Question

is one way ANOVA generalization of 2 sample t test and a special case of regression?

If an observational study's sample is randomly selected, can ANOVA result conclude cause and effect?

Does large F-stat from ANOVA conclude cause and effect?

Answer 1

1) is one way ANOVA generalization of 2 sample t test and a special case of regression?1

yes, when there are more than or equal to 2 levels, we can use ANOVA , if we use ANOVA for two levels,

we get same result with that of 2-sample independent t-test with equal variance assumed

2) If an observational study's sample is randomly selected, can ANOVA result conclude cause and effect?

For some statisticians, they assume a cause effect relationship and say that one or more independent, controlled variables (the factors) cause the significant difference of one or more characteristics. The way this works is that the factors sort the data points into one of the groups and therefore they cause the difference in the mean value of the groups

hence yes.

3) Does large F-stat from ANOVA conclude cause and effect?

yes.