ANOVA und Cohens d`?

#1
Hi there!

So, i did a psychological study where i tried to manipulate flow. In that study every subject had to play a racing game 6 times and after each round he or she had to do a questionaire for the measurement of flow. Every subject played 3 different Tracks 2 times. There were 3 types of manipulation. So every subject played 3 times with and 3 times without manipulation. To prevent training and other effects i balanced the whole thing with two interlaced latin squares to the effect that every manipulation existed with every track on every position in the sequence. For that 18 subjects would have been enough but i did 36 to be on the safe side.

Then i did a ANOVA on the data with SPSS.
Means:
without manipulation: 55,4722 (SD=7,33123) n=108
manipulation 1: 41,1944 (SD=8,38645) n=36
manipulation 2: 51,3333 (SD=7,81574) n=36
manipulation 3: 46,4722 (SD=6,95490) n=36

Now im not sure if i can calculate a Cohens d like with T-tests because i cant decide if the samples are connected or not...

Can somebody help me with this? Can i even calculate a effectsize here?

Thanks

hasenkuchen