A study was performed to relate aspects of childhood diet to measurements of bon

Question

A study was performed to relate aspects of childhood diet to measurements of bone density in middle age (50- to 70-year-old) women. The data in Table 4 were reported from a Norwegian study relating cod liver oil supplementation in childhood to bone mineral density (BMD) in the distal forearm.

Table 4. Cod liver oil intake during childhood.

a) The one-way ANOVA test is performed for the four groups and reported in Table 5.

We are interested to compare women who used cod liver oil for the entire year during childhood vs. women who never used it.

i) Perform this comparison using the LSD method, and report a p- value;

ii) Perform this comparison using the Bonferroni method. Are the results significant at the 5% level after Bonferroni correction? Why or why not? Assume that the tdf distribution is the same as an N(0,1) distribution of df ? 200.

Explanation / Answer

1) The t critical value for alpha=0.05, dfw=2850 is 3.34.

LSD=t0.05/2,dfwsqrt[MSW(1/n1+1/n2), where n1 and n2 represent women who used cod liver oil for entire year during chilhood and who never used it.

=3.34sqrt[0.0038(1/237+1/267)]

=0.0184

If |whole year bar-never bar|>=LSD, reject H0,

|0.420-0.435|=0.015<0.0184, therefore, fail to reject H0.

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