There are three major principles of a Completely Randomized Design experiment (CRD):

Control:  To control an experiment, keep all variables the same, except the variable you wish to compare.  The variable you wish to compare is called the factor.  If all members of one group have a similar characteristic, other than the factor, that is different from the other group, then the results of the experiment are confused between the factor and this characteristic.  Here we say this characteristic confounds the results and that this characteristic is a confounding variable. 

Example: Suppose you wanted to compare the number of baskets made in a minute between varsity and junior varsity basketball players. 

The correct way to control this CRD experiment is to randomly sample members of the varsity and junior varsity teams.  The randomly selected varsity team will include some males, some females, some tall, some short, some offensive, some defensive, some juniors, some seniors, etc.  The same is true for the randomly selected junior varsity team.  It does not matter that one group may have more offensive players than the other group as long as the selection process was random.  If the selection process is random, where each member of the varsity and junior varsity teams has an equally likely chance of being selected, then we say these groups are the same, except for the fact that they are varsity or junior varsity. 

Here is an example of a way this experiment can violate the principle of control:  Suppose we sampled only offensive players from the varsity team and only defensive players from the junior varsity team.  If there were a difference in the numer of baskets made, we would not know if the results were because of the varsity level or because of the position of the players.  No valid inference can be made because the varsity group all have the characteristic “offensive” while the junior varsity group all have the characteristic “defense.”  The results are confounded by position.

Note:  We may want to compare varsity to junior varsity for offensive players only.  This is fine.  Our target population here is all high school offensive basketball players.  It is helpful to define the target population as to decide how to establish control. 

Randomization:  To help control an experiment, we randomly sample individuals or objects from the population(s).  When appropriate, we randomly allocate the members of this sample into groups. 

Note:  Sample sizes of each group do not have to be equal.  Randomization techniques will be deferred to quarter four.

Replication:  Replication provides us with a measure of variation between and among groups.  Without replication, and hence variation, it is impossible to make inferences.  Note, replication here does not mean that you must redo the experiment.

Example:  It would be silly to compare baskets made between only one varsity member and one junior varsity member.  We would want several players to shoot baskets to sense of the variation between members of each respective group, as well as the variation between these groups.