If you change the variables that you're adjusting for

in your regression model, actually the null hypothesis change

because the null hypothesis depends on all the regression coefficients you're saying.

In the previous model we only had one coefficient that we were fitting and so

the null and the alternative hypothesis were very easy to define.

But if you have a large number of adjustment variables

then you're saying that the effect is equal to zero.

Once you adjust for all of the other variables variables in your model.

In general,

you have to be very careful to make sure that the null makes intuitive sense.

And you can really twist yourself into knots if you're not careful about

defining, very clearly in advance, what would be the no effect scenario.

In this particular modeling strategy.

And it's very important to get this step right.

This is the reason why hypothesis testing is often very highly

criticized by a number of statisticians is because it's very easy

to get the null hypothesis wrong.

Or at least to argue about what the null hypothesis is.

This is actually a case where this was actually discussed in very great depth.

On a blog, on Lior Pachter's blog,

he talked about a particular null hypotheses from a particular paper

that he disagreed with the way they had defined the null hypotheses, and

then discussed the how you would define that null hypothesis in a case.

I'm pointing you to this article because there was this very long discussion

in the comments section on this blog post about how to define the null hypothesis.

And I think it gives you some insight into looking at

how difficult it is to get the null hypothesis right,

particularly when dealing with complex and high dimensional genomic data.

But this is a point that's worth paying a lot of attention to.

Again I'd point you to this inference class if you want to learn a lot

more about hypothesis testing.

And the Statistics and R for the Life Sciences course also has a lot more about

inference and hypothesis testing in particular if you care about that.

But again the key point is to remember to get your null and

alternative hypothesis right.

And the null hypothesis in general, usually for genomics,

is defining what would this model look like if there was no effect?