Researchers compared protein intake among three groups of postmenopausal women: (1) women eating a standard American diet (STD), (2) women eating a lacto-ovo-vegetarian diet (LAC), and (3) women eating a strict vegetarian diet (VEG).GroupMean protein intake (mg)SDnSTD75910LAC571310VEG47176a. Without using MATLAB ANOVA functions, determine if there is a significant difference in mean protein intake between these groups.

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Explanation:

The statistical procedure for comparing the 3 groups was the F test with 2 degrees of freedom in the numerator (groups - 1) and 23 df in the denominator (N total - groups)

It is calculated as SSB/2/(SSW/23) = 10.22754

As Fcrit =

from Excel, finv(.05,2,23) = 3.4221, we can reject the null hypothesis of no difference between groups.

SSW = the sum of std i ^ 2 * (n i - 1)

SSB = the sum of ni (mean i - mean)^2

2. From Excel, we get the pvalue from fdist(10.22754,2,23) = .000664

3. For LSD, we calculate (mean 1 - mean 2)/(s * sqrt(1/n1+1/n2))

This is the pooled s = sqrt(SSW/23)

Then, we found t crit from tinv(.05,23) = 2.068

Making use of the chart i made, We found significant differences between std and lac as well as std and veg, but no significant difference between lac and veg.

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