Name: Kate Alyssa Caton Date Performed: November 18, 2010Co-Worker: Prem Patrick Parcon Date Submitted: November 26, 2010

Experiment No. 1

Title: Application of Statistical Concepts in the Determination of Weight Variation in Samples

I. Theoretical Framework

Being able to properly evaluate the data and claims that bombard you every day, is one important thing. If you cannot distinguish well from faulty reasoning, then you are vulnerable to manipulation and to decisions that are not in your best interest. Statistics provides tools that you need in order to react intelligently to information you hear or read. In this sense, statistics is one of the most important subject matter.

Statistics, together with chemometrics, is the application of mathematical methods to the solution of chemical problems of all types – is due to the ease with which small or large quantities of data can be handled, and complex calculations done, with calculators and computers. These devices are available to the analytical chemist at several levels of complexity and cost. With the help of statistics, we can check the precision of our experiment and verify its results. It also helps in maintaining the reliability and validity of the data by critically organizing it.

II. Data and Results

A. Weight of Samples

Coin Sample Weight (g)

1 6.0083

Data

Set

2

Data

Set

12 5.38053 5.92424 6.08835 5.45106 6.0768

7 5.2355

8 5.3991

9 6.0938

10 5.4305

Arranged OrderData Set 1 Data Set 2

5.38055.45105.92426.00826.07686.0883

5.23555.38055.39915.43055.45105.92426.07686.00826.08836.0938

B. Q-test

Data Set Suspect Values *Qtab Qexp Remarks

1 (Highest): 6.0883 0.625 0.0162 Accept at 95% confidence level(Lowest): 5.3805 0.625 0.0996 Accept at 95% confidence level

2 (Highest): 6.0938 0.466 0.0064 Accept at 95% confidence level(Lowest): 5.2355 0.466 0.1688 Accept at 95% confidence level

C. Reported Values

Data Sheet S RSD R RR CL PSD1 5.8215 0.3185 0.0547 0.7078 121.5838 5.8215 0.3342

0.10922 5.7080 0.3369 0.0590 0.8584 150.3854 5.7080 0.2408

III. Calculations

(Q-test)

(Reported Values)DATA SET 1 DATA SET 2

Data Set 1(Highest)

(Lowest)

Data Set 2(Highest)

(Lowest)

=5.8215 = 5.7080

S

6.0082 0.1867 0.03485.3805 -0.441 0.19455.9242 0.1027 0.10556.0883 0.2668 0.07125.4510 -0.3705 0.13736.0768 0.2553 0.0652

= 0.3185

= 5.7080

6.0082 0.3002 0.09015.3805 -0.3275 0.10735.9242 0.2162 0.04676.0883 0.3803 0.14465.4510 -0.2570 0.06606.0768 0.3688 0.13605.2355 -0.4725 0.22335.3991 -0.3089 0.09546.0938 0.3858 0.14885.4305 -0.2775 0.0770

=0.3369

RSD

=

=

= 0.0547

=

=

= 0.0590

R= Highest – Lowest=6.0883 – 5.3805= 0.7078

= Highest – Lowest=6.0938 – 5.2355=0.8584

RR

=

=

=121.5838

=

=

= 150.3854

CL

= 5.8215 0.3342 = 5.7080 0.2408

PSD

=

=

= 0.1092

IV. Discussion and Interpretation of Results

Significance of Standard Deviation

Standard deviation is a statistical tool used to determine how tight or spread out your data is. In effect, this is quantitatively calculating your precision, the reproducibility of your data points. It is more useful when compared to range, the difference between the highest and lowest values because it utilizes all the values.

Significance of Confidence Limits

It is important to appreciate that for a significance level of 5% there is still a chance of 5%, or 1 in 20, of incorrectly rejecting the suspect value. This may have a considerable effect on the estimation of the precision of an experiment. The wider the confidence interval, the less precise the data is, and the narrow the interval, the more precise the data is.

Significance of Q-test

Dixon’s test (sometimes called the Q-test) is another test for outliers in which the calculation is simple. For small samples (size 3 to 7) the test assesses a suspect measurement by comparing the difference between it and the measurement nearest to it in size with range of the measurements. The critical values of Q for P = 0.05 for a two-sided test. If the calculated value of Q exceeds the critical value, the suspect value is rejected.

Comparison of statistical parameters calculated from Data Set 1 to Data Set 2

Data set 1 are generally higher than those from the data set 2 using different statistical parameters. This obtained the means of 5.8215 and 5.7080 consecutively. The numbers of data taken for each set, the variations in weight were the most probable considerations. To conclude, the heavier coins were recorded to belong to Data Set 1.

Significance of Pooled Standard deviation

Pooled standard deviation is a statistical tool to find a better estimate of the true standard deviation given several different samples taken in different circumstances where the mean may vary between samples but the true standard deviation is assumed to remain the same. The experimental and control group standard deviations differ only as a result of sampling variation. It is calculated by the equation:

Correlation of the means obtained by our group and others as well.

Among the groups, the obtained average mean varies. Since the samples used are not the same for every group and also because of errors that have been committed by the students during the experiment.

The mean of our group is varies with the other groups in terms of range. Since samples used also vary, the weight of the coin also differ which leads us to the differences in also to different statistical parameters. Errors, also as one consideration that have been committed by the students during the experiment, vary too.

V. Conclusions and Recommendations

Statistical parameters are precisely used in order to appropriately carry out its functions in data analysis and evaluation. Application of these parameters can lead to significant results such as determination of the level of precision, determination of errors and application of quality control especially in an industrial scale. The experiment focused more on the quantitative analysis of the weight variations, in our case, one-peso coin samples. By getting the standard deviation, Q-test, relative range, and other statistic parameters, we were able to determine the precision of our data and we had the chance to compare and contrast our results with the other groups that goes to show, their result vary with ours.

Errors in experiments are impossible to eliminate, but they can still be minimized. This is one importance of using statistical analysis in interpreting quantitative results. It makes us aware of the discrepancies or inconsistencies made in collecting and gathering the data.

I recommend using the same type of samples for this experiment since others used 25-centavo , 5-peso and 10-peso coins. Also, during washing the coins, some students may have not done the exact procedure properly resulting to more variations in data.

VI. ReferencesSkoog, Douglas, et. al. Fundamentals of Analytical Chemistry. 8th Ed. Singapore: Thomson Learning Asia, 2004.

Statistics in relation with Analytical Chemistry. Retrieved at http://www.britannica.com/EBchecked/topic/132013/confidence-limit

http://science.widener.edu/svb/stats/descript.html

Encarta 2008