Article:
Random versus NonRandom  A Simple Illustration
The
concept of random
versus nonrandom is
not a difficult one. A better approach might be to state that
the difference between random
versus nonrandom is not a difficult one (so the author claims). If we are
armed with a realistic but simple illustration, the differences
between random and nonrandom may seem a little more obvious.
Definition
of Random
Let
us first look at a definition of RANDOM:
1.
… lacking any definite plan
or prearranged order ^{(1)}
^{
}
2.
… occurring or done
without definite aim, reason, or pattern^{
(2)}
^{
}
When
referring to randomness we can also state that each
“thing”or “item” in the set of data has an equal chance at being
selected; there are no favorites. This is a property that is key
in statistical sampling. The properties of randomness must be
obtained, as best as possible, in order to ensure unbiased
results.
The
Illustration – Part 1:
You
will now be asked to examine a series of numbers, as shown
below. The numbers range from 1 to 100, and no two entries are
the same. They have been randomly entered into a 10by10
matrix.
You
are now challenged to look over the data for 30 seconds. At the
end of the allotted time, try to recreate the above table on a
blank sheet of paper, without looking at the matrix above. You
may take up to 90 seconds to complete this step. It should
become apparent, that unless you possess a photographic or
eidetic memory, the task to recreate the above table accurately
might be a challenge.
So,
how well did you do? How many numbers did you remember? Score
yourself one point for each number you correctly remembered (or
even guessed at) by row and by column. TOTAL:.
The
Setup – Part 1:
The
numbers were generated using a statistical software program
called Minitab 17^{®(3)}. The steps included the
following:
Calc>
Make Patterned Data >Simple Set of Numbers
{to generate a simple set of one hundred numbers from 1 to 100}.
The
resulting column of 100 observations were randomized using:
Calc>
Random Data > Sample from Columns {referring
back to the string already generated}.
The
resulting string of 100 numbers was then formatted into a
10by10 matrix – as randomly as possible.
Note:
some will argue that no series of random numbers are truly
“random”, but that’s a whole other story.
Definition
of NonRandom
Now,
we will address the second part of this discussion – NonRandom.
Trying to find an appropriate description led me to the synonym
– BIAS:
1.
… tending to yield one outcome more frequently than others …
^{(4)}
^{
}
2.
… having an expected [pattern] different from the quantity or
estimate … ^{(4)}
The
Illustration – Part 2:
You
will now be asked to examine the series of numbers below. The
numbers, again range from 1 to 100, and no two entries are the
same. They have also been entered into a 10by10 matrix.
You
are now, once again challenged to look over this data set for 30
seconds. At the end of the allotted time, take another blank
piece of paper and recreate the table, without looking at the
matrix above. You may take up to 90 seconds to complete this
step.
Score
yourself one point for each number you correctly remembered (or
even guessed at) by row and by column. So, how well did you do?
How many numbers did you remember? TOTAL:.
The
Setup – Part 2:
The
numbers in the above table were also generated using the
following steps in Minitab 17^{®(3)}:
Calc>
Make Patterned Data > Simple Set of Numbers
{to generate two strings of patterned data}.
The
first string of 50 observations was generated by listing the odd
numbers from 1 to 99. The second string of 50 observations were
generated by listing the even numbers from 2 to 100. The two
strings were then formatted into the patterned 10by10 matrix
above. That’s it!
The
reader may have noticed that this time around, Minitab 17^{®(3)}
was used to generate only the 10by10 matrix with preplanned
pattern. The second step that was used to create the first
10by10 matrix {Calc>Random Data> Sample from Columns} was not used.
Summary:
Hopefully,
the reader can see that with a simple illustration such as the
one above, the concept of random and nonrandom
becomes a little clearer. The first set of 100 numbers represent
the best possible picture of random data, in that there was no
reference to “Patterned
Data”. The second series of numbers were created using “Patterned
Data”. Patterns in data and anywhere else are a result of
nonrandomness, otherwise known as bias.
References:
1.
Collins
English Dictionary – Complete and Unabridged ^{©}
HarperCollins Publishers 1991, 1994, 1998, 2000, 2003
2.Random House
Kernerman Webster's College Dictionary ^{©}
2010 K Dictionaries Ltd. Copyright 2005, 1997, 1991 by Random
House, Inc. All rights reserved.
3.
Minitab^{®}
17.2.1
4.
www.merriamwebster.com/dictionary/biased
