Application of Statistical and mathematical equations in Chemistry Part 2 Accuracy Precision Propagation of Error Confidence Limits F-Test Values Student’s t-test Paired Sample t-test Q test Least Squares Method correlation coefficient

2. Chapter 2
Precision
Propagation of Errors
Confidence Limit
Standard Tests for Analytical Methods
Linear Least Squares
Correlation Coefficient
Accuracy

4. Problem
•Example: Calculate the mean x ,
absolute error , and the %relative error
of the sea sample which include
102meq/l F , when repating the test two
times the result was
•(100.102 meq/L) ?

7. Problem
• Calculate the absolute average deviation and
• the %relative average deviation for Na+ ug/g
in soil sample
• measurements:
• (25.67,25.69 and 26.03), N = 3 ?
• Q1/ Determine (S, S mean, %RSD, and
%RSD mean)
• for the following measurements:
(20.22,20.28, 20.31, 20.33), N = 4 ?

8. Q1/ Determine (S, S mean, %RSD, and
%RSD mean)
for the following measurements:
(20.22,20.28, 20.31, 20.33), N = 4 ?
Q2:Calculate the absolute average
deviation and
the %relative average deviation for Na+
ug/g in soil sample
measurements:
(25.67,25.69 and 26.03), N = 3 ?

10. Problem1
• Q10/116: Determine Sa and (Sa)rel for the
following three Copper samples ,the
results are :4.0±0.004, 3.0±0.003 and
5.0±0.003 ?

12. Problem2
Example: Find pH for acid has
the following concentration:
•(4.6 ± 0.03) * 10-4 M ? ( pH = -Log [H+] )

14. Problem3

17. Problem
• Q14: What is the C. L. of the following
results
6.044,6.047,6.041,6.049,6.043,6.05,6.045
ug/g of Ni in the oil samples

18. 6.044+6.047+6.041+6.049+6.043+6.05+6.045

20. Problem1
• Q15/117: Make the F-test for the following
two methods:
• method (AAS):
(0.92,1.05,0.97,1.15,1.16,0.93,1.01,1.12) .
• method (Gravimetric):
(1.09,1.01,1.06,1.12,0.97,1.00) .

21. 0.92+1.05+0.97+1.15+1.16+0.93+1.01+1.12
1.09+1.01+1.06+1.12+0.97+1.00

22. Problem2

24. Problem3

25. while, t (table at 95%) is 2.571 is smaller that the
experimental t(8.68) , which indicate that there is static
differences between the two methods , as a result of the
method is wrong

26. Problem4

27. conclusion:
when comparing the t (table) at 95% for 7 free degree)
which equal (2.365) with t (experimental 9.87) . this
indicate there is static differences between the two
methods

28. Problem5

29. conclusion:
while Q from the table at level 90% = 0.76 , which is bigger than that
experimental Q 0.36 , as a result of that this value is acceptable

31. Problem
•Find the straight line equation for the following
measurements:
•Absorbance Concentration
•0.0 0.0
•0.2 2.9
•0.4 6.1
•0.8 11.2
•1.6 21.6

35. Problem
•Find the correlation coefficient for the following
measurements:
•Absorbance Concentration
•0.0 0.000
•2.0 0.086
•4.0 0.153
•6.0 0.265
•8.0 0.320