The discussion clarifies the differences between the sign test and the Wilcoxon signed rank test, both of which are used for analyzing paired samples from non-normally distributed populations. The sign test requires only knowledge of which paired values are larger, while the Wilcoxon signed rank test necessitates that the values be ordered, allowing for more information to be utilized. When the data can be ordered, the Wilcoxon signed rank test is generally preferred due to its increased statistical power. However, if the data cannot be ordered, the sign test remains a valid option.
PREREQUISITESStatisticians, data analysts, and researchers who work with paired sample data and need to choose appropriate non-parametric tests for hypothesis testing.
So , if the college statistics question didn't ask for whether we should put the results in increasing order or not , both can be used ? Am i right ?FactChecker said:The sign test only requires that you know which of the paired tests are larger. The signed rank test requires that you can put all the results in increasing order. So the signed-rank test has a lot more information to work with. If you can put all the results in order, use the signed-rank test.
PS. For a general statistics question like this, where you are not asking about a specific homework problem, there is a section for Statistics under Math that might be a better place to post.
Do you mean If I can put them in order , then it's recommended to use signed-rank test over sign test ?FactChecker said:If you can put them in order, it is probably better to do that. The signed-rank test may be a stronger test. But often there is no such thing as order -- you just have a (greater-than, less-than) boolean paired-data sample. Then you can not use the signed-rank test.
There is a trade-off. By putting them in ranks, you are gaining the ranking information but giving up the pairing information. I believe that there are examples where each is stronger. Certainly, pairs of data like (1,2) (3,4) (5,6) (7,8) are very clear, whereas the rank ordering of 1, 2, 3, 4, 5, 6, 7, 8 hides the important information and is weak. On the other hand, (1, 7), (3, 2) (5,8) (4,6) looks much stronger in the form of 1, 2, 3, 4, 5, 6, 7, 8 because when the second entries of the pairs are larger, they are not just larger than the first entry of that pair -- they tend to be larger than all first entries of all pairs.tzx9633 said:Do you mean If I can put them in order , then it's recommended to use signed-rank test over sign test ?
why ? Can you explain further ?FactChecker said:whereas the rank ordering of 1, 2, 3, 4, 5, 6, 7, 8 hides the important information and is weak.
The ordering of the two sets is entirely swapped if the lowest ranked element is deleted. So it is my assumption that the statistical result will be weak and insignificant. In the paired results, (1,2) (3,4) (5,6) (7,8), it is very clear, and I assume statistically significant, that the second set ranks above the first set.tzx9633 said:why ? Can you explain further ?