B-2 APPENDIX B 



Methods of Analysis 



Inspection of the data indicated that, with a few obvious and correctible exceptions, the 

 differences among test laboratories were negligible. The balanced part of the data could then 

 be viewed as a full single replicate of a '43" experiment, with four materials, four fabri- 

 cators and four thicknesses. But it was known beforehand that the several types of material 

 would not have the same random variation, nor would they respond in the same way to the 

 several factors. 



The five materials used were grouped into three sets. Ml and M4, mat and cloth faced 

 mat were put in one group; M2 and M5, woven roving and cloth faced woven roving, were put 

 in another group; and finally M3, 10 ounce cloth, was put by itself in the third group. The 

 two pairs behaved sufficiently alike to justify this grouping. 



Secondly, the largely isotropic Ml and M4 measurements for all three angles were 

 analyzed together. Although M2 and M5 were by no means isotropic, it was possible to 

 analyze the degrees and 90 degrees data together in all cases. For some properties the 

 45 degrees data could be included in the same analysis. 



For Ml and M4, then, we have a split-plot analysis, with angle and its interactions as 

 sub-plot variables. Similarly for M2 and M5. A typical example is given below. 



If the error distribution is normal, the cumulative distribution of the specimen ranges 

 should be the "half-normal ' distribution. The empirical cumulative distribution (called ecd ' 

 hereafter) should then fit a straight line on a half -normal grid. Such a plot was made for 

 every set of duplicate specimen ranges. In some cases all ranges fell nicely on a straight 

 line. In most cases, however, a small proportion of excessive values, not fitting the pattern 

 set by the rest, was found. The number of such coupon mavericks is shown in the columns 

 headed "c" and in lines "e", in the Table of Standard Deviations, Table B-l. These values 

 were excluded from later analysis. As an example the plot for Ml and M4 tensile strength 

 specimen ranges is shown in Fig. B-l. 



A similar half-normal plot was made for the panel ranges in each grouping with similar 

 conclusions. But since there were so few duplicate comparable panels, it is not often possi- 

 ble to speak of the pattern set or of the assured reliability of the corresponding distribution. 

 The results are shown in the columns headed "d" in the Table of Standard Deviations, Table 

 B-l. Fig. B-2 is an example of such an "ecd". 



As a numerical example the analysis of tensile strengths for materials Ml and M4 for 

 all three angles is given below. 



First a full MxFxTxA table, with two materials, four fabricators, four thicknesses, 

 three angles and with all subtotals and differences was made up. 



From the table above, the analysis of variance, shown in Table B-2 was computed. 

 All computations were written down, and the FxT and MxFxT discrepancies were 

 all computed for inspection. (For several other properties some bad values were 

 discovered from these discrepance tables). 



There were clear material and fabricator differences and there was an MxA inter- 

 action. The latter was expected, being due to the anisotropy of the M4 cloth faced mat 

 compared to the isotropy of the Ml mat. The conclusions must reflect these differences. 



