The following data is the concentration of three amino acids, alanine, aspartic

Question

The following data is the concentration of three amino acids, alanine, aspartic acid, and tyrosine, in centipede hemolymph (mg/100 ml) in males and females. (a) Using appropriate analysis to test whether the concentration of alanine, the concentration of aspartic acid, and the concentration of tyrosine arc the same in males and females. (b) If there it difference between male and female, then what type(s) of amino acid has different concentration (i.e., it the concentration of alanine the same between male and female, is the concentration of aspartic acid the same between male and female, is the concentration of tyrosine the same between male and female, respectively)?

Explanation / Answer

We carry out the MANOVA analysis to determine if the concentration of the acids is same in males and females:

> tt <- read.csv("clipboard",sep=" ")
> head(tt)
Alamine Aspartic Tyrosine Gender
1     7.0     17.0     19.7   Male
2     7.3     17.2     20.3   Male
3     8.0     19.3     22.6   Male
4     8.1     19.8     23.7   Male
5     7.9     18.4     22.0   Male
6     6.4     15.1     18.1   Male
> ?manova
> tt$Gender <- as.factor(tt$Gender)
> concentration_Manova <- manova(cbind(tt$Alamine,tt$Aspaartic,tt$Tyrosine)~Gender,tt)
> summary(concentration_Manova)
          Df   Pillai approx F num Df den Df     Pr(>F)   
Gender     1 0.705604 15.5791      2     13 0.00035323 ***
Residuals 14                                              
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Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Since the p-value is very small, we reject the hypothesis that the acid concentration among males and females are different. To determine which of the acids has different concentrations, we carry out the univariate analysis on each of the acids:

> t.test(Alamine~Gender,tt)

        Welch Two Sample t-test

data: Alamine by Gender
t = 0.22771, df = 13.4121, p-value = 0.82331
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-0.74005951 0.91505951
sample estimates:
mean in group Female   mean in group Male
              7.5000               7.4125

> t.test(Aspartic~Gender,tt)

        Welch Two Sample t-test

data: Aspartic by Gender
t = 3.36414, df = 13.352, p-value = 0.0049126
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
1.110082 5.064918
sample estimates:
mean in group Female   mean in group Male
             20.7000              17.6125

> t.test(Tyrosine~Gender,tt)

        Welch Two Sample t-test

data: Tyrosine by Gender
t = 5.50065, df = 13.8135, p-value = 8.2003e-05
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
3.1012896 7.0737104
sample estimates:
mean in group Female   mean in group Male
             25.9125              20.8250

We see hat only Alamine acid is similar for the two groups while the other two acids are different in the two genders.

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