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

K. MANGONON1

1 INSTITUTE OF CHEMISTRY, COLLEGE OF SCIENCEUNIVERSITY OF THE PHILIPPINES, DILIMAN, QUEZON CITY 1101, PHILIPPINESDATE SUBMITTED: 2 FEBRUARY 2016DATE PERFORMED: 28 JANUARY 2016

ANSWERS TO QUESTIONS

1. Give the significance of Grubbs test.During experiments, using proper laboratory methods should yield data values that are expected to be accurate and precise. However, in data sets with numerous trials, getting a value which is quantitatively different from the rest, an “outlier”, is inevitable. An inconsistent data point is termed as the suspected outlier. The suspected outlier can significantly influence the statistic values, giving an inaccurate representation of the entire sample [1]. One may opt to reject the outlier from the rest of the values by using the Grubbs test.

The formula used by the Grubbs test basically compares the distance of the outlier to the supposed allowance of a data point’s deviation from the mean. The Grubbs test also takes into account the confidence level to decide the limit of the calculated g value in a given set of tabulated g expected values for the rejection of the outlier. The inconsistent data point would then be analyzed to find out if whether an error of any type (method, instrumental or operative) was produced [1]. It can point out the possible contaminations or errors in execution from the experiment administration, which will help in the evaluation of the methodology.

2. Give the significance of the mean and standard deviation.

The mean, is a statistical tool that gets the average of all the values in the data set. Termed as a measure of central tendency, one can use it in comparison with a data point to note the data point’s distance from the center. However, it lacks to quantify the distribution of the data values from the mean. According to Steele (2006), the standard deviation can be used to determine the “scatter” of the values around the mean [4].

When gathering data, these sample statistics are vital when evaluating the accuracy and precision of the set. When the mean is analyzed, it gives a mock bull’s eye value in a data set. Simply put, all the other values circulate around the central mean value. Although it is a general characteristic (which may not be accurate if the data set has outliers), it can imply the accuracy of a particular data point. The standard deviation quantifies the precision of the data. If the mean was a mock bull’s eye value, the standard deviation points out how close the gathered values are about the mean. From the mean, it can imply a theoretical range of where to expect the values. The standard deviation is an important way to know if the method used in the experiment is prone to produce outliers, or to give meaningful data values.3. Give the significance of the confidence interval.According to Easton & McColl (n.d.), the confidence interval is considered as an

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estimated range in which there is a degree of certainty (noted by the confidence level) that it contains a population parameter [2]. While the computed range of values only target the population parameter in an estimate, it can pave way for how well the parameter can be concluded from a sample statistic. Note that the confidence interval computed can also have a limited scope. When a specific confidence interval is wide, which encompasses a large portion of the sample, it can denote that there is an uncertainty on where the pinpoint the “correct” population parameter [3]. It is then suggested to take different samples, to define a more precise and defined interval. This can then produce a certain estimate can be accurate in determining a desired population parameter.

4. How do the statistics calculated from data set 1 differ from those obtained from data set 2?The conditions of the two data sets were that the number of data values in data set 1 is six (6) while data set 2 has ten (10). In comparison, data set 1 had a smaller standard deviation compared to data set 2, with a much more limited range of data for analysis of values. In comparing the confidence intervals of both data sets, data set 2 has a smaller confidence interval, although it has a higher value for standard deviation. This means that although the dispersion of the data values in data set 1 is more clumped together, the estimate of the real population parameter is still more uncertain in it, compared to data set 2.

REFERENCES

[1] Alfassi, Z. B., Boger, Z., & Ronen, Y. (2005.) Statistical treatment of analytical data. Florida, USA: CRC Press LLC.

[2] Easton, V. J. & McColl, J. H. (n.d.). Statistics glossary: Confidence intervals. Retrieved February 2, 2016 from http://www.stats.gla.ac.uk/steps/ glossary/confidence_intervals.html

[3] GraphPad Software, Inc. (2015). Interpreting a confidence interval of a

mean. Retrieved February 2, 2016 from http://www.graphpad.com/guides/ prism/6/statistics/index.htm?stat_more_about_ confidence_interval.htm

[4] Steele, G. W. (2006). Statistical considerations in sampling and testing. Significance of Tests and Properties of Concrete and Concrete-making Materials, (169), 23.

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