# Thread: Distribution free test

1. ## Distribution free test

•When pairs of observations are independent and

– the sample size is large or small and data normal then use the t-test.

– the sample size is small and the data not normal then use the Wilcoxon rank sum (Mann-Whitney U) test.

• pairs of observations are dependent and

– the sample size is large or small and data normal then use the paired t-test.

– the sample size is small and the data not normal then use the Wilcoxon signed rank test.

the above is the parts of notes ... I cant understand what is the meaning of when pairs of observation are independent and dependent , can someone explain about it by giving relevant examples ?

2. ## Re: Distribution free test

independent paired samples are what you'd expect, two independent pieces of information that just happen to be grouped as pairs.

Pick any two unrelated pieces of information and pair them.

(daily population or borneo, price of beans in china) for example.

dependent paired samples occur when one of the data in the pair depends upon the value of the other. An example of this might be (height, weight).

You would expect larger heights to be associated with heavier weights.

Or perhaps (hrs of daylight, avg daily temperature).

You would expect the summer temperatures to correspond to longer summer days.

3. ## Re: Distribution free test

Originally Posted by romsek
independent paired samples are what you'd expect, two independent pieces of information that just happen to be grouped as pairs.

Pick any two unrelated pieces of information and pair them.

(daily population or borneo, price of beans in china) for example.

dependent paired samples occur when one of the data in the pair depends upon the value of the other. An example of this might be (height, weight).

You would expect larger heights to be associated with heavier weights.

Or perhaps (hrs of daylight, avg daily temperature).

You would expect the summer temperatures to correspond to longer summer days.
I have an example below , the author used Wilcoxon signed rank test for this question . Wilcoxon signed rank test is for dependent relationship . However , computer software are different ... Why there' re dependent on each other ? I couldn't understand . Can you explain about it ?

4. ## Re: Distribution free test

Originally Posted by xl5899
I have an example below , the author used Wilcoxon signed rank test for this question . Wilcoxon signed rank test is for dependent relationship . However , computer software are different ... Why there' re dependent on each other ? I couldn't understand . Can you explain about it ?]
I'm guessing that because the two different pieces of software have to perform identical tasks that they conclude that task per task the software are related.

5. ## Re: Distribution free test

Originally Posted by romsek
independent paired samples are what you'd expect, two independent pieces of information that just happen to be grouped as pairs.

Pick any two unrelated pieces of information and pair them.

(daily population or borneo, price of beans in china) for example.

dependent paired samples occur when one of the data in the pair depends upon the value of the other. An example of this might be (height, weight).

You would expect larger heights to be associated with heavier weights.

Or perhaps (hrs of daylight, avg daily temperature).

You would expect the summer temperatures to correspond to longer summer days.
i have another example here , i assume this is dependent relationship ( test whether the
the position on the plant affect the number of seeds in the pods or NOT )

am i right ? For dependent test , there are only 2 choices , right ? Which are Mann's whiteny and t-test , am i right ???? Why the author use z -test in this example ?