Hypothesis Testing

“If it’s true what is said, that only the wise discover the wise, then it must also be true that the lone wolf symbolizes either the biggest fool on the planet or the biggest Einstein on the planet.” 

― Criss Jami, Diotima, Battery, Electric Personality

What is Hypothesis?
It is a premise or claim that we want to test.

Null Hypothesis – Ho – Currently accepted value for a parameter.
Alternative Hypothesis (Research Hypothesis) – Ha – Claim to be tested.

Let’s understand it with an example.

Example – It is believed that a candy machine makes chocolate bars that are on average 5g. A worker claims that the machine after maintenance no longer makes 5g bars. What would be Ho and Ha here?

Ho: μ = 5g
Ha: μ ≠ 5g

• Ho and Ha are mathematical opposites.
• You assume null hypothesis to be true unless evidence points otherwise.

Possible Outcome of this test:
– Reject the null hypothesis.
– Fail to reject Null Hypothesis.

Next is, How do we do that?

Test Statistic – calculated from sample data, used to decide.
Let’s continue to understand it with our example above.

We sample 50 chocolate bars (not practical to take all the bars produced).
– Get Average Value for 50 bars.
– use this information to calculate test statistic.

What do we mean when we say ‘statistically significant’ ?
– It is where do we draw the line to make a decision.

Continuing…
Let’s say the average of the sample of 50 bars comes out to be 5.12 g (sampled on Monday), 5.72 g (sampled on wednesday), 7.23 g (sampled on Friday)
Avg: 5.12 g, Avg: 5.72 g, Avg: 7.23g

Now most of us will see these averages and form different opinions . Some people might say we should reject the null hypothesis based on third sample which averages 7.23. Some might say we can accept the null hypothesis based om first sample which averages 5.12 g.

But there is no concreteness here. We’re all talking here.

Statistics is not about how you think it should be. We have to have a concrete way, looking at the null hypothesis, collecting the data and having a concrete method to decide when we accept the null hypothesis and when we leave it there.

And that is what a hypothesis test does!

A hypothesis test collects a data, put it in a equation, get a number back, and that number is going to show you how you decide when that test statistic is too high or too low, and when you reject a null hypothesis and when you don’t ( based on concrete boundaries).

Level of confidence (LOC) : C – 95 %, 99%
It is how confident are we in our decision.

Don’t forget we are doing a hypothesis test. We are testing something and we are deciding to reject the null hypothesis, or to fail to reject a null hypothesis. The level of confidence is telling us how sure we are that we did the right thing (rejecting or failing to reject the null hypothesis).

Level of Significance :
denoted by ‘α’.
α = 1 – C
if LOC = 95 %, C = 0.95
the, α = 1 – 0.95 = 0.05

YOU DON’T HAVE TO PROVE THAT NULL HYPOTHESIS IS TRUE, HYPOTHESIS TESTING ALREADY ASSUMES NULL HYPOTHESIS TO BE TRUE. YOU EITHER REJECT A NULL HYPOTHESIS OR FAIL TO REJECT A NULL HYPOTHESIS.
This is what statistics do.