All language subtitles for 27031x_PR_Laws_Inheritance_09_Hypothesis_Testing_v2-en

PETER REDDIEN: Hypothesis testing.

We have a null hypothesis, our model,

which is our hypothesis 3.

And what we want to know is can we reject it?

Or are our data inconsistent with hypothesis 3.

And the statistical test will use here

is a chi-square test, where what we'll

do is for all of our classes we're

going to sum up our data of the observed data

minus the expected squared.

Over the expected.

So what did we observe and expect?

Well, so if we say we have paralyzed flies, not paralyzed,

and then we have some observations,

and some expectations.

So what we observed was we had four paralyzed, 12 not

paralyzed, and we expected seven and nine.

So we have two classes and our observed and expected data,

so now we can calculate this chi-square value.

So it will be 7 minus 4 squared over 7.

Well, I'll do it the other way.

It doesn't matter, but--

and then 12 minus 9 squared over 9.

We'll get some value for this, which is 2.28.

And that is our chi-square value.

And now, we can ask with this chi-square value

how likely would it be to get a chi-square value of 2.28

if our hypothesis was right.

And we can look at a lookup table, where

we can see the probabilities of getting a chi-square value

of 2.28 with this data.

So let's just look at this first row for now.

We see 2.28 is falling somewhere between 0.05 and 0.2,

but we do have to consider this y-axis here,

these other rows, which are the degrees of freedom.

So the Degrees of Freedom, or df, we're going to be equal--

is going to be equal to the number of classes minus 1.

It's referring to the number of independent,

normally distributed variables.

And because if we know the total in one class,

we can calculate the other class,

then we have one independent, normally distributed variable.

So that's why you subtract 1.

So if you had three classes, we have two classes.

If we had three classes, we'd have two degrees of freedom.

If we have two classes, we have one degree of freedom.

So we have one degree of freedom here.

So our degrees of freedom is 1.

So now then looking at our chi-square table,

we see that our probability of getting this chi-square value

is greater than 0.05 and less than 0.2.

So our p-value is greater than 0.05 and less than 0.2.

So we have greater than a 1 in 20 chance

if we do this experiment of getting

data that deviates this far or more from our expected.

So that's in some sense a less than a one in five chance.

So in that, in some sense, is our answer

to what is the probability of getting this data

under the hypothesis 3.

Now, can we reject it?

By convention, you need a p-value of less than 0.05

to reject.

Now, that's just convention, doesn't mean necessarily

that the hypothesis is wrong, just

means that you would expect to get data

like this with a probability of less than one in 20.

By convention, that is a threshold for rejection.

You can set different thresholds, but anyway--

so what do we conclude from this, from our data?

Can we reject the hypothesis?

We cannot.

So our data, we cannot reject hypothesis 3.

You could go through some practice

yourself by making bigger sample sizes

and figure out what would happen.

And general one wants to think about with experiments,

so we won't do a lot of this here--

the sample size you have, if you have two hypotheses you're

trying to consider between, I want

to do something called power analysis to figure out

what sample size you would need to distinguish between data.