Question

do all pairwise comparisons using the bonferroni method

11.4.2 It is thought that stress may increase susceptibility to illness through suppression of the immune system. In an experiment to investigate this theory, 48 rats were ran- domly allocated to four treatment groups: no stress, mild stress, moderate stress, and high stress. The stress condi tions involved various amounts of restraint and electric shock. The concentration oflymphocytes (ceils/ml x 10-0) in t pesipheral blood was measured for each raž, wIn the s -given in the acccapanying tabte 4 Caicuiations oses rav data yielded SS(oetw S2 within)340 24. veen) 89.036 sd NoMild Moderate High stress 2.92 1.45 stress 6.64 stress stress 4.84 2.772.42 3.98 3.91 12 12 12 /n 12

Answer 1

no. of treatment , k =   4
df between = k-1 =    3
N = Σn =   48
df within = N-k =   44

mean square within groups , MSW = SSW/N-k = 340.1189/44 = 7.73

The Bonferroni correction sets the significance cut-off at α/n = 0.05/6 = 0.0083

where n is number of comparisons = 6

Level of significance	0.0083
no. of treatments,k	4
DF error =N-k=	44
MSE	7.730
t-critical value,t(α/2,df)	2.763

Bonfenorni critical value=tα/2,df √(MSE(1/ni+1/nj))

if absolute difference of means > critical value,means are significnantly different ,otherwise not                      
                      

population mean difference		critical value			result
µ1-µ2	1.800	3.1359			means are not different
µ1-µ3	2.660	3.1359			means are not different
µ1-µ4	3.720	3.1359			means are different
µ2-µ3	0.860	3.1359			means are not different
µ2-µ4	1.920	3.1359			means are not different
µ3-µ4	1.060	3.1359			means are not different

means of no stress and High stress is significant different