Block design or completely randomized? I have 5 conditions in my experiment: A,B,C,D,E and my sample size is 200 subjects.
I want to have 40 subjects per condition, so I assign a condition to a person randomly without replacement.
E.g. Person 1 gets condition B, so I still need 40 people for conditions A,C,D,E and 39 for condition B. Now person 2 has a slightly smaller chance to get condition B again.
I don't have a prespecified list of say EABCDDEBAC... etc., where I cycle through the five options It's a random allocation for every person until the 40 people per condition fill up.
So I am confused whether this is a block design or completely randomized design?
 A: In your case, the "treatment" is the condition that you assign to the subjects at random. As Bruce explained, this is simply a randomized assignment of the treatment but not a blocking factor.
A blocking factor is a part of an experimental design where you control a specific part of the experiment, so that it doesn't confound the results. It is specifically meant to avoid having "nuisance" factors add noise or variability in your results.
Say, originally the conditions are not randomly applied on weekdays, but that they follow a specific order so that

*

*condition all group A on Monday

*condition all group B on Tuesday

*condition all group C on Wednesday

*condition all group D on Thursday

*condition all group E on Friday

Then, day of the week would be an example of a "nuisance" variable. In this case, the day of the week might add noise/interfere with the results (i.e., maybe people are happier Friday vs. Mondays potentially confounding with the Tx effect).
However, if you don't want to study but you don't want it to affect your results, you have to control against it, so you "block" it and now you have to control against. Say by saying

*

*assign 8 folks in each of groups A,B,C,D,E Monday

*assign 8 folks in each of groups A,B,C,D,E Tuesday

*assign 8 folks in each of groups A,B,C,D,E Wednesday

*assign 8 folks in each of groups A,B,C,D,E Thursday

*assign 8 folks in each of groups A,B,C,D,E Friday

And now, each condition's results are not confounded by day of the week, since they've been assigned across the week days.
The wiki page: https://en.wikipedia.org/wiki/Blocking_(statistics) offers more info. Hope this helps!
