M******8
发帖数: 22 | 1 One suggested test for trend in a univariate population is as follows:
Group the unordered scores into nonoverlapping groups of 3 adjacent
observations. The test statistic D is the number of monotonic (either
increasing or decreasing) triples. Assume for now that N is always a
multiple of 3 (no partial triples).
Example (triples are underlined)
33, 16, 20 61, 44, 38 29, 40, 56, 22, 43, 31
no order decrease increase no order D = 2
H0: random ordering (independent, random)
HA: linear trend
What is the distribution of D? What is the expected value of D if the null
hypothesis is true? Note we’re talking generic formulas, not specific to
the example.
If there are 24 scores, what is the critical value of D? (Now you can get
specific). | l*********s
发帖数: 5409 | 2 under null, D is binomial with expectation n/3 | k****i
发帖数: 347 | 3 如果我没算错的话，呵呵，0-1的uniform distribution,x1
monotonic的概率就是1/3
所以楼上应该是对的。binomial distribution,不过expectation是N/9
好奇的是，你这个unordered scores是怎么定义的？把数据shuffle一遍还算是
unordered scores么？在这个shuffle后的test statistic你们care不？ | M******8
发帖数: 22 | 4
这个unordered scores他也没给详细解释什么意思。不过我觉得，这里他说unordered
是在分group的时候不用重新order那个N scores sample。只要按照给出的顺序分成
triples就成了～～
所以是不是要考虑the total permutaion of the sample?
为啥expectation是N/9呢？
【在 k****i 的大作中提到】
: 如果我没算错的话，呵呵，0-1的uniform distribution,x1: monotonic的概率就是1/3
: 所以楼上应该是对的。binomial distribution,不过expectation是N/9
: 好奇的是，你这个unordered scores是怎么定义的？把数据shuffle一遍还算是
: unordered scores么？在这个shuffle后的test statistic你们care不？
|
|
