Search the Internet or your library to find a study that is interesting to you and that used one-way ANOVA to analyze the data. First describe the question or questions of interest and then give the details of how ANOVA was used to provide answers. Be sure to include how the study authors examined the assumptions for the analysis. Evaluate how well the authors used ANOVA in this study. If your evaluation finds the analysis deficient, make suggestions for how it could be improved.
The One-Way ANOVAapplet lets you see how the F statistic and the P-value depend on the variability of the data within groups and the differences among the means.
(a) The black dots are at the means of the three groups. Move these up and down until you get a configuration that gives a P-value of about 0.01. What is the value of the F statistic?
(b) Now increase the variation within the groups by dragging the mark on the pooled standard error scale to the right. Describe what happens to the F
statistic and the P
-value. Explain why this happens.
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. One of the foods was yesiga wet, beef cut into small pieces and prepared with several Ethiopian spices. The iron content of four samples of yesiga wet cooked in each of the three types of pots is given below. The units are milligrams of iron per 100 grams of cooked food. The data below MUST be separated into 3 columns of data: one for Aluminum, one for Clay, and one for Iron. Put these labels in the first row and the 4 observations of each beneath them (from the 'iron' content column). data369.dat
(a) Make a table giving the sample size, mean, and standard deviation for each type of pot. Is it reasonable to pool the variances? Note that with the small sample sizes in this experiment, we expect a large amount of variability in the sample standard deviations.
|Type of pot || n|| || s |
(b) Run the analysis of variance. Report the F
statistic with its degrees of freedom and P
-value. What do you conclude?F
obs typepot g iron
1 Aluminum 1 1.74
2 Aluminum 1 2.19
3 Aluminum 1 1.98
4 Aluminum 1 1.77
5 Clay 2 2.46
6 Clay 2 2.62
7 Clay 2 2.36
8 Clay 2 2.15
9 Iron 3 4.61
10 Iron 3 4.81
11 Iron 3 4.53
12 Iron 3 4.76