Chapter 3 Experimental Errors Statistics

1. SLIDE | 1
Dr. Wan Norfazilah Wan Ismail | FIST | norfazilah@ump.edu.my
BSK1153
ANALYTICAL CHEMISTRY
CHAPTER 3
EXPERIMENTAL ERRORS AND STATISTICS
DR WAN NORFAZILAH WAN ISMAIL
FACULTY OF INDUSTRIAL SCIENCES AND TECHNOLOGY
norfazilah@ump.edu.my

2. SLIDE | 2
Dr. Wan Norfazilah Wan Ismail | FIST | norfazilah@ump.edu.my
Measurement and Readings
Depends on what apparatus or instruments you used or read.
Example:
50 mL burette with 0.1 graduation, readings must be to the nearest 0.01 mL
Calibrated mm ruler, readings must be to the nearest 0.1 mm
Others:
Analytical balance??
Top loading balance??
pH meter??

3. SLIDE | 3
Dr. Wan Norfazilah Wan Ismail | FIST | norfazilah@ump.edu.my
Errors in Chemical Analysis
There are two types of error:
1. Systematic error - always too high or too low (improper shielding and
grounding of an instrument or error in the preparation of standards).
2. Random error - unpredictably high or low (pressure changes or
temperature changes).
Precision = ability to control random error.
Accuracy = ability to control systematic error.

4. SLIDE | 4
Dr. Wan Norfazilah Wan Ismail | FIST | norfazilah@ump.edu.my

5. SLIDE | 5
Dr. Wan Norfazilah Wan Ismail | FIST | norfazilah@ump.edu.my
Basic Statistics in Analytical Chemistry
Mean
ത
x =
σi xi
N
Deviation di = |xi - ҧ
𝑥|
Range ω = xhighest - xlowest
Variance
variance =
σi di
2
N − 1
Standard deviation
s =
σi(xi − ത
x)2
N
Relative standard deviation Relative standard deviation =
s
ത
x
Standard error of mean (Sm) s
n

6. SLIDE | 6
Dr. Wan Norfazilah Wan Ismail | FIST | norfazilah@ump.edu.my
Exercise
For data 0.725, 0.756, 0.752, 0.751 and 0.760. Calculate:
i. Mean
ii. Median
iii. Standard deviation
iv. Variance
v. Relative standard deviation
vi. Range
0.749
0.752
0.0125
1.898 × 10−4
0.0167
0.035

7. SLIDE | 7
Dr. Wan Norfazilah Wan Ismail | FIST | norfazilah@ump.edu.my
Statistics to Data Evaluation
Statistics
Statistics
Q-test
Q-test
Rejecting
outliers
Rejecting
outliers
t-test
t-test
Compared
measured result
with a known value
Compared
measured result
with a known value
Compare replicate
measurement
Compare replicate
measurement
Compare individual
differences
Compare individual
differences
Qexp =
gap
range
*Reject if Qexp > Qtable
Different from known value
if tcalc > ttable
μ = ത
x ±
ts
N

8. SLIDE | 8
Dr. Wan Norfazilah Wan Ismail | FIST | norfazilah@ump.edu.my
Q-test (Rejection of data)
Values of Q for Rejection of Data.
Number of
observations
Q (90% confidence) Q (95% confidence) Q (99% confidence)
3 0.941 0.970 0.994
4 0.765 0.829 0.926
5 0.642 0.710 0.821
6 0.560 0.625 0.740
7 0.507 0.568 0.680
8 0.468 0.526 0.634
9 0.437 0.493 0.598
10 0.412 0.466 0.568

9. SLIDE | 9
Dr. Wan Norfazilah Wan Ismail | FIST | norfazilah@ump.edu.my
Exercise
The concentrations of metal, M in a water sample were determined in a
set of five measurements: 4.85, 6.18, 6.28, 6.49, and 6.69 ppm. Can we
reject observation 4.85 as an outlier at:
i. 95% confidence level?
ii. 99% confidence level?
Reject
Accept

10. SLIDE | 10
Dr. Wan Norfazilah Wan Ismail | FIST | norfazilah@ump.edu.my
t-test (Student’s t)
Values of Student’s t.
Degree of
freedom
Confidence interval (%)
50 90 95 98 99 99.5 99.9
1 1.000 6.314 12.706 31.821 63.657 127.32 636.62
2 0.816 2.920 4.303 6.965 9.925 14.089 31.598
3 0.765 2.353 3.182 4.541 5.841 7.543 12.924
4 0.741 2.132 2.776 3.747 4.604 5.598 8.610
5 0.727 2.015 2.571 3.365 4.032 4.773 6.869
6 0.718 1.943 2.447 3.143 3.707 4.317 5.959
7 0.711 1.895 2.365 2.998 3.500 4.029 5.408
8 0.706 1.860 2.306 2.896 3.355 3.832 5.041
9 0.703 1.833 2.262 2.821 3.250 3.690 4.781
10 0.700 1.812 2.228 2.764 3.169 3.581 4.587
…
15 0.691 1.753 2.131 2.602 2.947 3.252 4.073
20 0.687 1.725 2.086 2.528 2.845 3.153 3.850
30 0.683 1.697 2.042 2.457 2.750 3.030 3.646
40 0.681 1.684 2.021 2.423 2.704 2.971 3.551
∞ 0.674 1.645 1.960 2.326 2.576 2.807 3.291

11. SLIDE | 11
Dr. Wan Norfazilah Wan Ismail | FIST | norfazilah@ump.edu.my
Exercise
A soda ash sample is analyzed in the UMP laboratory by titration with
standard hydrochloric acid. The analysis is performed in triplicate with
the following results: 93.58%, 93.43% and 93.50% Na2CO3. Calculate
the range where the true value lies at 95% confidence level.
The mean = 93.50%
standard deviation, s = 0.075% Na2CO3
At 95% confident level and two degree of
freedom, t = 4.303
Confident limit = x ± ts / N
= 93.50 ± (4.303 x 0.075) / 3
= 93.50 ± 0.19 %
true value = 93.31 – 93.69%