level?

Solution:

t = 2.9

There are five measurements, so there are 4 degrees of freedom (N — 1).

From Table 3.1, we see that the tabulated value of t at the 95% confidence level is 2.776.

This is less than the calculated value, so there is a determinate error in the new procedure.

That is, there is a 95% probability that the difference between the reference value and the measured value is not due to chance.

(b) Comparing mean for two sets of data.(b) Comparing mean for two sets of data.

See Gary D.Christian (page 95)See Gary D.Christian (page 95)

Example 1: Two bottles of beer were Example 1: Two bottles of beer were analyzed for the alcohol content. Four analyzed for the alcohol content. Four samples from the first bottle with a mean samples from the first bottle with a mean value of 12.61 % alcohol and six samples value of 12.61 % alcohol and six samples from the second bottle with a mean value from the second bottle with a mean value of 12.39 % alcohol. The pooled standard of 12.39 % alcohol. The pooled standard deviation is 0.07 %. Is there a significant deviation is 0.07 %. Is there a significant difference between the content of the two difference between the content of the two bottles?bottles?

t t calculatedcalculated > t > ttabletable for 80, 90, 95 and 99 % for 80, 90, 95 and 99 %

levels of confidence (Table 3.1). levels of confidence (Table 3.1). This shows that the analysis gives a This shows that the analysis gives a

significant difference in the alcohol significant difference in the alcohol content.content.

Example: A new gravimetric method is Example: A new gravimetric method is developed for iron (III) in which the iron is developed for iron (III) in which the iron is precipitated in crystalline form with an precipitated in crystalline form with an organoboron “cage” compound. The accuracy organoboron “cage” compound. The accuracy of the method is checked by analyzing the iron of the method is checked by analyzing the iron in an ore sample and comparing with the in an ore sample and comparing with the results using the standard precipitation with results using the standard precipitation with ammonia and weighing of Feammonia and weighing of Fe220033. The results, . The results, reported as % Fe for each analysis, were as reported as % Fe for each analysis, were as follows:follows:

Is there a significant difference between Is there a significant difference between the two methods?the two methods?

The tabulated t for nine degrees of The tabulated t for nine degrees of freedom (N1 + N2 — 2) at the 95% freedom (N1 + N2 — 2) at the 95% confidence level is 2.262, so there is no confidence level is 2.262, so there is no statistical difference in the results by the statistical difference in the results by the two methods.two methods.

(c) For special case, that is M = N.(c) For special case, that is M = N.

3.3 THE Q TEST: REJECTION OF A 3.3 THE Q TEST: REJECTION OF A RESULTRESULT

• Not all data obtained from an Not all data obtained from an experiment can be used. experiment can be used.

• There is a possibility that some data There is a possibility that some data have a great difference from the true have a great difference from the true value and therefore should be value and therefore should be removed. removed.

• The rule for data rejection is known The rule for data rejection is known as Q test.as Q test.

• The Q test is used for rejection of values The Q test is used for rejection of values that are further away from the true value.that are further away from the true value.

• The Q value can be obtained as follows:The Q value can be obtained as follows:

• (i) Arrange the values in an order.(i) Arrange the values in an order.

• (ii) Calculate the differences between the (ii) Calculate the differences between the highest and lowest values.highest and lowest values.

• (iii) Calculate the difference between the (iii) Calculate the difference between the uncertain value and the nearest value to uncertain value and the nearest value to it. Divide this value with the value it. Divide this value with the value calculated in (ii) to obtain the Q calculated in (ii) to obtain the Q calculated.calculated.

• (iv) Compare this Q(iv) Compare this Qcalculatedcalculated with the Q with the Q from the Q Table (Table 3.3). The from the Q Table (Table 3.3). The doubtful value is removed with 90 % doubtful value is removed with 90 % confidence level if the Qconfidence level if the Qcalculatedcalculated is is greater or equals to the Q value greater or equals to the Q value obtained from the Q table.obtained from the Q table.

Example:Example: An analysis of iron ore gives the An analysis of iron ore gives the following results: 33.78 %, 33.84 %, 33.60 following results: 33.78 %, 33.84 %, 33.60 % and 33.15 % at 90% confidence level. % and 33.15 % at 90% confidence level. Which of the values should be removed?Which of the values should be removed?

Solution:Solution: Doubtful values are 33.15 % and 33.84 %Doubtful values are 33.15 % and 33.84 % Arrange the values:Arrange the values: 33.84, 33.78, 33.60, 33.1533.84, 33.78, 33.60, 33.15 The difference between the highest and the The difference between the highest and the

lowest value = 33.84 — 33.15lowest value = 33.84 — 33.15 = 0.69 %= 0.69 %

Testing for 33.15%:Testing for 33.15%: The difference between the doubtful value The difference between the doubtful value

and the nearest one to it:and the nearest one to it: = 33.60—33.15= 33.60—33.15 = 0.45 %= 0.45 %

From the Q Table, From the Q Table, Q Q table table = 0.76 (for 4 observations).= 0.76 (for 4 observations).

The highest value (33.84 %) can also be The highest value (33.84 %) can also be tested using the same method as above.tested using the same method as above.

Tutorial Q3: Using the Q test for the Tutorial Q3: Using the Q test for the following results, determine whether the following results, determine whether the value 8.75 should be rejected as an outlier value 8.75 should be rejected as an outlier at 90% confidence level.at 90% confidence level.

8.20, 8.35, 8.64, 8.25, 8.75, 8.45.8.20, 8.35, 8.64, 8.25, 8.75, 8.45.

Answer:Answer: a) Arranging according to descending order: a) Arranging according to descending order:

8.75, 8.64, 8.45, 8.35, 8.25, 8.208.75, 8.64, 8.45, 8.35, 8.25, 8.20 b) Calculate difference between the highest b) Calculate difference between the highest

and lowest values: 8.75-8.20 = 0.55%and lowest values: 8.75-8.20 = 0.55%

c) Calculate difference between uncertain c) Calculate difference between uncertain value and nearest value to it : 8.75- 8.64 = value and nearest value to it : 8.75- 8.64 = 0.11%0.11%

d) Divide this value with the value calculated d) Divide this value with the value calculated in (b) to obtain Qcalculatedin (b) to obtain Qcalculated

Therefore, Therefore, 0.110.11% = 0.2% = 0.2 0.55%0.55%

e) Compare Q calculated with the Qtable at e) Compare Q calculated with the Qtable at 90% confidence level. N = 690% confidence level. N = 6

Qcalculated = 0.2Qcalculated = 0.2 Qtable = 0.56Qtable = 0.56 Qcalculated < QtableQcalculated < Qtable 0.2 < 0.560.2 < 0.56

Therefore, the value 8.75 should be Therefore, the value 8.75 should be accepted at 90% confidence level (8.75 accepted at 90% confidence level (8.75 cannot be removed).cannot be removed).