Previous studies suggest that vegetarians may not receive en

Previous studies suggest that vegetarians may not receive enough zinc in their diets. As the zinc requirement is particularly important during pregnancy, researchers conducted a study to determine whether vegetarian pregnant women are at greater risk from low zinc levels than are nonvegetarian pregnant women. Twenty-three women were monitored: twelve vegetarians who were pregnant, six nonvegetarians who were pregnant and five vegetarians who were not pregnant. None of these women were smokers, and none of the nonpregnant women were taking oral contraceptives (I’m not sure why that might be even important..that information was just provided -> perhaps they influence zinc levels?). The zinc status in each woman was measured by zinc content in the blood, urine, and hair. The following table presents the zinc level in the hair (Data from King et al., 1981. American Journal of Clinical Nutrition 34: 1049-1055). Pregnant Nonvegetarians (Population 1) Pregnant Vegetarians (Population 2) Nonpregnant Vegetarians (Population 3) 185 171 210 189 174 139 187 202 172 181 171 198 150 207 177 176 125 189 179 163 174 184 186 Check the basic ANOVA assumption using a residual plot and modified Levene\'s test. What would you conclude? Carry on with this problem assuming that there is no need to transform the data. Consider the following null hypotheses: Ho: m1 - 1/2 m2 - 1/2 m3 = 0 Ho: m2 - m3 = 0 Describe (in layperson terms) what two hypotheses are being tested. Carry out the two-tailed tests and draw some conclusions.

Solution

ANSWER: df (Between Groups) = 3 [ there are three groups so that df = 3 -1 = 2]

ANSWER: df (Within Groups) = 19 [ (seven -1) + (ten - 1) + (five -1)]

ANSWER: Reject Null Hypothsis the Groups are the same due to 91.6% likelihood the groups are difference.

SUPPORT COMPUTATIONS
Anova: Single Factor

SUMMARY
Groups Count Sum Average Variance
Pregnant nonvegetarians 7 1345 192.1428571 174.80…
Pregnant Vegetarians 10 1689 168.9 380.5444444
Nonpregnant vegetarians 5 830 166 513


ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 2825.333766 3 941.7779221 2.59770…
Within Groups 6525.757143 18 362.5420635

Total 9351.090909 21