NEAR IR SURFACTANT ANALYSIS 447 Automatic Volatility Computer. Moisture was determined via Karl Fischer titration. Benzoic acid (Aldrich, Milwaukee, WI) was determined spectrophotometrically using the method of standard addition in the ultraviolet range at 222 rim. Viscosity was measured using a Brookfield Model RVTD viscometer at a speed of 20 rpm for 3 minutes and spindle 3 at 80øF. DATA ANALYSIS The raw optical data was subjected to step-up multiple linear regression search for one to nine wavelengths. Plots of the standard error of calibration (SEC) (difference between the primary analysis and the optical predictions can also be referred to as standard error of estimate (SEE)) and F-level (ratio of variances which gives an indication of the ro- bustness of regression) were constructed versus the number of wavelengths. The final number of wavelengths chosen for best correlation with each primary constituent ana- lyzed was determined to be that number which gave the highest F-level and corre- spondingly smallest SEC. Figure 1 indicates that the maximum number of wavelengths for statistical significance in predicting the active detergent in ammonium lauryl sulfate is five. The raw data were then subjected to an all-possible-combination (combo) search F-LEVEL ß SEE -t -.8 -.6 -.4 -.2 • "' •" • • • • i 0 t 2 13 •4 5 15 7 8 9 t0 NUNBER OF NAVELENGTHS Figure 1. Plot of statistical parameters of F-level and standard error of calibration used to determine maximum number of wavelengths before overfitting of data occurs for the active detergent prediction in ALS.

448 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS Table I Calculation of Pooled Standard Deviation for CEM Volatility Computer Sample Duplicate d d 2 1 30.42 30.61 0.19 0.04 2 31.01 31.45 0.44 0.19 3 30.05 30.40 0.35 0.12 4 29.60 29.65 0.05 0 5 30.70 31.16 0.46 0.21 6 31.56 31.40 0.16 0.03 7 30.52 30.57 0.05 0 8 30.45 30.70 0.25 0.06 9 29.88 30.05 0.17 0.03 10 29.35 29.34 0.01 0 TOTAL 0.68 N = 10. PSD = 0.17. using the above-determined maximum number of wavelengths for all 700 data points. A combo search was also done using only those wavelengths which could be transferred to a wavelength filter-based instrument. Often the combo search required fewer wave- lengths for robustness than did the step-up search. Indicator variables were used to tag the various Brand X types. These were added to the regression analysis to account for any physical difference such as color or fragrance that might affect the sample set but were not quantitated. Spectra from various color and fragrance variants of both brand types of shampoo were stored as separate data files. From these files the program PICKS (8), a method of spectral subtraction, was used to select the ten most spectrally unique samples from those in the larger pool. These samples were then combined into a shampoo variety calibration set on which primary analyses were performed. Ten random samples of each of the above were used for the prediction/validation set. The results were wavelengths and their coefficients in the form of equation 1 for each constituent measured by chemical analysis. The coefficient of correlation (r) relating the fit of near infrared predictions versus primary laboratory analyses was also obtained for each constituent. The standard error of prediction (SEP) on a sample set not included in the training set was used for verification. Table II Standard Deviations of Lab Analyses Analysis PSD RSD Potentiometric Active Titration 0.31 0.21 Volatility Computer 0.17 0.31 Karl Fischer Moisture Titration 2.79 3.00 Ultraviolet -* 0.01 Not run in duplicate.