PROTEUS

              

 

 

 

 

 

 

 

Back to ENH440 Problems & Solutions

Solution in detail: # 45

Ho1: no effect on hygiene score due to frequency of inspection

Ho2: no effect on hygiene score due to size of restaurant

Ho3: no interaction between freq and size in terms of hygiene score

 

(Calculations added Oct 16):

 Tot SS   =     995.00  _   1312

                                      18

            =         41.6112

 AllGr SS =     182 + 192 + 212 + 232 + 202 + 202 + 302  _   1312      

                      3       3       3       3       3       3        3          18 

             =          984.9993  -  953.3888             =      31.6104

 Freqency SS  =    372  +  442  +  502  _    1312     

                                        6                    18    

                    =      5805  _  1312    =    967.500 - 953.3888   =    14.1112

                              6         18

 Size SS  =      592   +   722     _    1312 

                               9                  18

                      962.7778  -  953.3888   =    9.3889       

 Freq x Size SS  =    31.610 - 14.111 - 9.389   =   8.110

 

 Residual SS  =     41.6112  - 31.6104   =   10.0008

 

 

source        SS           df         MS           F              P     

Groups     31.610        5         

freq         14.111        2       7.056        8.471     P <  0.01 

size          9.389         1       9.389       11.271    P <  0.01

fr x size    8.110         2       4.055        4.868     P < 0.05 

Resid       10.001       12       0.833                              

Total       41.61         17  

   

Ho1:  no effect on hygiene due to frequency

 F(calc):  MS(fr) / MS(res) = 8.471        F(0.01)(2,12): 6.69    Reject Ho1  (P<0.01)  

 

 Ho2:  no effect on hygiene due to size

 F(calc):  MS(size) / MS(res) = 11.271       F(0.01)(1,12): 9.33     Reject  Ho2    (P<0.01)

 

 H03:  no interaction between frequency and size in terms of hygiene

 F(calc):  MS(frXsize) / MS(res) = 4.868     F(0.05)(2,12): 4.75     Reject Ho3    (P<0.05)

 

Interaction is present.  Effects of the two main factors will each be described in detail for each of the levels of the other factor.

Frequency:   Overall, this was found to have a statistically significant (P<0.01) effect upon hygiene score.  Low freq had lowest hygiene scpore (mean: 6.165) and high freq the highest/best hyg score (mean: 8.34).  Within each the size categories, however, the freq effect was different.  In small restaurants, the best score was in med freq premises (7.0), with higher and lower freq premises showing lower scores (6.0 and 6.3 respectively).  In Large size restaurants the high freq premises achieved the best score of 10, med freq scored 7,7 and low freq the worst score at 6.7

Size:  Overall, the effect was statistically significant (P<0.01). Small premises showed a mean of 6.67 and large premises a mean of 8.0.  Within the freq categories, however, the size effect varied.  Low freq: large had very slightly greater score than small (6.3. v 6.0).  Med freq: large had slightly higher than small (7.7 v 7.0). But in high freq premises, the Large prem achieved the highest score (10.0) whereas small prem recorded only 6.7)

 

Clearly larger premises appear to benefit from increased inspection frequency, but this effect was not as evident among small premises.  

 

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    <6         7-11       12+

          small size

    <6        7-11        12+

        large size

 

     S                L

           <6/YR

     S                 L

            7-11 /YR

     S                 L

            12+/YR