Post
Topic
Board Meta
Re: Time Series Analysis on Distributed Merits in the forum (daily, weekly, monthly)
by
tranthidung
on 14/11/2018, 13:28:11 UTC
Weekly Analysis:
Updated at 19th Nov. 2018:

Overview plot and trend
General trend has been downward, despite of one spike due to adjustment on rank requirements aims at Junior Member rank.


Mean +/- standard deviation; Median (Interquartile range)
1)   The first period, with 4 weeks from 24th Jan. to 18th Feb. 2018 [the first week in these fours is incomplete one).
The mean of weekly merit is 18983 with standard deviation is 8739.
Minimum and maximum of the period are 11722 and 30949, respectively.
2)   The second period, since 19th Feb. 2018, with 38 weeks in total.
The median of the 38-week period is 4423, with 50% of those weeks have total weekly merits in the range from 3854 to 5487 (the interquartile range). 25% of those weeks have total weekly merit above 5487 and 25% of them have total weekly merits below 3854.
Minimum and maximum of the period are 3065 and 8806.

Potential Outliers
Interquartile Range (Q1 - Q3), with Q1 = 3854, Q3 = 5487.
--> IQR = Q3- Q1 = 5487 - 3854 = 1633.
---> 1.5*IQR = 1633*1.5 = 2450.
Therefore, extremely potential outliers are weeks with total distributed merits above 7937 or below 1404.

Formula to calculate potential outliers:
- Q3 + 1.5* IQR = 5487 +2450 = 7937;
- Q1 - 1.5*IQR = 3854 - 2450 = 1404.
Now, let’s see how many extremely potential outliers we have. Only two.

Code:
    +----------------+
     |   week   merit |
     |----------------|
  1. | 2018w8    8758 |
  2. | 2018w9    8806 |
     +----------------+
They are from those days:
Code:
. list if id >26 & id < 41

     +----------------------------------------------------------------+
     | id   day   month2   year   merit        date     week    month |
     |----------------------------------------------------------------|
 27. | 27    19        2   2018    1403   19feb2018   2018w8   2018m2 |
 28. | 28    20        2   2018    1169   20feb2018   2018w8   2018m2 |
 29. | 29    21        2   2018    1266   21feb2018   2018w8   2018m2 |
 30. | 30    22        2   2018    1279   22feb2018   2018w8   2018m2 |
 31. | 31    23        2   2018    1046   23feb2018   2018w8   2018m2 |
     |----------------------------------------------------------------|
 32. | 32    24        2   2018    1409   24feb2018   2018w8   2018m2 |
 33. | 33    25        2   2018    1186   25feb2018   2018w8   2018m2 |
 34. | 34    26        2   2018    1382   26feb2018   2018w9   2018m2 |
 35. | 35    27        2   2018    1326   27feb2018   2018w9   2018m2 |
 36. | 36    28        2   2018     991   28feb2018   2018w9   2018m2 |
     |----------------------------------------------------------------|
 37. | 37     1        3   2018    1333   01mar2018   2018w9   2018m3 |
 38. | 38     2        3   2018    1696   02mar2018   2018w9   2018m3 |
 39. | 39     3        3   2018    1089   03mar2018   2018w9   2018m3 |
 40. | 40     4        3   2018     989   04mar2018   2018w9   2018m3 |
     +----------------------------------------------------------------+
The most interesting thing is even when new rank requirements implemented on Junior Member rank, impacts of the one did not last for too long, and ranged from the end day of week 2018w37 to the first 3 days of week #2018w38.
Consequently, both of weeks #2018w37 and #2018w38 are not extremely potential outliers.
Code:
. list if id > 234 & id < 241

     +------------------------------------------------------------------+
     |  id   day   month2   year   merit        date      week    month |
     |------------------------------------------------------------------|
235. | 235    15        9   2018     463   15sep2018   2018w37   2018m9 |
236. | 236    16        9   2018    2463   16sep2018   2018w37   2018m9 |
237. | 237    17        9   2018    1862   17sep2018   2018w38   2018m9 |
238. | 238    18        9   2018    1294   18sep2018   2018w38   2018m9 |
239. | 239    19        9   2018    1268   19sep2018   2018w38   2018m9 |
     |------------------------------------------------------------------|
240. | 240    20        9   2018     846   20sep2018   2018w38   2018m9 |
     +------------------------------------------------------------------+
Anyway, those two weeks are still potential outliers because they are higher than the 74th quartile (Q3, at 5487).
Code:
.         list

     +-----------------+
     |    week   merit |
     |-----------------|
  1. |  2018w4   30949 |
  2. |  2018w5   19958 |
  3. |  2018w6   13304 |
  4. |  2018w7   11722 |
  5. |  2018w8    8758 |
     |-----------------|
  6. |  2018w9    8806 |
  7. | 2018w10    7253 |
  8. | 2018w11    7309 |
  9. | 2018w12    6941 |
 10. | 2018w13    6707 |
     |-----------------|
 11. | 2018w14    6415 |
 12. | 2018w15    5487 |
 13. | 2018w16    4631 |
 14. | 2018w17    4585 |
 15. | 2018w18    4953 |
     |-----------------|
 16. | 2018w19    4753 |
 17. | 2018w20    4346 |
 18. | 2018w21    3854 |
 19. | 2018w22    4183 |
 20. | 2018w23    4527 |
     |-----------------|
 21. | 2018w24    3818 |
 22. | 2018w25    4921 |
 23. | 2018w26    4457 |
 24. | 2018w27    4253 |
 25. | 2018w28    4239 |
     |-----------------|
 26. | 2018w29    4159 |
 27. | 2018w30    3652 |
 28. | 2018w31    3798 |
 29. | 2018w32    3994 |
 30. | 2018w33    3618 |
     |-----------------|
 31. | 2018w34    3789 |
 32. | 2018w35    3065 |
 33. | 2018w36    3574 |
 34. | 2018w37    5630 |
 35. | 2018w38    7825 |
     |-----------------|
 36. | 2018w39    4388 |
 37. | 2018w40    4271 |
 38. | 2018w41    3800 |
 39. | 2018w42    4821 |
 40. | 2018w43    3945 |
     |-----------------|
 41. | 2018w44    3339 |
 42. | 2018w45    4513 |
 43. | 2018w46    1740 |
     +-----------------+