A-Level Maths: O1-02 [Hypothesis Testing: Explaining the Significance Level]

[@slimeyfrog1241]

Please could you make a video on what p-values are and how they are used?

[@hemragulyusuf4069]

My blooooodclart saviour

[@beans5673]

Very helpful video you’re a great teacher

[@TheGamingWattsit]

So values within the significance level are extreme? And if so why does this give us evidence that the null hypothesis is incorrect?

[@TLMaths]

Think about this situation: I want to determine whether a coin is weighted in favour of heads. I decide I'm going to flip the coin 100 times. How many times would heads have to come up for you to believe you have strong-enough evidence that the coin is weighted in favour of heads? Let's say we'll believe we've got strong evidence if 96 or more heads appear. So you start with your null hypothesis, which in the case would be the assumption that the coin is fair. Now, what you need to understand is that I could flip the coin 100 times and get 100 heads and the coin COULD still be fair. So if I flip the coin 100 times and I get 96, 97, 98, 99 or 100 heads, the coin could still be fair but by the level I have set, I would say that I have evidence to suggest that the coin is weighted in favour of heads. The significance level is the level at which I say I have strong evidence to suggest that the coin is weighted in favour of heads. But because the coin could still be fair, even if I arrive at these extreme values, the significance level is the probability of rejecting the null hypothesis when in fact it is true.

[@TheGamingWattsit]

TLMaths if we set a significance level of 5% for some experiment and H1 is lower, this means it has a low likelyhood of occurring. Why does this mean we have evidence to reject H0? (Sorry for being an idiot, I’ve been trying to understand this for a while)

[@TLMaths]

If p is the probability of flipping a coin and getting heads, if we use H0: p = 0.5 and H1: p < 0.5, that means we're testing that the probability of landing heads is less than expected (that the coin is in fact weighted towards tails).

[@archjanasivasuthan6252]

Thank you for this video! Why do we always reject the hypothesis if the test statistic is less than the significance value?

[@TLMaths]

Because we've found the probability of the event occurring under the assumed circumstances is very unlikely, giving evidence that the assumed circumstances are incorrect

[@nosir1479]

Wait, why the significance level the probability of *incorrectly* rejecting H0? isn't it just the probability of rejecting H0? What does the incorrectly part mean?

[@TLMaths]

A very good explanation here: statisticsbyjim.com/glossary/significance-level/

[@alexireade3408]

I’m confused, my text book states that you reject the null hypothesis when your probability is less then the significance level (1tailed test). Have I just misunderstood what you said?

[@TLMaths]

I did say that at 0:50 ?

[@josephparsons7896]

is the significance level just set arbitrarily?

[@TLMaths]

Yes

[@User-ei2kw]

where did u buy the hoodie from

[@TLMaths]

qwertee

[@johng5295]

Thanks in a million. Awesome.

[@johng5295]

Thanks in a million.A++

[@TLMaths]

Glad to help!

[@thespacedogster8869]

This helped so much thanks

[@favouraleph829]

Thanks