Hypothesis testing

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dan94adibi
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#1
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#1
I have a set of data, the type of distribution is not known.
The data is discreet. It's a number of lines in a shop.
I'm carrying out a hypothesis testing to see if the mean differs from a certain value. I have the SD and the mean of the sample.

Can I carry out a such a test without assuming that my data is a normal distribution? or is that the only way forward?
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MathsNerd1
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#2
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#2
(Original post by dan94adibi)
I have a set of data, the type of distribution is not known.
The data is discreet. It's a number of lines in a shop.
I'm carrying out a hypothesis testing to see if the mean differs from a certain value. I have the SD and the mean of the sample.

Can I carry out a such a test without assuming that my data is a normal distribution? or is that the only way forward?
I would personally assume that your data has a normal distribution, or can be set up to have one as it then sounds like a 1-sample z test to me, are you trying to check if the number is smaller, greater or just not equal to the certain value?
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dan94adibi
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#3
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(Original post by MathsNerd1)
I would personally assume that your data has a normal distribution, or can be set up to have one as it then sounds like a 1-sample z test to me, are you trying to check if the number is smaller, greater or just not equal to the certain value?
Yup. Checking to see if the mean is different from 150.
I've assumed a normal population and an unknown standard deviation. So I've used a one sample t-test.


How would I be able to calculate the power of the test?
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MathsNerd1
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#4
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#4
(Original post by dan94adibi)
Yup. Checking to see if the mean is different from 150.
I've assumed a normal population and an unknown standard deviation. So I've used a one sample t-test.


How would I be able to calculate the power of the test?
I've only been taught how to calculate the power of the test for known standard deviations, so unfortunately I can't help you with that problem And I'm guessing you've got a two tailed test then? Sounds a lot like the stuff I'm currently doing in my Statistics module
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dan94adibi
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(Original post by MathsNerd1)
I've only been taught how to calculate the power of the test for known standard deviations, so unfortunately I can't help you with that problem And I'm guessing you've got a two tailed test then? Sounds a lot like the stuff I'm currently doing in my Statistics module
Yup two tailed test.

H0: μ=150
Η1: μ ≠ 150

I remember doing power of a test from my S4 days but not for a t-test. :/
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MathsNerd1
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#6
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(Original post by dan94adibi)
Yup two tailed test.

H0: μ=150
Η1: μ ≠ 150

I remember doing power of a test from my S4 days but not for a t-test. :/
Very nice and are you not given the standard deviation, I thought it was only possible to work out the power for a z-test, it'll be interesting to see how its done for a t-test in the future, if I were to continue with this type of module anyway
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dan94adibi
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#7
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#7
(Original post by MathsNerd1)
Very nice and are you not given the standard deviation, I thought it was only possible to work out the power for a z-test, it'll be interesting to see how its done for a t-test in the future, if I were to continue with this type of module anyway
No. I have the sample SD but not the population SD.

I'm sure there is a method for t-test.

Check this out: http://www.cyclismo.org/tutorial/R/power.html

I just can't make any sense of it.
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MathsNerd1
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#8
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#8
(Original post by dan94adibi)
No. I have the sample SD but not the population SD.

I'm sure there is a method for t-test.

Check this out: http://www.cyclismo.org/tutorial/R/power.html

I just can't make any sense of it.
What's said there makes some sense, but I wouldn't know where to begin if instructed to do it myself, mainly because I'm not the best with R as of yet, so I'd struggle just to do the basics
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dan94adibi
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#9
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(Original post by MathsNerd1)
What's said there makes some sense, but I wouldn't know where to begin if instructed to do it myself, mainly because I'm not the best with R as of yet, so I'd struggle just to do the basics
Not to me. Man this coursework is killing me.
I can't wait to get it out of the way. Last piece for this term and then a long break before the exams.
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davros
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#10
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(Original post by dan94adibi)
Not to me. Man this coursework is killing me.
I can't wait to get it out of the way. Last piece for this term and then a long break before the exams.
If you ever get the answer to this, I'd be interested to know exactly what method you were expected to use. If this is the store data thing you posted about the other day it seems implausible that you could draw conclusions from such a small sample without making some pretty big assumptions somewhere along the line!
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dan94adibi
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#11
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#11
(Original post by davros)
If you ever get the answer to this, I'd be interested to know exactly what method you were expected to use. If this is the store data thing you posted about the other day it seems implausible that you could draw conclusions from such a small sample without making some pretty big assumptions somewhere along the line!
I was just plotting the cumulative probabilities for each of the data and this is what I've got.

Name:  Screen Shot 2014-03-30 at 22.01.22.png
Views: 143
Size:  21.9 KB

Any conclusions from this

Ignore the thumbnail one, i've updated the new one.
Attached files
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dan94adibi
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#12
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#12
(Original post by davros)
If you ever get the answer to this, I'd be interested to know exactly what method you were expected to use. If this is the store data thing you posted about the other day it seems implausible that you could draw conclusions from such a small sample without making some pretty big assumptions somewhere along the line!
Finally reached a solution.
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