H_o2  :   no difference between humidity in terms of dust particles/cm³  (₁ = ₂)

    H_o3 : no interaction between these main effects in terms of dust particles/cm³

 source of    sum of     degrees of      mean      F ratio        P

 variation    squares     freedom        square                       

 ~~~~~~~~    ~~~~~~     ~~~~~~~~~     ~~~~~~~    ~~~~~~     ~~~~~~~~~

 all groups     134.00             3       

 filters            25.00             1           25.00        15.79      <0.01        

 humidity         9.00             1             9.00          5.85      <0.05 

 FxH  inter     100.00            1          100.00          63.17    <0.01

 residual          19.00          12             1.583       

 Total            153.00          15   

 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

 Interaction F ratio =  MS_(inter)÷ MS_(resid)  = 63.17     

                                      F_{(0.01, 1,12df)} >9.33    .... reject H_o      

 Filters F ratio =  MS_(filters)÷ MS_(resid)  = 15.79     

                                      F_{(0.01, 1,12df)} >9.33      .... reject H_o  

 Humidity F ratio =  MS_(humid)÷ MS_(resid)  = 5.85     

                                      F_{(0.05, 2,54df)} >4.75       .... reject H_o  

 Interaction.    Interaction was observed (stat.sig at 0.01), so the effect of each main variable will be reported

   separately within each level of the other variable.   F: 63.17, 1,12 df.  P<0.01  

 Filters.  The two filters produced results that were different.  In High humidity conditions the Z filter captured more  dust particles/cm³ (mean: 45) than the Y filter (mean: 35).  Under Low humidity conditions, the effect is rever sed, with the Y filter more effective (mean: 49) than the Z filter (mean 19).  Although the overall "filter effect" is statistically significant ( F: 15.79, 1,12 df. P<0.01), the statement is not reliable due to the interaction present.

 Humidity.  Humidity effected the filter performance considerably.  Low humidity produced a better result (mean 49) than the High humidity (mean: 35) when the Y filter was used.  But high humidity produced a better result (mean 45) than low humidity (mean 19), when the Z filter was used.  Although the overall "humidity effect" statistically significant (F: 5.85, 1,12 df. P<0.05) the statement may not be reliable because of the interaction present.

 In summary,  the Z filter is preferred for high humidity conditions, while the Y filter is preferred for low humidity conditions.