How to analyze post hoc Tukey test's results?

#1
I carried out a study in which I compared the quantitative data of six groups (n=10). SPSS version 17 was used to analyze the result at .05 level of significance. All One-Way ANOVA’s assumptions were fulfilled. The ANOVA's test was performed and the mean comparison showed statistical significant (p=0.002). Well, Tukey post hoc test was performed and the result was:

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As it can be seen, the means of groups 1 to 5 were at the same subset, indicating that there is no significance difference between them (p=0.082). The same can be observed in relation to the groups 3 to 6 (p=0.072). If the results of groups 3, 4 and 5 are similar to groups 1 and 2 and, at the same time, to group 6, is it not logical to infer that groups 1 and 2 are equal to group 6?
What is the correct way to interpret this result? What are the similar groups? What are the different ones?
Thanks in advance
Marco Versiani
 
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Dragan

Super Moderator
#2
The correct interpretation is:

(a) The mean of Group 1 is significantly different from the mean of Group 6

and

(b) The mean of Group 2 is significantly different from the mean of Group 6.
 
#3
Hi Dragan,

Thank you for your fast and precise answer. It is quite clear for me that those groups you referred are statistically different. But how about groups 3, 4 and 5? I know they are similar each other, but should I consider them similar to 1 and 2 or to 6? That is what is bothering me...
 

Dragan

Super Moderator
#4
Hi Dragan,

Thank you for your fast and precise answer. It is quite clear for me that those groups you referred are statistically different. But how about groups 3, 4 and 5? I know they are similar each other, but should I consider them similar to 1 and 2 or to 6? That is what is bothering me...
You should consider groups 3, 4, and 5 to be similar to 1 and 2 AND also similar to 6. That is why they (3,4,5) appear in both subsets.
 
#5
Hi Dragan,

That's what I supposed to at first. However, isn't it weird to think that A=B, B=C BUT A is not equal to C? It is against mathematical logic. It is almost philosophical. Don't you think?
Marco Versiani
 

Dragan

Super Moderator
#6
Hi Dragan,

That's what I supposed to at first. However, isn't it weird to think that A=B, B=C BUT A is not equal to C? It is against mathematical logic. It is almost philosophical. Don't you think?
Marco Versiani
You're thinking too deeply.:)

It's just a technique that SPSS uses to simply show graphically which groups statistically differ from each other.