The article \"effects of household fabric softeners on thermal comfort of ctton

Question

The article "effects of household fabric softeners on thermal comfort of ctton and polyester fabrics after repeated launderings" (Family and Consumer Science Research J., 2009: 535-549) reported the results of a three-factor ANOVA carried out to investigate the impact of fabric softener treatments (A: no softener, rinse-cycle softener, dryer-sheet softener), fabric type (B: 100% cotton, 100% polyester), and number of laundering cycles (C:1, 5, 25) on air permeability of fabric, which is an important determinant of thermal comfort. a.) Five observations were made for each combination of factor levels. Resulting sums of squares were SSA=1043.27, SSB=112,148.10, SSC=3020.97, SSABC=54.13, SSE=339.30. Create an ANOVA table and carry out tests of all relevant hypotheses using a significance level of 0.01. b.) Because the test for the presence of three-factor interactions is insignificant, it makes sense to investigate two-factor interactions. Use the following values of various sample means to create interaction plots, and comment as to whether they are consistent with the test results of (a).

The solutions says "f_ABC=2.87, P-value=0.029 for testing H_0ABC. However, all two-factor interaction F ratios are highly significant"

A1 A2 A3 B1 67.10 56.50 65.93 B2 138.00 131.93 131.40 C1 110.25 105.55 103.30 C2 101.80 90.45 97.10 C3 95.60 86.65 95.60

Explanation / Answer

(a)

For B and C the null hypothesis is reject.

(b)

SS DF MS F Fcritcal A 1043.27 2 521.635 9.224315 10.92477 B 112148.1 1 112148.1 1983.167 8.683117 C 3020.97 2 1510.485 111.6191 6.358873 ABC 54.13 4 13.5325 0.239302 4.89321 Sse 339.3 6 56.55 Total 116605.8 15

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