Lab Assignment: Data Analysis
CH3360: Instrumental Analysis
Plymouth State University
The final result of an instrumental analysis is often a series of numbers determined by the
instrument. It is imperative as an operator that you interpret and analyze these data. Statistical analysis
of data enables you to determine how likely it is that your result is reflective of the “true” answer. In
this assignment you will perform three analyses:
1. Linear regression
2. Test for outliers
3. Comparison of Means
Instructions
1. Download the Excel spreadsheet “DataAnalysis.xls” from the course website.
2. Save the spreadsheet with your name (ie Name-DataAnlysis.xls).
3. Download the Excel spreadsheet with your assigned data (DataAnalysis-data-X.xls)
4. Copy the data from the data worksheet into your worksheet. Note there are 3 tabs in each
spreadsheet containing data: “Linear Regression,” “Outliers,” and “MethodValidation.”
5. Analyze the data in each of the three “experiments,” as outlined below.
6. Save the spreadsheet. Make sure you name is in the spreadsheet and appears in the filename.
7. Submit the spreadsheet to me via Blackboard by midnight, Feb 18.
Note: You may find the following websites useful for this assignment:
http://chemistry1.che.georgiasouthern.edu/chem2031/Data/Data1/data1.html
http://www.chemistry.nmsu.edu/studntres/chem435/Assignment/
Linear Regression
A student conducted a kinetics experiment to determine what factors are important in the rate of a
reaction. The progress of the reaction was monitored by measuring the volume of gas (in mL)
generated every minute for 20 minutes.
Use your Excel spreadsheet to do the following:
1. Calculate the slope, intercept, and R2 for the best fit line of the data.
2. Calculate the “best fit y-values” for the trendline. (Note: it is possible to have Excel
automatically generate a trendline from a scatter plot, but you must calculate the theoretical y-
values this way for the next calculation).
3. Calculate vertical deviation between each experimental and theoretical y-value (di)
4. Calculate the squares of your x-values and vertical deviations (xi2 and di2).
5. Calculate the number of data and the sums of xi, xi2 and di2.
6. Calculate the denominator used for standard deviations of slope and intercept (D).
7. Calculate the standard deviation of the y-value deviations (sy)
8. Calculate the standard deviation of the slope and intercept of the best fit line.
9. Provide the formula for the best fit line in the form: y ±s y =[ m±sm ] x [b ±sb ]
10. Make a scatter plot of volume of gas versus time. Make sure the plot has the following
features:
y axis showing volume in mL, x axis showing time in minutes
no lines connecting the data points
plot created inside the “Linear Regression” workbook a proper title
labeled axes
no gridlines
a colorless background to the plot
the trendline from the calculated theoretical y-values, connected by dashed line
Outliers
A student used a UV-Vis spectrophotometer to find the molar absorptivity ( in M -1·cm-1) of a newly
synthesized compound. Use your spreadsheet to do the following:
1. Sort the data from smallest to largest.
2. Use built-in functions to count the number of data points and find the largest and smallest
values.
3. Calculate the degrees of freedom, mean, and standard deviation
4. Develop a table of Student’s t values for 90%, 95%, and 99% confidence intervals for 1-100
degrees of freedom (you may skip every 5 or 10 above 25 degrees of freedom).
5. Perform Grubb’s and Dixon’s tests for outliers (calculate Gcalc and Qcalc).
6. Reject one outlier, if appropriate (Note: both Grubb’s and Dixon’s tests can only reject one
outlier at a time. If one outlier is rejected, the mean and standard deviation must be re-
calculated for the remaining data).
7. Sort the data, with the outlier rejected, from smalled to largest.
8. Re-calculate the number of data points, degrees of freedom, mean, and standard deviation for
the Analyzed Data
9. Find the 95% confidence interval for the mean of the Analyzed Data.
Method Validation
A researcher wishes to determine whether a new method of analysis yields better results than the old
standard method. Use your spreadsheet to do the following:
1. Calculate the number of data points, degrees of freedom, mean, and standard deviation for the
data from both methods
2. Calculate the pooled standard deviation (spooled) for the two sets of data.
3. Calculate t for the two sets of data.
4. Look up the 95% confidence value of ttable in the table of Student’s t you constructed in the
“Outliers” worksheet.
5. Run the t-test (compare the two values of t) to determine whether Method 2 yields a
significantly different result than Method 1 with 95% confidence.
6. Consider whether Method 2 is more precise than Method 1 by comparing the standard
deviations.
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