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 ?
A sign test is a non-parametric statistical test used to determine if there is a significant difference between two related samples. It is based on the number of positive and negative differences between the paired samples. A Wilcoxon signed rank test, on the other hand, is also a non-parametric test but it takes into account the magnitude of the differences between the paired samples.
A sign test is more appropriate for small sample sizes as it does not require the assumption of normality and can be used with as few as 10 observations.
Yes, both tests are appropriate for dependent samples, where each observation in one sample is paired with a corresponding observation in the other sample.
The main assumption for a Wilcoxon signed rank test is that the differences between the paired samples are symmetrically distributed around zero.
In a sign test, the null hypothesis is that there is no difference between the two samples. If the p-value is less than the chosen significance level, the null hypothesis is rejected and it can be concluded that there is a significant difference between the samples. In a Wilcoxon signed rank test, the null hypothesis is that the median difference between the paired samples is zero. A significant p-value indicates that the null hypothesis can be rejected and there is a significant difference between the samples.