Each observation has been reported as a mean & a standard deviation. I do not have access to the underlying data.

A:

0.230, 0.104

0.245, 0.117

0.223, 0.098

0.246, 0.131

0.240, 0.135

B:

0.225, 0.121

0.218, 0.111

0.224, 0.125

0.231, 0.129

0.204, 0.092

C:

0.245, 0.14

0.225, 0.09

0.249, 0.104

0.229, 0.099

0.230, 0.104

0.245, 0.117

0.223, 0.098

0.246, 0.131

0.240, 0.135

B:

0.225, 0.121

0.218, 0.111

0.224, 0.125

0.231, 0.129

0.204, 0.092

C:

0.245, 0.14

0.225, 0.09

0.249, 0.104

0.229, 0.099

My initial attempt was just to use the means so I did some T tests between them & then an ANOVA on all 3 using Python & Scipy's stats library.

Python:

```
import numpy as np
import scipy.stats as stats
A = np.array([0.230, 0.245, 0.223, 0.246, 0.240])
B = np.array([0.225, 0.218, 0.224, 0.231, 0.204])
C = np.array([0.245, 0.225, 0.249, 0.229])
AB_ttest = stats.ttest_ind(A, B)
AC_ttest = stats.ttest_ind(A, C)
BC_ttest = stats.ttest_ind(B, C)
ABC_anova = stats.f_oneway(A, B, C)
print("A, B T test: ", AB_ttest)
print("A, C T test: ", AC_ttest)
print("B, C T test: ", BC_ttest)
print(" ")
print("ANOVA: ", ABC_anova)
```

A, B T test: statistic = 2.561, p value = 0.0336

A, C T test: statistic = -0.028, p value = 0.978

B, C T test: statistic = -2.263, p value = 0.058

ANOVA: statistic = 3.889, p value = 0.0528

A, C T test: statistic = -0.028, p value = 0.978

B, C T test: statistic = -2.263, p value = 0.058

ANOVA: statistic = 3.889, p value = 0.0528

Given that p < 0.05 implies a statitically significant difference (ssd) then the T test for A & B suggests such a difference and yet the ANOVA suggests that there is no ssd between them? Or am I reading this all wrong?

Also I'm not convinced that my approach is an acceptable statitical anlysis of this kind of data . If not how should I be approaching this?