What is Statistics? A Beginner's Guide to Statistics (Data Analytics)!

PROFESSOR: If you want to
finally understand statistics,

this is the place to be.

After this video, you will
know what statistics is,

what descriptive
statistics is, and what

inferential statistics is.

So let's start with
the first question.

What is statistics?

Statistics deals with
the collection, analysis,

and presentation of data.

An example.

We would like to investigate
whether gender has an influence

on the preferred newspaper.

Then gender and newspaper are
our so-called variables that we

want to analyse.

In order to analyse whether
gender has an influence

on the preferred newspaper,
we first need to collect data.

To do this, we create
a questionnaire

that asks about gender
and preferred newspaper.

We will then send out the
survey and wait two weeks.

Afterwards, we can display the
received answers in a table.

In this table, we have one
column for each variable,

one for gender and
one for newspaper.

On the other hand, each
row is the response

of one surveyed person.

The first respondent is male
and stated New York Post,

the second is female
and stated USA Today,

and so on and so forth.

Of course, the data does not
have to be from a survey.

The data can also come from
an experiment in which you,

for example, want to study the
effect of two drugs on blood

pressure.

Now, the first step is done.

We have collected data and we
can start analyzing the data.

But what do we actually
want to analyse?

We did not survey the
entire population,

but we took a sample.

Now the big question
is, do we just

want to describe
the sample data,

or do we want to
make a statement

about the whole population?

If our aim is limited to the
sample itself, i.e. we only

want to describe
the collected data,

we will use
descriptive statistics.

Descriptive statistics will
provide a detailed summary

of the sample.

However, if we want
to draw conclusions

about the population as a whole,
inferential statistics are used.

This approach allows us
to make educated guesses

about the population
based on the sample data.

Let us take a closer
look at both methods,

starting with
descriptive statistics.

Why is descriptive
statistics so important?

Let's say a company
wants to know how

its employees travel to work.

So the company creates a
survey to answer this question.

Once enough data
has been collected,

this data can be analyzed
using descriptive statistics.

But what is
descriptive statistics?

Descriptive statistics aims
to describe and summarize

a data set in a meaningful way.

But it is important to note
that descriptive statistics only

describe the collected data
without drawing conclusions

about a larger population.

Put simply, just because we know
how some people from one company

get to work, we cannot
say how all working people

of the company get to work.

This is the task of
inferential statistics,

which we will discuss later.

To describe data
descriptively, we now

look at the four
key components--

measures of central tendency,
measures of dispersion,

frequency tables and charts.

Let's start with the first one,
measures of central tendency.

Measures of central
tendency are, for example,

the mean, the
median, and the mode.

Let's first have a
look at the mean.

The arithmetic mean is the sum
of all observations divided

by the number of observations.

An example.

Imagine we have the test
scores of five students.

To find a mean score,
we sum up all the scores

and divide by the
number of scores.

The mean test score of these
five students is therefore 86.6.

What about the median?

When the values in a data set
are arranged in ascending order,

the median is the middle value.

If there is an odd
number of data points,

the median is simply
the middle value.

If there is an even
number of data points,

the median is the average
of the two middle values.

It is important to
note that the median is

resistant to extreme
values or outliers.

Let's look at this example.

No matter how tall
the last person is,

the person in the middle remains
the person in the middle.

So the median does not change.

But if we look at the mean,
it does have an effect

on how tall the last person is.

The mean is therefore
not robust to outliers.

Let's continue with the mode.

The mode refers to
the value or values

that appear most frequently
in a set of data.

For example, if 14 people
travel to work by car,

six by bike, five walk, and
five take public transport,

then car occurs most often
and is therefore the mode.

Great.

Let's continue with the
measures of dispersion.

Measures of dispersion
describe how spread out

the values in a data set are.

Measures of dispersion
are, for example,

the variance and standard
deviation, the range,

and the interquartile range.

Let's start with the
standard deviation.

The standard deviation
indicates the average distance

between each data
point and the mean.

But what does that mean?

Each person has some
deviation from the mean.

Now we want to know
how much the person's

deviate from the mean
value on average.

In this example, the average
deviation from the mean value

is 11.5 centimeters.

To calculate the
standard deviation,

we can use this equation.

Sigma is the standard deviation,
n is the number of persons,

xi is the size of
each person, and x bar

is the mean value
of all persons.

But attention, there are two
slightly different equations

for the standard deviation.

The difference is that we
have ones, 1 divided by n,

and ones, 1 divided
by n minus 1.

To keep it simple,
if our survey doesn't

cover the whole
population, we always

use this equation to estimate
the standard deviation.

Likewise, if we have
conducted a clinical study,

then we also use this
equation to estimate

the standard deviation.

But what is the difference
between the standard deviation

and the variance?

As we now know, the
standard deviation

is the quadratic mean of
the distance from the mean.

The variance now is the
squared standard deviation.

If you want to know more details
about the standard deviation

and the variance,
please watch our video.

Let's move on to range
and interquartile range.

It is easy to understand.

The range is simply
the difference

between the maximum
and minimum value.

Interquartile range represents
the middle 50% of the data.

It is the difference between
the first quartile, Q1,

and the third quartile, Q3.

Therefore, 25% of the
values are smaller

than the interquartile range and
25% of the values are larger.

The interquartile
range contains exactly

the middle 50% of the values.

Before we get to
the last two points,

let's briefly compare
measures of central tendency

and measures of dispersion.

Let's say we measure the
blood pressure of patients.

Measures of central tendency
provide a single value

that represents the
entire data set,

helping to identify a central
value around which data

points tend to cluster.

Measures of dispersion, like the
standard deviation, the range,

and the interquartile
range, indicate

how spread out the
data points are,

whether they are closely
packed around the center

or spread far from it.

In summary, while measures
of central tendency

provide a central point of the
data set, measures of dispersion

describe how the data is
spread around the center.

Let's move on to tables.

Here we will have a look at the
most important ones, frequency

tables and contingency tables.

A frequency table displays
how often each distinct value

appears in a data set.

Let's have a closer look at
the example from the beginning.

A company surveyed its
employees to find out

how they get to work.

The options given were
car, bicycle, walk,

and public transport.

Here are the results
from 30 employees.

The first answered car, the next
walk, and so on and so forth.

Now we can create a frequency
table to summarize this data.

To do this, we simply enter
the four possible options, car,

bicycle, walk, and public
transport in the first column,

and then count how
often they occurred.

From the table, it is evident
that the most common mode

of transport among the employees
is by car, with 14 employees

preferring it.

The frequency table thus
provides a clear and concise

summary of the data.

But what if we
have not only one,

but two categorical variables?

This is where the contingency
table, also called crosstab,

comes in.

Imagine the company doesn't
have one factory, but two.

One in Detroit and
one in Cleveland.

So we also asked the employees
at which location they work.

If we want to display
both variables,

we can use a contingency table.

A contingency table provides
a way to analyse and compare

the relationship between
two categorical variables.

The rows of a contingency
table represent the categories

of one variable, while the
columns represent the categories

of another variable.

Each cell in the
table shows the number

of observations that fall into
the corresponding category

combination.

For example, the first cell
shows that car and Detroit

were answered six times.

And what about the charts?

Let's take a look at
the most important ones.

To do this, let's
simply use datatab.net.

If you like, you can
load this sample data

set with the link in
the video description.

Or you just copy your
own data into this table.

Here below you can see the
variables-- distance to work,

mode of transport, and site.

Datatab gives you a hint about
the level of measurement,

but you can also change it here.

Now, if we only click
on Mode of Transport,

we get a frequency
table and we can also

display the percentage values.

If we scroll down, we get a
bar chart and a pie chart.

Here on the left, we can
adjust for the settings.

For example, we can
specify whether we

want to display the frequencies
or the percentage values,

or whether the bars should
be vertical or horizontal.

If you also select Site,
we get a cross-table here

and a grouped bar
chart for the diagrams.

Here we can specify
whether we want the chart

to be grouped or stacked.

If we click on Distance to
Work and Mode of Transport,

we get a bar chart where
the height of the bar

shows the mean value of
the individual groups.

Here we can also
display the dispersion.

We also get a histogram,
a box plot, a violin plot,

and a rainbow plot.

If you would like to know more
about what a box plot, a violin

plot, and a rainbow plot are,
take a look at my videos.

Let's continue with
inferential statistics.

At the beginning, we
briefly go through what

inferential statistics
is, and then I'll

explain the six key
components to you.

So what is inferential
statistics?

Inferential statistics allows
us to make a conclusion

or inference about a population
based on data from a sample.

What is the population,
and what is the sample?

The population is the whole
group we are interested in.

If you want to study,
the average height

of all adults in
a United States,

then a population would be all
adults in the United States.

The sample is a smaller
group we actually study

chosen from the population.

For example, 150 adults were
selected from the United States.

And now we want
to use the sample

to make a statement
about the population.

And here are the six
steps how to do that.

Number one, hypothesis.

First, we need a statement, a
hypothesis that we want to test.

For example, we want to
know whether a drug will

have a positive effect
on blood pressure

in people with high
blood pressure.

But what's next?

In our hypothesis,
we stated that we

would like to study people
with high blood pressure.

So our population is all
people with high blood pressure

in, for example, the US.

Obviously, we cannot collect
data from the whole population,

so we take a sample
from the population.

Now we use this sample to make a
statement about the population.

But how do we do that?

For this we need
a hypothesis test.

Hypothesis testing is a
method for testing a claim

about a parameter in
a population using

data, measured in a sample.

Great.

That's exactly what we need.

There are many different
hypothesis tests,

and at the end of this
video, I will give you

a guide on how to
find the right test.

And of course, you
can find videos

about many more hypothesis
tests on our channel.

But how does a
hypothesis test work?

When we conduct a
hypothesis test,

we start with the research
hypothesis, also called

alternative hypothesis.

This is the hypothesis we are
trying to find evidence for.

In our case, the
research hypothesis

is the drug has an
effect on blood pressure.

But we cannot test this
hypothesis directly with

the classical hypothesis test.

So we test the
opposite hypothesis

that the drug has no
effect on blood pressure.

But what does that mean?

First, we assume that the drug
has no effect in the population.

We therefore assume
that, in general,

people who take the drug and
people who don't take the drug

have the same blood
pressure on average.

If we now take a random
sample and it turns out

that the drug has a large
effect in the sample,

then we can ask how likely it
is to draw such a sample, or one

that deviates even more if the
drug actually has no effect.

So in reality, on average,
there is no difference

in the population.

If this probability is very
low, we can ask ourselves maybe

the drug has an effect
in the population,

and we may have enough evidence
to reject the null hypothesis

that the drug has no effect.

And it is this probability
that is called the p-value.

Let's summarize this
in three simple steps.

Number one, the null
hypothesis states

that there is no difference
in the population.

Number two, the
hypothesis test calculates

how much the sample deviates
from the null hypothesis.

Number three, the p-value
indicates the probability

of getting a sample that
deviates as much as our sample,

or one that even deviates
more than our sample,

assuming the null
hypothesis is true.

But at what point is the
p-value small enough for us

to reject the null hypothesis?

This brings us to the next
point, statistical significance.

If the p-value is less than
a predetermined threshold,

the result is considered
statistically significant.

This means that the result
is unlikely to have occurred

by chance alone, and that
we have enough evidence

to reject the null hypothesis.

This threshold is often 0.05.

Therefore, a small
p-value suggests

that the observed
data our sample

is inconsistent with
the null hypothesis.

This leads us to reject the
null hypothesis in favor

of the alternative hypothesis.

A large p-value suggests
that the observed data

is consistent with
the null hypothesis,

and we will not reject it.

But note, there is always
a risk of making an error.

A small p-value does not prove
that the alternative hypothesis

is true.

It is only saying that it is
unlikely to get such a result,

or a more extreme when the
null hypothesis is true.

And again, if the null
hypothesis is true,

there is no difference
in the a population.

And the other way
around, a large p-value

does not prove that the
null hypothesis is true.

It is only saying that it is
likely to get such a result,

or a more extreme when the
null hypothesis is true.

So there are two
types of errors,

which are called type
I and type II error.

Let's start with
the type I error.

In hypothesis testing,
a type I error

occurs when a true null
hypothesis is rejected.

So in reality, the null
hypothesis is true,

but we make the decision to
reject the null hypothesis.

In our example, it means that
the drug actually had no effect.

So in reality, there is no
difference in blood pressure.

Whether the drug
is taken or not,

the blood pressure remains
the same in both cases.

But our sample happened to
be so far off the true value

that we mistakenly thought
the drug was working,

and a type II error occurs when
a false null hypothesis is not

rejected.

So in reality, the null
hypothesis is false,

but we make the decision not
to reject the null hypothesis.

In our example, this means
the drug actually did work.

There is a difference
between those

who have taken the drug
and those who have not.

But it was just a coincidence
that the sample taken did not

show much difference,
and we mistakenly

thought the drug
was not working.

And now I'll show
you how Datatab

helps you to find a
suitable hypothesis test,

and of course, calculates it and
interprets the results for you.

Let's go to datatab.net and
copy your own data in here.

We will just use this
example data set.

After copying your
data into the table,

the variables appear down here.

Datatab automatically
tries to determine

the correct level
of measurement,

but you can also
change it up here.

Now we just click on hypothesis
testing and select the variables

we want to use for
the calculation

of a hypothesis test.

Datatab will then suggest a
suitable test, for example,

in this case, a chi-square
test, or in that case,

an analysis of variance.

Then you will see the
hypotheses and the results.

If you're not sure how
to interpret the results,

click on Summary in words.

Further, you can
check the assumptions

and decide whether you want
to calculate a parametric

or a nonparametric test.

You can find out the
difference between

parametric and nonparametric
tests in my next video.

Thanks for watching, and I
hope you enjoyed the video.