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

Result:

a).

SUMMARY	Meat	Legumes	Vegetables	Total
Aluminum
n	4	4	4	12
Average	2.0575	2.33	1.2325	1.873333
sd	0.251976	0.111056	0.231283	0.522274
Clay
n	4	4	4	12
Average	2.1775	2.4725	1.46	2.036667
sd	0.621309	0.071356	0.460072	0.601337
Iron
n	4	4	4	12
Average	4.68	3.67	2.79	3.713333
sd	0.628278	0.172627	0.239861	0.884291
Total
n	12	12	12
Average	2.971667	2.824167	1.8275
sd	1.350824	0.637815	0.776357

b).

The plot shows the lines are crossing. The iron content depends on type of pot.

c).

ANOVA table
Source	SS	df	MS	F	p-value
Factor 1 (type of pot)	24.8940	2	12.44698	92.26	0.0000
Factor 2 (iron content)	9.2969	2	4.64844	34.46	0.0000
Interaction	2.6404	4	0.66011	4.89	.0042
Error	3.6425	27	0.13491
Total	40.4738	35

To test for pot effect, calculated F=92.26, P=0.0000 which is < 0.05 level. The pot effect is significant.

To test for iron content effect, calculated F=34.46, P=0.0000 which is < 0.05 level. The iron content effect is significant.

To test for interaction effect, calculated F=4.89, P=0.0042 which is < 0.05 level. The interaction effect is significant.