# How to analyze post hoc Tukey test's results?

#### marcoversiani

##### New Member
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:

[/URL]</noscript>[/IMG]

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?
Marco Versiani

Last edited:

#### Dragan

##### Super Moderator
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.

#### marcoversiani

##### New Member
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
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.

#### marcoversiani

##### New Member
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
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.