Testing of Hypothesis in Business Analytics: An Analogy from Everyday Life
One advanced technique you need to
learn in business analytics is how to test your hypotheses. Learning how to
test a hypothesis is important for analysts because they will use the process
in many situations, such as when testing correlation, testing regression
coefficients, testing parameter estimates in time-series analysis, testing the
goodness of fit in logistic regression, and so on.
Let’s
use a simple real-life example to conduct a test. Say you want to buy a
50-pound cake for a big party. You walk into a cake shop and ask for one. The
store manager says it’s ready, and she shows it to you. You might get
suspicious about its taste and quality. Fifty pounds is a giant cake, and
obviously you don’t want to take any risks, even if the store manager assures
you that it’s the best quality. In fact, you may want to test the cake. In
other words, you would like to test the statement made by the store manager
that the cake is of good quality. Obviously, you can’t eat the whole cake and
claim you are just testing. So, you will ask the manager to cut a small piece
out of the cake give it to you for testing. You might want to cut this test
sample randomly from the cake. The following are the possibilities that might
result from your test:
·
The test piece is awesome and
tastes like the best cake you have ever had. It may be an instant buy decision.
·
The test piece is contradictory to
your expectations. You will definitely not buy it in that case.
·
The quality is not the best, but
it is still satisfactory. You may want to buy it if nothing better is
available.
You
had an assumption to begin with, you then took a sample to test it, and you
made a conclusion based on a simple test. In statistical terms, you made an inference on the whole population based
on testing a random sample. This process was the essence of the testing of
hypothesis, in other words, the science of confirmatory data analysis.
Let’s
consider one more example. A giant e-commerce company claims that half of its
customers are male and another half female. To test this statement, you take a
random sample of 100 customers and count how many of them are male. Again, the
following three scenarios may arise:
·
Exactly 50 percent are males, and
the other 50 percent are females.
·
One gender dominates. For example,
almost 90 percent are males, and only 10 percent are females.
·
One gender is near 50 percent. For
example, 52 percent are males in the sample.
In
the first scenario, you agree to the statement made by the e-commerce company
that the count of male and female customers is the same. In the second
scenario, you simply reject the company’s claim. In the third scenario, you may
tend to agree with the claim. Once again, you are making an inference on the
whole population based on the sample measures.
These
are reasonably good examples of the process of testing a hypothesis. It is
summarized as follows:
1.
You start with an assumption.
a.
The whole cake is good in the
first example.
b.
Overall, the gender ratio is 50
percent in the second example.
2.
You take a sample that represents
the population.
c.
You try a piece of cake in the
first example.
d.
You look at 100 customers in the
second example.
3.
You do some kind of test on the
sample gathered in step 2.
e.
You test the piece of cake by
putting it in your mouth.
f.
You actually count the number of
male and female customers in the sample.
4.
You make a final interpretation
and inference based on the testing of random sample.
g.
You make a decision about whether
the cake is good or bad.
h.
You make an inference about
whether the gender ratio is really 50 percent or not.
What
Is the Process of Testing a Hypothesis?
Testing
of hypothesis is a process similar to the examples discussed in the previous
section. Using this process you make inferences about the overall population by
conducting some statistical tests on a sample. You are making statistical
inferences on the population parameter using some test statistic values from
the sample.
In
inferential statistics, you make an assumption about the population. That
assumption is called the hypothesis
(the null hypothesis to be precise).
You take a sample and calculate a test statistic, and you expect this test
statistic to fall within certain limits if the null hypothesis is true.
Table
1-1 contains a few more examples involving the process of testing a hypothesis.
Table 1-1. Examples of Testing a Hypothesis
Scenario
|
Null Hypothesis
|
Sample
|
Sample Statistic
|
Inference
|
Bank customers salary
|
The average income is
$35,000.
|
You take a simple random
sample of 300 customers.
|
The sample statistic is the
average salary of 300 sampled customers.
|
Accept the null hypothesis
if the salary of the sample falls near $35,000, or reject the null
hypothesis.
|
Drug testing
|
The drug has 1.5 percent
alcohol.
|
You take a random sample of
100 ml.
|
The sample statistic is the
measured alcohol percentage in the sample.
|
Accept the null hypothesis
if the sample test value is near 1.5 percent.
|
Product feedback
|
Our product customer
satisfaction is 80 percent.
|
You take a simple random or
stratified sample of users across various segments.
|
You conduct a survey and
take the sample C-SAT score (formal customer satisfaction score).
|
Accept the null hypothesis
if the sample C-SAT falls near 80 percent.
|
Student training
|
The training has no
significant effect on students.
|
You take a sample of
students who took the training.
|
Students take a test before
the training and a test after the training.
|
If there is a significant
increment in the marks, then accept the null hypothesis.
|
Smoking causes cancer
|
Smoking does not cause
cancer (smoking and cancer are independent).
|
You take a random sample
from the population (contains smokers and nonsmokers).
|
The sample statistic is the
proportion of cancer in smokers and nonsmokers.
|
If the proportion of cancer
is not significantly different in smokers than in nonsmokers, then accept the
null hypothesis.
|
This article was taken from the
following book of Venkat Reddy And Shailendra Kadre..
Practical Business Analytics Using
SAS: A Hands-on Guide
ISBN-10:
1484200446
ISBN-13:
978-1484200445
