Chi squared in inheritance: Using chi-squared to prove Mendelian genetics.

Hi there, and welcome to learn
A-level Biology for free with Ms Estruch.

In this video, I'm going to be showing you
how the statistic chi squared

can be applied to inheritance questions.

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So just a recap, first of all,
about the statistic chi squared.

It's one of the three that you
need to know for A-level Biology.

And the reason you would use this,
or the circumstances,

would be if you're investigating whether
there's a difference between

frequency data.

And that's going to be the key here,
differences between frequencies.

Now if you're not confident
on chi squared, I'll link my first video

on chi squared, which goes through
all the details you need to know.

In this video, I'm just going to be showing
you how it can be applied

to inheritance questions.

And in this first example,
I'm going to link it to a question to do

with the disease cystic fibrosis,
which is caused by a recessive allele.

And in this example,
I've got, two parents who are both

carriers and we want to know what's
the probability that those two parents

will have a girl with cystic fibrosis.

Now if they're both carriers,
their genotype would be heterozygous,

which we can see here.

I've done the Punnett square and we can
see that we have, one quarter

would have cystic fibrosis,
but they also want to know what's

the probability that it will be a girl
with cystic fibrosis.

So that's why the next step is I've
multiplied by 50%, and our overall

probability is 12.5%
using a Punnett square.

Now the way you can use chi squared is
to investigate whether

what you expect is going to be
significantly different

to what we actually observe.

Because using Punnett squares is all
probabilities and saying,

This is what I expect to happen,
it's not based on observation.

So that is how we use
chi squared in inheritance.

First of all, you would use your Punnett
square to work out what is

the frequency that you expect to see.

Then you'll have to record what you
actually observe,

and then we can do the statistic to see
is there a significant difference between

what we expected and what we observed?

So I'm going to go through a whole example
with you, and this is the example that I

always do each year
with students at my school.

And it's using ear of corn.

And in the UK,
you're probably not familiar with seeing

corn on the cob like this,
'cause at supermarkets we

just get it as yellow corn.

But in reality, there's lots of different
variations, which is

determined by their alleles.

And you can get corn which is purple,
yellow, smooth, wrinkly in texture.

So it's quite a good one 'cause you can
clearly observe the different phenotypes,

quite...
So we're going to go through an example,

and that is looking at does the frequency
of purple and yellow corn

match what the Mendelian genetics
probability states we would expect?

So first step is we need to do our Punnett
square to have a look at what is

the frequency that we would expect.

So purple is the dominant allele,
yellow is recessive.

And in this exam question, in this example
was stating that there were two

heterozygous parents that were crossed,
and here's the Punnett square.

So the result is we have 75%
of the offspring we would expect to be

purple and 25% we would
expect to be yellow.

So the expected ratio is three to one.

The next step is, that is our expected,
but we need to see what is the actual.

And to do this, you need to then count all
of the purple and all of the

yellow on your ear of corn.

So in this example,
the student then counted and there were

21 purple kernels and 13 yellow kernels.

So we then need to use chi square to see
does this follow the expected ratio,

and therefore Mendelian genetics?

So the next step is a null hypothesis.

So the null hypothesis in this case is
there is no significant difference between

the expected and the observed
frequency of the color of corn kernels.

So we're saying that the expected of three
to one,

is going to be exactly the same as
what we observe,

a three to one ratio overall.

Now you don't actually have to be able
to calculate chi squared for the exam.

You would just be given the chi squared
value or the P value

to come to a conclusion.

But I'm just going to show you how you would
do this because some of you might be asked

to do this as an experiment in lessons,
and you've got this to help.

So as I said, the observed
frequency was 21 purple, 13 yellow.

So that means in total
we have 34 corn kernels.

The expected ratio was three to one,
but we need to turn that into a frequency.

So three out of four will be purple,
but we actually have 34, corn kernels.

So we needed to do 75% of 34,

which is 25.5. And then 25% of 34,

which is 8.5. So we now have our observed

frequency and our expected frequency.

We can then do the stages of chi squared.

So I've implemented these results already.

So observed minus expected.

That is then squared,
divided by the expected value

and then the sum of that column is
3.176. So that is our chi squared value.

So in an exam, you'd be given that value.

You wouldn't have to do this table here.

So we've now got our chi squared value.

The degrees of freedom is one,
and that is because it's the number

of categories minus one, so n-1.

And we have two categories,
purple and yellow, minus one.

We only have one degree of freedom.

So we then need to see
what our critical value is.

And to do this, we need to look at the one
degree of freedom row

and we always look at 0.05,
which is 5% probability

that the difference is due to chance
for our P-value,

because that means you can be 95%
confident that the difference

is significant.

So the critical value that we are using is
3.841, and we have to compare

that to our chi squared value.

So the calculated value of chi squared we
said was 3.176,

and that is less than the critical value

of 3.841 at the P-value of 0.05.

So that means that this value,
we know there would be 5%

probability it's due to chance.

Now because our chi squared value does not
exceed that threshold,

that critical value,
that means there's actually more than 5%

probability
that the results are due to chance.

And in this case, what we mean by results
is the difference between the expected

and the observed frequency.

So we have to accept the null hypothesis,
which we stated up here in green.

And because we're accepting that,
what that means is there is no significant

difference between what we
observed and what we expected.

So if we then finally link that back
to the Mendelian genetics and say what

that means,
it means that the corn kernels that we

observed did follow the expected ratio
of three to one, and therefore

it did follow Mendelian genetics.

So we've managed to use chi squared to say
that there is a significant,

match between what we expected using
our Punnett square

and what we actually used.

And in that way, we've used the statistic
to prove Mendelian genetics.

(UPBEAT MUSIC) So that is it
for using chi squared in inheritance.

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