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One is that each participant has an equal chance of being assigned to each condition (e.g., a 50% chance of being assigned to each of two conditions).The second is that each participant is assigned to a condition independently of other participants.
Those in a trauma condition and a neutral condition, for example, should include a similar proportion of men and women, and they should have similar average intelligence quotients (IQs), similar average levels of motivation, similar average numbers of health problems, and so on.
This matching is a matter of controlling these extraneous participant variables across conditions so that they do not become confounding variables., which means using a random process to decide which participants are tested in which conditions.
The former are called between-subjects experiments and the latter are called within-subjects experiments.
students might assign half of them to write about a traumatic event and the other half write about a neutral event.
It is always possible that just by chance, the participants in one condition might turn out to be substantially older, less tired, more motivated, or less depressed on average than the participants in another condition.
However, there are some reasons that this possibility is not a major concern.
Thus one way to assign participants to two conditions would be to flip a coin for each one.
If the coin lands heads, the participant is assigned to Condition A, and if it lands tails, the participant is assigned to Condition B.
However, for a fixed number of participants, it is statistically most efficient to divide them into equal-sized groups.
It is standard practice, therefore, to use a kind of modified random assignment that keeps the number of participants in each group as similar as possible. In block randomization, all the conditions occur once in the sequence before any of them is repeated.