Control compared to 4 treatment groups I'm not very strong as far as stats go, and not super familiar with this site, so I'm sorry if any formatting is wrong here. I've tried searching for this answer but I'm still lost.
I'm interested in determining if 3 new treatments (W1, W2, W3; n=100 in each W group) are similar to an established treatment (D, n=150), and different from a control (C, n=150). I have one discrete, numerical dependent variable (DV, a score out of 10). I'm a broke student, so I'm trying to do this in R as we don't have budget for SPSS, etc.
Normality is iffy (when looking at visual outputs in R via ggplot, the curve tends to be highest at lower scores - as in highest near 3 as opposed to in the actual middle at 5, again sorry if I'm reporting this in an incorrect way). BUT I've been reading that doesn't always rule out t-tests/other things that assume normality.
If I understand things right, multiple t-tests risk losing information, as this increases chances or error with each test.
Running a linear regression with dummy variables might be what I want to do, but I'm at a loss as how to do that in R.
Any help at all would be greatly appreciated, and happy to give more information if aspects are missing.
#edited to add histogram of residuals from one-way ANOVA
 A: With your sample sizes I would try the (unbalanced) one-way ANOVA, checking to see if residuals are nearly normal. Also, look to see if the five groups have similar variances.

*

*If so, do Tukey HSD multiple
comparisons. Various pages online, perhaps this one
should show the way. [BTW, be sure to declare your factor variable as.factor and that the F-statistic has 4 numerator degrees of freedom.]


*If residuals are nearly normal and variances obviously unequal, begin with oneway.test in R. If there are significant differences, then use Bonferroni ad hoc comparisons via t tests.


*If residuals are clearly not normal, explore Kruskal-Wallis nonparametric "ANOVA." If there are significant differences to explore, use
suitable ad hoc tests to avoid 'false discovery' due to
multiple analyses on the same data.
Ordinarily, I would try to show analysis of an example with fictitious
data, but I don't have enough insight into the nature of
your data to avoid a possibly misleading example. If you
are in doubt following my outline above, maybe you can show boxplots of the five
groups and a normal probability plot (Q-Q plot. in R qqnorm) of residuals
in an edited version of your question.
A: A classic test for multiple treatments against a baseline is Dunnett's Test. That does multiple t-tests for each treatment against the baseline group in a way that pools data from the groups and takes the multiple comparisons into account. That is implemented for example in the DescTools package. There's an example of implementation on this page. It would probably make the most sense to compare the new treatments against the established treatment rather than against the control. With your group sizes you might be able to get away with t-tests, as the critical assumption is normality of the sampling distribution of group means rather than within-group normality.
You might better use the non-parametric Mann-Whitney-Wilcoxon Test, which is almost as powerful as a t-test when normality holds and can outperform it otherwise. That's implemented in the two-sample version of wilcox.test() in R. You only have a small number of pairwise comparisons of interest (each of 3 new treatments against standard treatment, perhaps standard treatment against control), so restricting yourself to those few comparisons and using the R p.adjust() function with a "holm" correction for multiple comparisons could work well while controlling for false-positive errors.
