What is a hypothesis test? A beginner's guide to hypothesis testing!

(speaker)
What is hypothesis testing?

Hypothesis Testing is used to determine

whether there is enough evidence
in a sample of data

to infer that a certain condition
is true for the entire population.

Therefore, it is a method
to test an assumption or theory

about a parameter
of a population based on 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 the United States,

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

The sample
is the 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, you 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 a 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 a 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 a 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 a 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 or 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 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 Data Tab

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 dataset.

After copying your data into the table,

the variables appear down here.

Data Tab 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 the hypothesis test.

Data Tab
will then suggest a suitable test.

For example,
in this case, a Chi squared test,

or in that case, an analysis of variance.

Then you will see the hypotheses
and the results.

If you are 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 non-parametric test.

You can find out the difference

between parametric and non-parametric
tests in my next video.

Thanks for watching
and I hope you enjoyed the video.