12. Memory experiment(James Bost, 1987)

The memory experiment was planned in order to examine the effects of external distractions

on short-term memory and also to examine whether some types of words were

easier to memorize than others. Consequently, the experiment involved two treatment

factors, "word type" and "type of distraction." The experimenter selected three levels

for each factor. The levels of "word type" were

Level 1 (fruit): words representing fruits and vegetables commonly consumed;

Level 2 (nouns): words selected at random from Webster's pocket dictionary,

representing tangible (i.e., visualizable) items;

Level 3 (mixed): words of any description selected at random from Webster's pocket

dictionary.

A list of 30 words was prepared for each level of the treatment factor, and the list was

not altered throughout the experiment.

The levels of "type of distraction" were

Level 1: No distraction other than usual background noise;

Level 2: Constant distraction, supplied by a regular banging of a metal spoon on a

metal pan;

Level 3: Changing distraction, which included vocal, music, banging and motor noise,

and varying lighting.

The response variable was the number of words remembered (by a randomly selected

subject) for a given treatment combination. The response variable is likely to have approximately

a binomial distribution, with variance 30p (1p ) where p is the probability

that a subject remembers a given word and 30 is the number of words on the list. It is

unlikely that p is constant for all treatment combinations or for all subjects. However,

since np (1p ) is less than 30(0. 5)(0. 5) = 7. 5, a reasonable guess for the variance 2

is that it is less than 7.5.

The experimenter wanted to reject each of the main-effect hypotheses H0^A :{ the memorization rate for the three word lists is the same} and H0^B:{ the three types of distraction

have the same effect on memorization} with probability 0. 9 if there was a difference of

four words in memorization rates between any two word lists or any two distractions

(that is delta A = delta B = 4), using a significance level of = 0. 05. Calculate the number

of subjects that are needed if each subject is to be assigned to just one treatment

combination and measured just once.