Question

Low density lipoprotein (LDL) levels were measured in the serum of adults from the MM, MN, and NN blood groups. Four males and four females were measured from each blood group. Test for significant differences in LDL due to gender (factor A), blood group (factor B), and test for a significant interaction between gender and blood group. Use a 5% level of significance for each test.

Gender Blood Group

MM MN NN

Male 111 93 96

107 102 88

   98 90 102

112 99 90

Female 103 103 86

96 100 79

107 94 99

90 111 84

Answer 1

Using Minitab software, (Stat -> ANOVA -> General Linear Model -> Fit general linear model), we get the following output :

To test the significance of interaction between Gender and Blood group,

i.e. H₀ : there is no interaction effect on response against H₁ : there is interaction effect on response

we get P-value = 0.108 > 0.05, so we fail to reject the null hypothesis s at 5% level of significance and we can conclude that there is no significant effect of interaction present between Gender and Blood group.

To test the significance of Gender,

i.e. H₀ : there is no effect of Gender on response against H₁ : there is effect of Gender on response

we get P-value = 0.304 > 0.05, so we fail to reject the null hypothesis at 5% level of significance and we can conclude that there is no significant effect of Gender on the response variable.

To test the significance of Blood Group,

i.e. H₀ : there is no effect of Blood Group on response against H₁ : there is effect of Blood group on response

we get P-value = 0.007 < 0.05, so reject the null hypothesis at 5% level of significance and we can conclude that there is significant effect of Gender on the response variable.