Can Someone explain the Maximum likelihood Z-test for me in laymen's terms please?

Alpha6

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Can Someone explain the Maximum likelihood Z-test for me in laymen's terms please?

I have been trying to get a grasp of it, but everything I read drives me into further confusion. Can anyone explain it to me like a child please?
 
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I have been trying to get a grasp of it, but everything I read drives me into further confusion. Can anyone explain it to me like a child please?

I'm not sure I know it well enough to explain but I'll try. Other thoughts would certainly be welcome for my point of view.

First the Maximum likelihood Z test is a test about whether there is a relationship between two measured things. A typical use is to see if a subgroup of a larger population is different than that gereral population. The weigh of the cattle brought by a particular rancher to market compared to all the cattle brought to market. The color of the red roses grown by a particular grower compared to all growers. The amount of gold extracted from a particular mine compared to all mines in a certain area. ...

Example for explanation: I'll use the one from wikipedia
http://en.wikipedia.org/wiki/Z-test
Suppose I wanted to know about the performance of some particular school [first thing] compared to the general population [second thing]. I choose the test averages for a particular test as the comparison vehicle. If the students in this particular school were like the general population of all those who were tested then I would expect their average to be about the same as the average for the general population. If I were to look at a lot of particular schools, I would expect the averages for those particular schools to be about normally distributed about the average of the general population. So, I have a sample from that group of tested schools [the first thing above]. What is the likelihood their average will be, say 2 standard deviations, less than the general population average[the second thing]. Well we have assumed the averages for the particular schools are normally distributed, look it up in the normal CDF table [Z test].

Now the test: It is mechanical, you just measure the data and plug in the numbers from the normal distribution. I mentioned 'What is the likelihood their average will be, say 2 standard deviations, less than the general population average[the second thing]' above. Well we have how many standard deviations the particular school average was from the general population. How likely is that? Look it up in the Normal CDF table.

BTW: Since you see the variable for the CDF of the Normal distribution show as z, you should know why it is the Z test and not, for example, the W test.
 
I'm not sure I know it well enough to explain but I'll try. Other thoughts would certainly be welcome for my point of view.

First the Maximum likelihood Z test is a test about whether there is a relationship between two measured things. A typical use is to see if a subgroup of a larger population is different than that gereral population. The weigh of the cattle brought by a particular rancher to market compared to all the cattle brought to market. The color of the red roses grown by a particular grower compared to all growers. The amount of gold extracted from a particular mine compared to all mines in a certain area. ...

Example for explanation: I'll use the one from wikipedia
http://en.wikipedia.org/wiki/Z-test
Suppose I wanted to know about the performance of some particular school [first thing] compared to the general population [second thing]. I choose the test averages for a particular test as the comparison vehicle. If the students in this particular school were like the general population of all those who were tested then I would expect their average to be about the same as the average for the general population. If I were to look at a lot of particular schools, I would expect the averages for those particular schools to be about normally distributed about the average of the general population. So, I have a sample from that group of tested schools [the first thing above]. What is the likelihood their average will be, say 2 standard deviations, less than the general population average[the second thing]. Well we have assumed the averages for the particular schools are normally distributed, look it up in the normal CDF table [Z test].

Now the test: It is mechanical, you just measure the data and plug in the numbers from the normal distribution. I mentioned 'What is the likelihood their average will be, say 2 standard deviations, less than the general population average[the second thing]' above. Well we have how many standard deviations the particular school average was from the general population. How likely is that? Look it up in the Normal CDF table.

BTW: Since you see the variable for the CDF of the Normal distribution show as z, you should know why it is the Z test and not, for example, the W test.

I appreciate your explanation. Thank you.
 
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