Comparing multiple means to a hypotetical value

I have 4 independent groups (with different n) with values ranging from 0.0 to 1.0 and want to check if the mean of each group differs significantly (p<0.05) from a hypothetical value. Is it possible to do this with multiple t-tests and correct for the family-wise error rate with the Bonferroni method or the FDR approach?

For example following imaginary dataset of group I-IV containing, ideally gaussian distributed, mortalities. Hypothetical mean value to test against: 0.2

Data set:

Data t.PNG

Column statistics with t-test against a theoretical mean of 0.2 (p=0.05).

Data t p.PNG
With Bonferroni correction the adjusted p-value would be 0.0125 (4 tests -> 0.05/4=0.0125), therefore the mean of group II does not differ significantly from 0.2 although its t-test p-value is smaller than 0.05.
Can it be done this way (or in a similar way with the FDR approach)?


TS Contributor
Thats more of a basic asumption we made to simplify the further statistics (and its often done with biological data). I hope were not completly wrong there.
Unfortunately, making assumptions to simplify analysis or making assumptions cause bozos in the field do it does not make it right or even reasonable. Medical researchers often insist on chopping up continuous variables into categorical ones but almost no relationships in biological systems follow these discrete jumps imposed by the categorical variable.

I don't think that is at all a tenable assumption. Let's go back to the beginning: what specific research question are you trying to address (and all the relevant variables labeled as outcome, predictor, covariate, and how each is recorded such as 1-50, yes/no, etc.)? What is this grouping variable?