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The other commonly used
statistical distribution

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is known as the Student's
T-distribution.

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William Sealy Gosset
specified the T-distribution.

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In fact, he published a
paper in Biometrika in 1908,

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and he published it under
the pseudonym Student.

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He worked for the Guinness
Brewery in Dublin,

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Ireland, where he worked
with small samples of body.

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Mr. Gosset is the unsung
hero of statistics.

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He published his work under

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a pseudonym because of

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the restrictions
from his employer.

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Apart from his published work,

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his other contributions to

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statistical analysis are
equally significant.

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The cult of statistical
significance,

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a must read book for anyone
interested in Data Science,

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chronicles Mr.
Gosset's work and how

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other influential
statistician's of the time,

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namely Ronald Fisher
and Egon Pearson,

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by way of their
academic bonafide,

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ended up being more
influential than the

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equally deserving Mr. Gosset.

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The normal distribution describes

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the mean for the population,

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whereas the
T-distribution describes

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the mean of samples
drawn from a population.

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The T-distribution for each
sample could be different and

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the T-distribution resembles
the normal distribution

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for large sample sizes.

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Here, I present
normal distribution

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which is drawn in blue,

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and the T-distribution with
a degree of freedom of one,

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as the degrees of
freedom increase,

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the T-distribution curve becomes

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more similar to the
normal distribution.

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In statistical analysis,

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several statistical tests
rely on T-distribution.

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For instance, a comparison of

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means tests use the
T-distribution.

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And it's also known
as the T-test.

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We have been working
with a dataset

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comprising teaching
evaluations of

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instructors from
University of Texas.

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And I will illustrate
the use of T-tests

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or T-distribution
with the question of,

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does instructor evaluation
score differ by gender?

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Do males and females get

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different teaching
evaluations from students?

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Now, if I were to take

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the same dataset and

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compute the means and
standard deviations.

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I can test this statistically.

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I have computed the
visual representation of

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the average teaching
evaluation score

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for male and female instructors.

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The blue bar represents

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the average teaching
evaluation value for females.

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The orange bar represents

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the average teaching
evaluation value for males.

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By eyeballing it, it is around

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four and slightly
less for females.

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Now it's a small difference
between males and females.

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The question is, is

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this difference
statistically significant?

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To use a T-test,

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you have to make some
assumptions are met.

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The first assumption for a T-test

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is that the scale of
measurement applied

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to the data collected

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follows a continuous
or ordinal scale.

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The second assumption is that
the data is collected from

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a representative randomly
selected portion

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of the total population.

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The third assumption is
the Data when plotted,

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will follow a normal
distribution.

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And the final assumption is
homogeneity of variance.

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To avoid the test
statistics to be

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biased towards
larger sample sizes.

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There's a test for this,

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which will be discussed later.

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Before we go perform
the test in Python.

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First, we will state
our hypothesis.

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The null hypothesis
is as follows.

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There is no difference in

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evaluation scores for
males and females.

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The alternate hypothesis
is there is a difference

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in evaluation scores
between males and females.

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Then set alpha level to 0.05.

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To do this in Python,

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we will use the T-test
independent sample

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in the Scipy stats function.

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The function takes
in the two samples

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it is trying to test.

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The statistical
difference of means for,

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in our example is

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the female's evaluation scores

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versus all the male's
evaluation scores.

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It will return a
T-statistic and a P-value.

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Since the P-value is less
than 0.05, the alpha level,

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we reject the null hypothesis

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as there is enough
evidence that there is

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a statistical
difference in teaching

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evaluations based on gender.