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1. HELP deciding which ANOVA to use

i think probably the repeated measures model is better. you maybe could also run two t-tests, one at each time point. What is the 'way' in your one-way ANOVA, seems not so clear to me.
2. Experiment degsin

I think you are right, it says 6 hospitals x 4 treatments = 24 people. To me it seems like the question already tells you the most important aspect of the experiment, that the 4 treatments are all given at each of the 4 hospitals, which would be a complete block as you mentioned above. I guess...

4. independent sample t test

the lines look suspiciously parallel...good thinking though always good to see some box plots.
5. Is multidimensional ROC Curve Analysis a thing?

For multiple endpoints, if they aren't ordinal, you end up with 3 dimensions to the ROC rather than 2 (sens and spec) this is an example https://onlinelibrary.wiley.com/doi/10.1002/9781118269787.ch3
6. Leniency of assessors

you need the ratings per consultant I would think.
7. Is multidimensional ROC Curve Analysis a thing?

for many predictors most logit regression packages compute the ROC curve based on the propensity scores, ie the predicted probablity of event. There are certain theories which say this is the best way as i recall. For multiple outcomes, this would lead to more than 2 states, ie a tri-state...
8. Help interpret an event study methodology used in a research paper

try drawing a mind map, it could help determine if boxplots are relevant.

10. Help interpret an event study methodology used in a research paper

Try drawing a boxplot.
11. Sample size calculation when comparing two coefficients of variation

is the measurement continuous, count, normal, lognormal or what? Need to have some idea of that. I'd suggest that this will work out best under log-normal model.
12. Repeated measures ANOVA - degrees of freedom

10 = (16 )- (2 + 2 + 1) - 1 = n - k - 1, like in a two-way non-repeated measures. ie (n-1) - any used up by the treatment, gender and interaction terms. denominator degrees of freedom in this type of setting is weird and debatable.
13. Repeated measures ANOVA - degrees of freedom

according tot he docs it is 'split plot'.https://www.stat.purdue.edu/~zhanghao/STAT514/handout/SplitPlot.pdf The treatment is (#treatments - 1), gender is 1 (number of biological genders - 1), and interaction is (#treatments - 1) * number of biological genders - 1). The reason 'why' these are...
14. Repeated measures ANOVA - degrees of freedom

The structure of the table leads me to believe it is apply a 'guyhoueser' correction for sphericity to obtain the dfs. https://en.wikipedia.org/wiki/Greenhouse%E2%80%93Geisser_correction#:~:text=is%20a%20statistical%20method%20of,and%20Seymour%20Geisser%20in%201959.
15. How to compare ratings from different sites?

do you have to use excel or do you have stats software? How common is it for some sites not to have ratings for a given pair of contractors?
16. How to compare ratings from different sites?

do you have access to the actual ratings (ie how many got each rating 1 to 5) or just mean/n. can you get stdev for each set?
17. How to do ANOVA (or similar) analysis when there are multiple groups?

heres how you did it: 1) open prism select grouped data, 20 replicates 2)each row is region, 2 columns A, B 3) analyze -> multiple t-tests per row (or something like that) 4) select mann whitney and whatever else you want to select great job!
18. independent sample t test

box plots ain't no linear algebra thing. You just look at them and they are what they are. Actually I had noticed something about the relationship between logistic regression and 2 sample exact tests. Namely the p-value for the exact logistic regression ends up being same as p-value for the...
19. How to do ANOVA (or similar) analysis when there are multiple groups?

change score. you can thank me later.
20. independent sample t test

with boxplots, you can rotate paper/head 90 degrees to change independant/dependant.