Page 22 - Monograph201601
P. 22
Population,
Sampling &
normal distribution
From the review, social science variable, is used. It is a function that
quantitative and qualitative methods in describes the relative likelihood for this
educational leadership research can be random variable to take on a given
inferred to subscribe to the goal of value.
identifying and analyzing data that
can inform about a population. The A simple example would explain this. If
researcher aims to collect data that we randomly select 20 school principals
either maximize generalization to the and arrange them in a room according
population in the case of quantitative to their heights. We would most likely
methods or provide explanation/ see a normal distribution with a few
interpretation of a phenomenon that principals who are shorter than many
represents a population in the case of others on the left, the majority in the
qualitative methods. In most cases, middle and a few principals who are the
definitive conclusions of a population tallest on the right. This has come to be
are rarely possible in social sciences known as the normal curve or
because data collection for an entire probability density function.
population is rarely achieved.
Most quantitative research involves the
Therefore, researchers apply sampling use of statistical methods presuming
procedures where the mean of the independence among data points and
sampling distribution will approximate Gaussian ?ormal??distributions
the mean of the true population (Andriani and McKelvey, 2007). The
distribution which we have come to Gaussian distribution is characterized
know as normal distribution. This by its stable mean and finite variance
concept has set the parameters of how (Torres?arrasquillo, Singer, Kohler,
we analyze data over many years. We Greene, Reynolds and Deller, 2002). As
have accepted that most data ought to in the example above, supposedly the
be near an average value, with a small shortest principal is 1.6m. If we ask a
number of values that are smaller, and question, ?hat is the probability that a
the other extreme where values are principal in the line is shorter than
larger. To calculate these values, the 1.5m? The answer would be ???? From
probability density function (PDF), or the total principals in the room there is
density of a continuous random no chance to find someone who is
18
