Statistics invokes certain phobia in
many. Numbers create awe and fear. There are apprehensions of faltering with
numbers. Moreover, when one works with numbers, they bring together their
numerous complexities woven into a single thread of sorts. It is difficult for
some layman to comprehend the intricacies of the numbers and their findings. There
are so many tests and measures and formulas with very little grasp of what they
mean to the common man. To an outsider, it is reflective of perhaps an inferiority
complex in referring themselves as unable to comprehend statistics or for that
matter on a broader terms, the logic of mathematics. Yet when one views the
same in its applied form, they are beautiful. Beauty might lie in the eyes of
the beholder. There exists beauty and fear in the same breadth. To many,
invocation of numbers might mean to suggest one upmanship over the rest. This might
actually yield prisoner’s dilemma.
For instance, there are contexts in
economics which might need or do with qualitative reasoning. For that matter,
many things might be explained with common sense. Yet there is someone who
wishes to explain in some grander terms to demonstrate their high competencies.
When everyone begins to do it, it conceivably turns into a rat race of sorts
thus leading to everybody being collectively worse off. There could have been a
scenario where everyone could have been better off collectively, but the pursuit
to maximize their gain or in other words be individually better off relative to
others will lead everyone in the field to adopt similar strategy – dominant strategy
and thus yield a scenario resembling of Prisoner’s Dilemma.
Yet as one looks at the conceptualization
of statistical measures, there does exist numerous common sense examples to
help people understand the logic behind statistics. One can take an instance of
current vaccination program. There might be a desire to know the better vaccine
of the two that are being used in India. The logical way of understanding this
would be whether there exists differences in terms of breakthrough infections
between these two groups. There is one group of those vaccinated by Covishield
and another group vaccinated by Covaxin. If there were to be differences in
breakthrough infection between these two groups, then there might have to be
adopted certain remedial measures whatever they might mean. Therefore,
naturally, the researchers would collect the data and then examine the same. If
there were to purely random observations, there would exist a certain pattern
of breakthrough infections. Therefore, they would seek to examine the
differences between the observed incidences and predicted incidences. To engage
in this, there gets applied what is called the chi-square test. All the statisticians
do is to collect the data and test it to chi-square to arrive at conclusions.
The question might of course be
expanded whether the breakthrough infections vary across these vaccines across
genders. Therefore, there gets added an extra qualification around which one
has to measure the efficiency. It is not suffice to say there is difference or
not but must be tested against an added parameter which in the current instance
in gender. The statistician has collected the data but he or she can longer do
with the chi-square but now will use another tool going by the name of t-test. So
in short t-test is used to test qualifiers over and beyond the chi-square test.
There might arise another question. The
comparisons across vaccines are right. However, it needs to be examined whether
everybody vaccinated with a certain vaccine generates a similar impact. In other
words, it must be examined whether the groups are uniform or there is a heterogeneity
in terms of impact within the groups. This might be for instance whether the
impact of vaccination is similar across all age groups for Covishield or
Covaxin or are there differences that exist across these age groups or between
these age groups. To test the variations within these groups or across the
groups, the statistician will now have to apply the analysis of variance of
course popularly called the ANOVA.
In this context, it would be useful for
the policy makers to understand the age patterns of those getting infected even
after vaccination. There is a possibility that certain age groups are more susceptible
than certain other age groups. One might assume all age groups are uniformly
vaccinated. The statistician would build up a data set of all those infected by
their age group. Further he or she would plot these frequencies on a graph. Implied
is they calculate how many 20 year olds have got infected, or how 60 year olds
have got infected and so on and so forth. Once these frequencies are plotted on
a graph, the pictorial representation will give the age groups that are more
susceptible for infection. A line running through these observations is drawn
around which is called building up of the distribution. The data distributed is
examined and the variation or its square root the standard deviation is calculated.
It helps us to examine whether every group is susceptible to be infected or do
there exists age groups which are outliers either in terms of getting infected
or not getting infected.
The above instances are perhaps tip
of the iceberg of what statistics or for that the quantitative tools can
provide one. There could be numerous other examples ranging from different
factors that would influence let us say the severity of infection. In this
context, there would be data collected about different factors by examining
each patient and their severity and a relationship would be built up.
Statistical tools are not something abstract. They are made to be felt abstract
and out of the world kind of feeling by the practitioners. Yet, when they are
applied through common sense approach, numerous practical applications are
found out and can be explained in quite easy manner. There is of course a need
to make statistics easier in terms of grasping the concept. If the concepts are
understood, the applications will open at a pace of increasing returns. This is what has to be thought of in
quantitative domain rather than a focus on increasing complexity.
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