APPLICATION OF STATISTICAL CONCEPTS IN THE DETERMINATION OF WEIGHT VARIATION IN SAMPLES

L. BENIGNATIONAL INSTITUTE OF MOLECULAR BIOLOGY AND BIOTECHNOLOGYUNIVERSITY OF THE PHILIPPINES, DILIMAN, QUEZON CITY 1101, PHILIPPINESDATE SUBMITTED: 3 FEBRUARY 2015DATE PERFORMED: 29 JANUARY 2015

INTRODUCTION

A common problem when dealing with measurements is that one or two of the measurements are ‘off’ [1]. To remove the outlier, Grubbs Test was applied to the measurements. Grubb’s Test omits one value that was deemed as an outlier based on a certain calculations.

In the experiment, 10-25 centavo coins were used. Each coin was weighed. An outlier was omitted using Grubb’s Test before calculating different statistics for the data sets.

RESULTS AND DISCUSSION

Among the data found in appendix, the highest and the lowest were chosen for each data set.

For both data sets, sample 1 is the lowest while sample 6 is the highest.Between the two, the one with the highest difference to the data set mean was subjected to Grubb’s Test. For both data sets, sample 6 was chosen.

Grubbs Test equation (1) was used to determine whether sample 6 is an outlier or not, where i is the sample number, xi is the sample weight,x is the data set mean, and s is the standard deviation. The calculated Gexp was compared to the G values found in the appendix.

Gexp=maxi=1…n

|x i−x|s

(1)

Table 1 below shows the result of the Grubbs Test

Table 1. Grubbs TestData Set

Suspect Values

Gtab Gexp Conclusion

1 H:3.7602 1.8872 1.92 RejectL:3.5648 Retain

2 H:3.7602 2.900 2.66 RejectL:3.5648 Retain

Table 4 below show the calculated statistical values for both data set.

Table 3. Reported Statistical Values

Data Set

x S RSD R RR CL

1 3.600 0.027 7.395 0.069 19.17 3.600±0.017

2 3.604 0.020 5.449 0.069 19.14 3.6042±0.043

Give the significance of Grubbs TestGrubbs Test was done so that an outlier can be omitted from the data set. An outlier needs to be omitted because the outlier can cause gross deviation even though it may agree with the rest of the data [2].

Give the significance of the mean and standard deviation

Standard deviation measures the precision of the data. It calculates how close the values are to the mean. The mean is the measure the distribution of the samples. [3]

Give the significance of the confidence intervalThe confidence interval is the interval where the population mean is expected to lie. Confidence interval because an infinite number of values is required to compute for the true value of the population mean [3]

How do the statistics calculated from data set 1 differ from those obtained from data set 2?Since both data sets have the same outlier, their statistical values do not differ greatly. Only the Relative Standard Deviation (RSD) has a relatively huge difference and that is because it is based on the mean and the standard deviation of the data sets.

SUMMARY AND CONCLUSION

The outlier for both data sets is the same. The calculated statistics for each data set do not differ that much because the outlier is the same. Since an outlier was found the application of Grubbs Test and different statistics were successful.

REFERENCES[1] Stats Tutorial - Instrumental Analysis and Calibration. (n.d.). Retrieved February 2, 2015, from http://www.chem.utoronto.ca/co ursenotes/analsci/stats/Outliers.html

[2]Grubbs, F. (1969, February 1). Procedures for Detecting Outlying Observations in Samples. Retrieved February 2, 2015, from http://spider.ipac.caltech.edu/staff/fmasci/home/statistics_refs/OutlierProc_1969.pdf

[3]Skoog, D., & West, D. (1996).Fundamentals of analytical chemistry (7th ed.). Fort Worth: Saunders College Pub.

APPENDIXTable 1. Weight of Samples

Sample No.

Weight, g

1 3.58432 3.61303 3.60634 3.56485 3.63386 3.76027 3.61018 3.61389 3.6010

10 3.6107

Table 2. Values of t for various levels of probabilityN-1 1 2 3 4 5 6 7 8 9 10T90% 6.31 2.92 2.35 2.13 2.02 1.94 1.90 1.86 1.83 1.81T95% 12.7 4.3 3.18 2.78 2.57 2.45 2.36 2.31 2.26 2.23T99% 63.7 9.92 5.84 4.60 4.03 3.71 3.50 3.36 3.25 3.17

Table 3. Critical Values for the Grubbs TestN 3 4 5 6 7 8 9 10

G95% 1.1543 1.4812 1.7150 1.8871 2.0200 2.1266 2.2150 2.900G99% 1.1547 1.4962 1.7637 1.9728 2.1391 2.2744 2.3868 2.4821

Mean, m

x=∑i=1

n

x i

n

Standard Deviation, s

s=√∑i=1n

( xi−x)2

n−1

Relative Standard Deviation, RSD

RSD= sx×1000 ppt

Range, RR=Xhighest−X lowest

Relative Range, RR

Data Set 2

Data Set 1

RR= Rx×1000 ppt

Confidence Interval, CI

Confidence limit= x± ts√n

Sample Calculations

x=3.5843+3.6130+3.6063+3.5648+3.63385

=3.60044≈3.600

RSD=0.0273.600

×1000 ppt=7.395

R=3.6338−3.5648=0.069

RR=0.0693.600

×1000 ppt=19.17