On Tue, 1 Nov 2016 15:52:58 -0700 (PDT), firstname.lastname@example.org
>I was just wondering if anyone would be able to share some insight on performing a one-way between-groups ANOVA (or a UNIANOVA) for three distinct groups.
>One group had high-intensity math assessments, another had minimal math assessment, and the last group has had no math assessment. These are all pre-determined data, and was therefore not subject to a traditional research design where students are randomly assigned to each group.
>I would like to compare each groups' performance in a math class, and am wondering if an ANOVA is appropriate, given how the assumption of the data being randomly sampled is being violated.
>Any help would be appreciated.
You can always perform the test, whatever test you wonder about.
Is it convincing to anyone?
It may or may not give you a number that is useful, in some sense, for
comparing to some other number. For instance, if your computation
shows that the groups are apparently equal, then lack of randomization
would have to be /offsetting/ some other difference, instead of
creating one -- which might or might not be conceivable.
What statistical theory says is something like, "you cannot assert
strong inferences-based-on-randomization when there is no
randomization." Whatever inference you draw should have to
explicitly take into account and try to account for the absence of
randomization. This is why simple "observational studies" take second
place to "randomized studies."