Stratified Random Assignment

Now, let's consider an example where we divide the sample into three relatively homogeneous blocks.

This will assure that the groups are very homogeneous.

Let's look at what is happening within the third block.

You can see that for any specific pretest value, the program group tends to outscore the comparison group by about 10 points on the posttest.

That is, there is about a 10-point posttest mean difference.

Would they be more homogeneous with respect to measures related to drug abuse?

Ultimately the decision to block involves judgment on the part of the researcher.Remember that the treatment effect estimate is a signal-to-noise ratio. But, we have changed the noise -- the variability on the posttest is much smaller within each block that it is for the entire sample.So, the treatment effect will have less noise for the same signal.The Randomized Block Design is research design's equivalent to stratified random sampling.Like stratified sampling, randomized block designs are constructed to reduce noise or variance in the data (see Classifying the Experimental Designs). They require that the researcher divide the sample into relatively homogeneous subgroups or blocks (analogous to "strata" in stratified sampling).If the blocks weren't homogeneous -- their variability was as large as the entire sample's -- we would actually get worse estimates than in the simple randomized experimental case.We'll see how to analyze data from a randomized block design in the Statistical Analysis of the Randomized Block Design.If you are wrong -- if different college-level classes aren't relatively homogeneous with respect to your measures -- you will actually be hurt by blocking (you'll get a less powerful estimate of the treatment effect). You need to consider carefully whether the groups are relatively homogeneous.If you are measuring political attitudes, for instance, is it reasonable to believe that freshmen are more like each other than they are like sophomores or juniors?Thus each estimate of the treatment effect within a block is more efficient than estimates across the entire sample.And, when we pool these more efficient estimates across blocks, we should get an overall more efficient estimate than we would without blocking. Let's assume that we originally intended to conduct a simple posttest-only randomized experimental design.