Question

hi I need to perform a post-hoc analysis using the bonferroni method of comparison and explain the results. I need walked through this in clear simple steps using the following information: using an alpha of 0.05

Average college debt at graduation

N.Y.- 14734, 16000, 14347, 14392, 12500

Virginia-14524, 15176, 12665, 12591, 18385

Cali- 13171, 14431, 14689, 13788, 15297

Penn.- 18105, 17051, 16103, 22400, 17976

i have set up the ANOVA table:

treatment ss: 56889041 df 3 MS 18963013.7 F- 5.543 p-value 0.008

error 54737476.8 df 16 MS 3421092.3

totals SS 11626517.8 df 20

Answer 1

alpha=0.05

number of comparisons = no. of treatment*(no. of treatment-1)/2 = 4*3/2 = 6

The Bonferroni correction sets the significance cut-off at α/n. = 0.05/6=0.00833

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	N.Y	Virginia	Cali	Penn
count, ni =	5	5	5	5
mean , x̅ i =	14394.600	14668.200	14275.200	18327.000

Level of significance	0.0083333
no. of treatments,k	4
DF error =N-k=	16
MSE	3421092.30
t-critical value,t(α/2,df)	3.0083339

Bonferroni critical value=t(α/2,df) √(MSE(1/ni+1/nj))

since all treatment are of equal size,so,

Bonferroni critical value=3.008*√(3421092.3*(1/5+1/5)) = 3519.1552
if absolute difference of means > critical value,means are significnantly different ,otherwise not                      
                      

absolute mean difference		critical value			result
µ1-µ2	273.600	3519.1552			means are not different
µ1-µ3	119.400	3519.1552			means are not different
µ1-µ4	3932.400	3519.1552			means are different
µ2-µ3	393.000	3519.1552			means are not different
µ2-µ4	3658.800	3519.1552			means are different
µ3-µ4	4051.800	3519.1552			means are different

-----------please revert for doubts