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One Way ANOVA: Bone-density Measurements

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It is believed that women in the post menopausal phase of life suffer from calcium deficiency. This is associated with a relatively high proportion of bone fractures were women in that age group. To determine this calcium deficiency is associated with estrogen deficiency, data were collected from three groups of women.

The first 14 women had undergone oophorectomy during adult womanhood and had lived for 15-25 years with an estrogen deficiency. A second group was identified as premenopausal, approximately same age as the previous group, except that they had never suffered a period of estrogen deficiency. The third group of 14 women were postmenopausal and had suffered estrogen deficiency for an average of 20 years. Means and standard deviations given below:

Group1: Mean= 0.93 SD= 0.52 n=14
Group2: Mean= 1.21 SD=0.39 n=14
Group3: Mean= 0.92 SD=0.52 n=14

Is there sufficient evidence to permit us to conclude that the mean bone-density measurements differ for the three groups of women? What can you conclude at the =0.05 level?

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The solution provides step by step method for the calculation of one-way ANOVA. Formula for the calculation and Interpretations of the results are also included.

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