Developmental psychology.pdf

Technology and Statistics 529
Sampling Procedures In making these predictions the investigator selects a sample
of subjects, which constitutes only a portion of all of the cases in which he or she is
interested. The sample may be 10, 20, or 100 subjects, depending upon the availability
of resources for obtaining them. All possible subjects are referred to as the population.
Every subject or item in a particular class or category is included in the population,
such as all the Dvorak users in the United States. Since all of these people cannot be
tested, the investigator makes estimates about this population based on the performance
of a sample. The investigator decides whether the findings obtained with a particular
sample are likely to recur regularly if the test were repeated with the same subjects
or even with different subjects from the same population.
To increase the chances of success, the investigator aims to select a representative
sample. A representative sample is one that accurately reflects the characteristics
of the population. Identified by careful methods, these subjects should give an indication
of the entire population.*
We test them on the Dvorak keyboard and then, using this result, we infer
how the whole population would perform with this same keyboard. If the mean score
is 41.7 words per minute after 45 hours of instruction, we might infer that the mean
for the whole population of beginning Dvorak operators would be this same speed.
Using the Standard Error But we cannot be certain. We wonder if the mean of
the Dvorak sample truly represents the mean of the whole population. The only way
to know for certain would be to test all of these beginning keyboard operators, but
since that is impossible, we take steps to deal with the uncertainty. We make use of a
procedure for estimating the probable error, which is possible because chance errors
in sampling, in the long run, tend to be distributed according to the normal curve.
Our sample mean was 41.7, and for other samples the means might have been
higher, lower, or the same. We simply do not know. But if we continued taking appropriate
samples from the total population and continued finding their means, eventually
we would discover that this distribution of sample means is very nearly a normal distribution.
Furthermore, the mean of this group of sample means would be close to the
population mean. It would reflect the true mean of the population of all beginning
Dvorak keyboard operators.
The problem is that we cannot take endless samples. In fact, we have only one,
but by employing the laws of chance and our knowledge of the normal curve, statisticians
have developed a method for determining how much our one sample mean is
likely to be in error. This measure, called a standard error, is used in determining the
amount of error likely in a sample statistic. It is calculated from the number of scores
in the sample and their standard deviation, which shows how closely the scores cluster
around the mean. When there are many scores and the deviation is small, the standard
error will be small, meaning the sample mean is likely to reflect the population mean.
Using this method for estimating the standard error of the mean in the Dvorak
sample, we find that the true mean for the population probably lies somewhere in the
interval from 40 to 43 words per minute, and the chances are approximately 95 out of
100 in this instance. This statement of probability is our best estimate of the performance
of the whole population of Dvorak users. If we want a higher degree of confix
dence in our estimate, then we obtain a wider interval. In more general terms, we can
say that it appears likely that the population mean is some value close to 41 words per
minute for beginning Dvorak users.
'Clearly, the Grand Old Man was
the choice of the great majority of
voters. The polls reflected his
overwhelming popularity and
predicted a landslide victory with
seventy percent of the popular
vote.
Election day turned out to be
rainy and somber. When the results
started trickling in everyone was
amazed—the two candidates were
running neck-and-neck. Later, the
underdog even ran up a slight
majority at no time exceeding
seven thousand votes. And when
all the votes were tallied, he was
declared the winner, and the Grand
Old Man's supporters were
flabbergasted.
The people working for the
underdog didn't seem that
surprised. For, when they heard of
the one-sided prediction from the
polls, they decided that they ought
to start working. Endless amounts
of telephone calls, pamphlets,
mailings, and speeches later, voters
who had never heard of their man
were ready to vote for him.
Furthermore, when the opponents
heard of the results of the poll, they
stayed in their dry homes. Nobody
in New Jersey was more surprised
whe;i the prediction, probably
accurate in the beginning, failed to
hold true.