1. Experiment 5: Statistical Evaluation of Acid-Base Indicators
Presentation by Natalie Chhim

2. Acid-Base Indicators
Acid-base indicators are themselves, acids or bases, and their protonated species have different colors. This experiment tested 5 different indicators, each with their own change in colors and transition ranges. The accuracy of each indicator’s ability to locate the end-point of a titration were compared using several statistical analytical techniques.

3. The Experiment
The purpose of this experiment was to introduce statistical analysis methods through the use of acid-base indicators. Each student was given a different pair of indicators to use in the titration of “tris” (tris(hydroxymethyl)aminomethane) with the same unstandardized solution of 0.1 M HCl. Each student performed at least 6 trials per pair of indicators and the class’ data was pooled.
With the individual data, the Q test was performed to determine if any of the trials should be excluded from statistical analysis, and from those remaining trials, the mean, standard deviation and relative standard deviation were calculated.

4. Qcalculated=gap/range (Eq. 4-13),
The Q test
Sample Data: HCl molarities (M)
The Q test is used to determine if certain pieces of data can be discarded.
Qcalculated=gap/range (Eq. 4-13),
where the gap is the difference between the questionable point and the nearest value and the range is the distance between the greatest and lowest value of data. If Qcalculated > Qtable, then the value can be discarded, if Qcalculated < Qtable, the data point can be kept.
.1048
.1028
.0943
.1051
.1059
.1032

5. The Experiment (cont’d)
For the pooled data, the mean HCl molarity, standard deviation, relative standard deviation and pooled standard deviation were calculated per each student’s pair of indicators. The t test was performed at the 95% confidence interval on the student’s pair of indicators to determine whether their average molarities were significantly different from each other.

6. Pooled Standard Deviation
spooled= [(Σ1(xi-x1avg)2+Σ2(xj-x2avg)2)/(n1+n2–2)]1/2
(Eq. 4-9)
Standard deviation is the measurement of how closely the data are clustered about the mean. Pooled standard deviation is used with two sets of replicate data.
The sum of the squared deviations from the mean for each set are added, then divided by the degrees of freedom, where n1 and n2 are the number of measurements for set 1 and set 2. Finally, the result is square-rooted.

7. tcalculated = [| x1avg - x2avg|/ spooled]x[n1n2/(n1+n2)]1/2
The t test
The t test is used to decide whether the two sets of replicate data give similar or different results within a confidence interval. As with the Q test, if tcalculated < ttable, then the two sets are statistically the same. If tcalculated > ttable, then the two sets are statistically different.
tcalculated = [| x1avg - x2avg|/ spooled]x[n1n2/(n1+n2)]1/2
(Eq. 4-8)
The absolute value of the difference between the mean of each set is divided by the spooled. Then it is multiplied by the square-root of the product of the number of measurements for each set, divided by the total number of measurements.

8. Question
What is the difference between the Q test and the t test? What is each test used to analyze?

9. Answer
The Q test is used to determine whether certain data values can be excluded when performing a statistical analysis. The t test is used to compare two sets of replicate data and determine whether they are significantly different.