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I would like to figure out if there are significant differences between the following groups. I use R:

group <- c(rep("A",7),rep("B",5),rep("C",8),rep("D",6))
values <- c(32,45,68,29,41,37,78,54,23,33,35,11,30,23,41,42,31,37,22,45,61,34,38,39,28,29)
data <- as.data.frame(group);data$values<-values

I suspect that group A is significantly different from the rest, but when performing ANOVA test:

car::Anova(lm(values~group, data),type=2)
Anova Table (Type II tests)

Response: values
          Sum Sq Df F value Pr(>F)
group      952.5  3  1.6008 0.2178
Residuals 4363.4 22  

Thus the p-value is 0.217>0.05 which means that there are no significant differences between groups. On the other hand, when using the Tukey test I see that substracting the mean of group A cause more variability concerning the general mean, but I don't know if it is enough to say that group A is significantly different from the rest.

TukeyHSD(AV, conf.level = 0.99)
Tukey multiple comparisons of means
    99% family-wise confidence level

Fit: aov(formula = values ~ group, data = T)

$p
          diff       lwr      upr     p adj
B-A -15.942857 -44.84640 12.96069 0.2435065
C-A -13.267857 -38.81522 12.27951 0.2908288
D-A  -8.976190 -36.43878 18.48640 0.6660606
C-B   2.675000 -25.46578 30.81578 0.9868982
D-B   6.966667 -22.92363 36.85696 0.8458237
D-C   4.291667 -22.36697 30.95030 0.9415981

My question is if there are significant differences between all groups and if the choice of the tests performed is correct. Thank you in advance,

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  • 1
    $\begingroup$ There is no indication in the results of the Tukey HSD test that group A is different than the other groups. The p values for each comparison are greater than 0.24. [e.g. 0.24, 0.29, 0.67]. Also, the confidence interval for each difference between groups includes 0. [e.g. B-A has limits of -44.8 and 12.96]. $\endgroup$ – Sal Mangiafico Feb 3 at 11:23
  • $\begingroup$ That's what I thought, thank you. $\endgroup$ – fina Feb 3 at 11:40
  • $\begingroup$ One other comment: In R, T is used as a synonym for TRUE. It's best to not redefine special names, like T. So, you might call your data frame Data or df or so on. $\endgroup$ – Sal Mangiafico Feb 3 at 11:51
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    $\begingroup$ For reserved names in R, see the documentation $\endgroup$ – Sal Mangiafico Feb 3 at 12:01
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(Partially from comments.)

There is no indication in the results of the Tukey HSD test that group A is different than the other groups. The p values for each comparison are greater than 0.24. [e.g. 0.24, 0.29, 0.67]. Also, the confidence interval for each difference between groups includes 0. [e.g. B-A has limits of -44.8 and 12.96].

The residuals from the analysis are relatively normal and homoscedastic, so the model is probably a reasonable one.

It does appear that with more data, one might find group A to have higher values that the others.

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