Question

Iron-deficiency anemia is the most common form of malnutrition in developing countries, affecting about 50% of children and women and 25% of men. Iron pots for cooking foods had traditionally been used in many of these countries, but they have been largely replaced by aluminum pots, which are cheaper and lighter. Some research has suggested that food cooked in iron pots will contain more iron than food cooked in other types of pots. One study designed to investigate this issue compared the iron content of some Ethiopian foods cooked in aluminum, clay, and iron pots. Foods considered were yesiga wet', beef cut into small pieces and prepared with several Ethiopian spices; shiro wet', a legume-based mixture of chickpea flour and Ethiopian spiced pepper; and ye-atkilt allych'a, a lightly spiced vegetable casserole. Four samples of each food were cooked in each type of pot. The iron in the food is measured in milligrams of iron per 100 grams of cooked food. The data are shown in the table below.

		Iron Content (mg/100 g) of Food Cooked in Different Pots
Type of pot		Meat					Legumes					Vegetables
Aluminum		1.77	2.36	1.96	2.14		2.40	2.17	2.41	2.34		1.03	1.53	1.07	1.30
Clay		2.27	1.28	2.48	2.68		2.41	2.43	2.57	2.48		1.55	0.79	1.68	1.82
Iron		5.27	5.17	4.06	4.22		3.69	3.43	3.84	3.72		2.45	2.99	2.80	2.92

(a) Make a table giving the sample size, mean, and standard deviation for each type of pot. Is it reasonable to pool the variances? Although the standard deviations vary more than we would like, this is partially due to the small sample sizes, and we will proceed with the analysis of variance.

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(b) Plot the means. Give a short summary of how the iron content of foods depends upon the cooking pot.

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(c) Run the analysis of variance. Give the ANOVA table, the F statistics with degrees of freedom and P-values, and your conclusions regarding the hypotheses about main effects and interactions.

Answer 1

a)

Type of pot

	Mean1	StDev1	N1
Aluminum	1.873333	0.522274	12
Clay	2.036667	0.601337	12
Iron	3.713333	0.884291	12

Make a table giving the sample size, mean, and standard deviation for each type of pot.

It is reasonable to pool the variances because the maximum standard deviation is less than twice the minimum variance.

No, the standard deviations do not vary more than we would like, this is partially due to the small sample sizes, and we will proceed with the analysis of variance.

b)

From the above plot, we can see that the mean for iron content at pots Aluminum and Clay are approximately equal whereas the mean of the iron contains in iron pot is differently larger than the remaining two means.

c)

Two-way ANOVA: Iron versus Pot, Food

Source	DF	SS	MS	F	P
Pot	2	24.894	12.4470	92.26	0.000
Food	2	9.2969	4.6484	34.46	0.000
Interaction	4	2.6404	0.6601	4.89	0.004
Error	27	3.6425	0.1349
Total	35	40.4738

S = 0.3673 R-Sq = 91.00% R-Sq(adj) = 88.33%

Conclusion: The estimated p-value for interaction is 0.004 and less than 0.05. hence, we can conclude that there is an interaction effect for types of pot and types of food at the iron contain on food cook at the 0.05 significance level.

The p-value for both the main effect types of pot and types of Food are less than 0.05. Hence, both the main effects have a significant effect on the food cooked.