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I have two groups of maybe 25 people each. I want to know if there a difference between the two on a happiness score depending if the from one group or another (A or B) and if they'r old or yougn (C or D). I previous chi-sqyare also show a difference on my groupes (a and B) on the age variable (C and D).

Would it be better do two t-test and leave with the possible type one error or do a facorial anova and see if group, age or interaction of group and age have an influence. I'm not sure about the force/puissance of the test.

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In general it would be best to fit a model with the interaction ince if there is an interaction any statements you make about your two t-tests might be misleading. As you say your estimate of the interaction will be less precise but better to be imprecise than misleading.

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    $\begingroup$ If I understang you, for you it's better to do the factorial anova, and say that the puissance can be woobly than doing to t-test? $\endgroup$
    – lili
    Commented Apr 14, 2016 at 12:38
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    $\begingroup$ That is my view, yes. $\endgroup$
    – mdewey
    Commented Apr 14, 2016 at 12:40
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    $\begingroup$ Last question about that, but what if there less then a thir of people in one categorie, like in B old there 5 people? $\endgroup$
    – lili
    Commented Apr 14, 2016 at 13:18
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    $\begingroup$ If the design is unbalanced then it is even more important to look for the interaction as if (say) old people are less likely to be in group B you need to be able to separate the effects of group and age. Incidentally you mean power (puissance is the French word). $\endgroup$
    – mdewey
    Commented Apr 14, 2016 at 13:30
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    $\begingroup$ Thank's I forgot what the english world was also thaks for you answer $\endgroup$
    – lili
    Commented Apr 14, 2016 at 13:41

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