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

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

(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) The table giving the sample size (count), mean and standard deviation for each pot type is as shown (Use Excel):

1. Table 1:

		Count	Mean	Std Deviation
Pot Type	Food Type	4	2.06	0.25
Aluminum	Meat
	Legumes	4	2.33	0.11
	Vegetables	4	1.23	0.23
Clay	Meat	4	2.18	0.62
	Legumes	4	2.47	0.07
	Vegetables	4	1.46	0.46
Iron	Meat	4	4.68	0.63
	Legumes	4	3.67	0.17
	Vegetables	4	2.79	0.24

2. Table 2:

Groups	Count	Average	Std Dev
Aluminium	12	1.873333	0.52227
Clay	12	2.036667	0.60134
Iron	12	3.713333	0.88429

It is reasonable to pool variances of table 1 but not that of table 2 as table 2 does not show the count, average and std deviation by 'Food type' but shows them only by 'Pot type', whereas Table 1 shows the count, average and std deviation by both 'Pot Type' and 'Food Type'.

(b) Plot of Means

The bar plot below using Excel, shows the mean iron content of various Pot types:

Summary:

From the bar chart above we see that the Iron pot has the highest mean Iron content and Aluminium pot has the least Iron content among the 3 pot types given.

(c) The Analysis of Variance, F statistics, P-values are as shown:

Using Excel, Choose Data Analysis ---> Anova: Single Factor --> Choose the data for Input Range --> Tick the Labels in First Row --> Chose the Output range option --> Click Ok to get the following Anova Table

Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	24.89396	2	12.44698	26.36428	1.44E-07	3.284918
Within Groups	15.5798	33	0.472115
Total	40.47376	35

As P-value < 0.05,  we reject the null hypothesis and conclude that there is significant difference in mean iron contents of all the 3 groups of pots.