GeorgeAndLennie
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I'm stuck on this.

So for every inferential test, no matter if the observed value should be greater than null hypothesis or the observed value should be less than the null hypothesis.

Is it rejected for all the TESTS? Like mann whitney u, wilcoxon.

The only time in the exam it will be accepted if say for a test the observed value is meant to be greater, but when you work it out or check it, it's less. Then you accept it, correct?
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iammichealjackson
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(Original post by GeorgeAndLennie)
I'm stuck on this.

So for every inferential test, no matter if the observed value should be greater than null hypothesis or the observed value should be less than the null hypothesis.

Is it rejected for all the TESTS? Like mann whitney u, wilcoxon.

The only time in the exam it will be accepted if say for a test the observed value is meant to be greater, but when you work it out or check it, it's less. Then you accept it, correct?
Lets use the example of a binomial test to see whether a coin toss is biased. If we do 10 tosses, then our null hypothesis is that we expect to see 5 heads and 5 tails.

We don't reject the null hypothesis if our observed value is different to the expected value, because we know that random error will mean that sometimes we will get 6 tails and 4 heads, or 7 tails and 3 heads. The significance test examine how likely it is that our observed results will occur compared to the null hypothesis.

If we get 6 heads (more than expect) out of 10 tosses, then our (two tailed) p-value will be .75 (75%)

If we get 9 heads however, then our (two tailed) p value will be .0215 (2.2%) which is significant. This means that the hypothesis that our coin toss is fair (50% heads and tails) is likely to be incorrect.


In the case of getting 6 heads, its different from the null hypothsis, but we don't reject the null hypothesis because our observed value is also influenced by chance which can mean that results slightly different from the null hypothesis are to be expected from time to time
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iammichealjackson
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(Original post by GeorgeAndLennie)
I'm stuck on this.

So for every inferential test, no matter if the observed value should be greater than null hypothesis or the observed value should be less than the null hypothesis.

Is it rejected for all the TESTS? Like mann whitney u, wilcoxon.

The only time in the exam it will be accepted if say for a test the observed value is meant to be greater, but when you work it out or check it, it's less. Then you accept it, correct?
On this final point, it depends if your doing a one-tailed or two-tailed test. For a one-tailed test, if you predict that a drug will improve memory, and it turns out that it actually statistically significantly reduces memory, you should not reject the null hypothesis (or you should accept the null hypothesis in your terminology**)

However, if you do a two-tailed test, it doesn't matter if the drug significantly improves or reduces memory, you reject the null hypothesis in either case.

In reality --- if you found that a drug significantly reduces memory, but you opted to do a one-tailed test that it should improve memory, most researchers would just go back and do a two-tailed test and report that. Your not meant to do this, and it means that the one-tailed test essentially becomes a bit useless. However, researchers need to produce published studies to keep their jobs to the temptation to do this is there...

**You don't accept the null hypothesis, you can only reject it. To understand why, you need some fairly sophisticated understanding of statistics, but take my word for it.
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GeorgeAndLennie
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(Original post by iammichealjackson)
On this final point, it depends if your doing a one-tailed or two-tailed test. For a one-tailed test, if you predict that a drug will improve memory, and it turns out that it actually statistically significantly reduces memory, you should not reject the null hypothesis (or you should accept the null hypothesis in your terminology**)

However, if you do a two-tailed test, it doesn't matter if the drug significantly improves or reduces memory, you reject the null hypothesis in either case.

In reality --- if you found that a drug significantly reduces memory, but you opted to do a one-tailed test that it should improve memory, most researchers would just go back and do a two-tailed test and report that. Your not meant to do this, and it means that the one-tailed test essentially becomes a bit useless. However, researchers need to produce published studies to keep their jobs to the temptation to do this is there...

**You don't accept the null hypothesis, you can only reject it. To understand why, you need some fairly sophisticated understanding of statistics, but take my word for it.
I got it now So in all cases just reject the null hypothesis whatever the result? I mean according to the one tailed test and two tailed test?

That makes sense
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GeorgeAndLennie
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(Original post by iammichealjackson)
On this final point, it depends if your doing a one-tailed or two-tailed test. For a one-tailed test, if you predict that a drug will improve memory, and it turns out that it actually statistically significantly reduces memory, you should not reject the null hypothesis (or you should accept the null hypothesis in your terminology**)

However, if you do a two-tailed test, it doesn't matter if the drug significantly improves or reduces memory, you reject the null hypothesis in either case.

In reality --- if you found that a drug significantly reduces memory, but you opted to do a one-tailed test that it should improve memory, most researchers would just go back and do a two-tailed test and report that. Your not meant to do this, and it means that the one-tailed test essentially becomes a bit useless. However, researchers need to produce published studies to keep their jobs to the temptation to do this is there...

**You don't accept the null hypothesis, you can only reject it. To understand why, you need some fairly sophisticated understanding of statistics, but take my word for it.
another question. I know a one tailed test = you reject the null hypothesis but two tailed = when you wrongly accept the null and retain it

Does it depend on the 4 types of test whether you accept it or reject it?
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L'Evil Fish
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(Original post by GeorgeAndLennie)
another question. I know a one tailed test = you reject the null hypothesis but two tailed = when you wrongly accept the null and retain it

Does it depend on the 4 types of test whether you accept it or reject it?
It depends on the p value.

If it's one tailed, and the p value is

Less than 0.01 - reject null
Between 0.01 and 0.05 - reject null
Bigger than 0.05 - can't reject null

If it's two tailed, you multiply the probability of it being at least as extreme as by 2 and use same rules above.
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iammichealjackson
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(Original post by GeorgeAndLennie)
another question. I know a one tailed test = you reject the null hypothesis but two tailed = when you wrongly accept the null and retain it

Does it depend on the 4 types of test whether you accept it or reject it?
You never accept the null hypothesis, you can only reject it (this requires undergraduate stats knowledge to understand why).

For both one tailed and two-tailed tests, you either reject the null hypothesis, or you say "no evidence to reject the null hypothesis". This isn't just because researchers like to confuse you, there are statistical reasons why you don't accept a null hypothesis.
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iammichealjackson
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(Original post by GeorgeAndLennie)
another question. I know a one tailed test = you reject the null hypothesis but two tailed = when you wrongly accept the null and retain it

Does it depend on the 4 types of test whether you accept it or reject it?
Different statistical tests exist (and there must be thousands of them, not just 4) for analysing different types of data, but they all work in the same way in that you reject the null hypothesis if the value is substantially different to the null hypothesis expected value.

You use a t-test for analysing continious parametric data (e.g. height).

You use a chi-square test for analysing binary data (e.g. coin toss)
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GeorgeAndLennie
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(Original post by iammichealjackson)
You never accept the null hypothesis, you can only reject it (this requires undergraduate stats knowledge to understand why).

For both one tailed and two-tailed tests, you either reject the null hypothesis, or you say "no evidence to reject the null hypothesis". This isn't just because researchers like to confuse you, there are statistical reasons why you don't accept a null hypothesis.
This is what I needed to know! Thank you.

I realised this now because. For Chi Squared and Spearmans rho if the observed value is greater than 1 or equal to critical value, you reject it.
In Wilcoxon and mann whitney U if the observed value is less than 1 or equal to, you reject it.

So either way you reject it but it depends on the observed value, phew this is the hard part done lol, just got confused on this for A2

and yep I got that for chi squared its stuff like nominal
and for T test it's.. ordinal or interval etc. !!
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GeorgeAndLennie
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(Original post by L'Evil Fish)
It depends on the p value.

If it's one tailed, and the p value is

Less than 0.01 - reject null
Between 0.01 and 0.05 - reject null
Bigger than 0.05 - can't reject null

If it's two tailed, you multiply the probability of it being at least as extreme as by 2 and use same rules above.
This confused me lol cuz we never got taught this. But i get it now thanks to michael lol
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iammichealjackson
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(Original post by GeorgeAndLennie)
This is what I needed to know! Thank you.

I realised this now because. For Chi Squared and Spearmans rho if the observed value is greater than 1 or equal to critical value, you reject it.
In Wilcoxon and mann whitney U if the observed value is less than 1 or equal to, you reject it.

So either way you reject it but it depends on the observed value, phew this is the hard part done lol, just got confused on this for A2

and yep I got that for chi squared its stuff like nominal
and for T test it's.. ordinal or interval etc. !!
Oh if we're talking about critical values then that is something different. Evil Fish is talking about p-values. I was talking about actual values (e.g. number of heads recieved). Critical values refer to calculations made from the actual observed values using a formula. So many numbers
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GeorgeAndLennie
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(Original post by iammichealjackson)
Oh if we're talking about critical values then that is something different. Evil Fish is talking about p-values. I was talking about actual values (e.g. number of heads recieved). Critical values refer to calculations made from the actual observed values using a formula. So many numbers
Lol yeah i was mainly talking about critical values and observed values and the tests
that was basically my question

So for example say for chi squared, the observed value is meant to be greater than critical value for you to reject the null hypothesis
but say that you found the observed value is actually less than critical value, you accept it?

I got the idea of the 4 tests and how to work it out but im confused about the above ^

(im sorry for so many questions, just need to really clear this up)
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iammichealjackson
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(Original post by GeorgeAndLennie)
Lol yeah i was mainly talking about critical values and observed values and the tests
that was basically my question

So for example say for chi squared, the observed value is meant to be greater than critical value for you to reject the null hypothesis
but say that you found the observed value is actually less than critical value, you accept it?

I got the idea of the 4 tests and how to work it out but im confused about the above ^

(im sorry for so many questions, just need to really clear this up)

Woops, i wasn't talking about these values at all, i was talking about the observed values (e.g. 101 cm, 6 heads out of 10 coin tosses, etc. etc.). You were talking about the test statistic which is different, i guess you could call it the observed value but the observed value could refer to a lot of different things!

I think for all statistical tests i know you reject the null hypothesis when the "observed test statistic/value" is higher than the critical value.

You were incorrect below, however, in that if the observed test statistic for the mann-whitney is higher than 1, this doesn't tell us anything. The critical value for every test depends on the sample size used (see this attachment for an idea of how to work out the critical value http://www.saburchill.com/IBbiology/downloads/002.pdf)

(Original post by GeorgeAndLennie)
This is what I needed to know! Thank you.

I realised this now because. For Chi Squared and Spearmans rho if the observed value is greater than 1 or equal to critical value, you reject it.
In Wilcoxon and mann whitney U if the observed value is less than 1 or equal to, you reject it.

So either way you reject it but it depends on the observed value, phew this is the hard part done lol, just got confused on this for A2

and yep I got that for chi squared its stuff like nominal
and for T test it's.. ordinal or interval etc. !!
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