Tuesday, 3 September 2013

Wilcoxon Signed Rank Test

The Wilcoxon Signed Rank test is a non-parametric test for paired/matched samples, and can be regarded as the non-parametric counterpart to the Paired Student's  t-test.  A worked example follows.

Suppose we have two groups of matched samples:

Group 1: 1,2,4,5,6,7,8,3

Group 2: 2,5,1,3,9,10,3,3

We first find the difference between these matched samples (Group 1 sample - Group 2 sample)

Group 1     Group 2      Difference
1                  2                     -1    
2                  5                     -3
4                  1                    +3
5                  3                    +2
6                  9                     -3
7                10                     -3
8                  3                      5
3                  3                      0

We discard the case where there is 0 difference (the last pair), so that the sample size $N_r$ is $7$. Then, we sort the difference by absolute value and rank them, and highlight where there are ties (i.e. the same absolute values of the difference).

Rank      Difference
  1               -1
  2              +2
  3               -3
  4               -3
  5               -3
  6              +3
  7              +5

The ranks for the ties are averaged out, resulting in

Rank      Difference
  1               -1
  2              +2
  4.5            -3
  4.5            -3
  4.5            -3
  4.5           +3
  7              +5

Next we sum the ranks for the negative difference (which is $14.5$), and the sum of the positive difference can be found by subtracting 14.5 from the total rank ($7\times 8 \times 0.5=28$), which is $13.5$.

The value of $W$ (the Wilcoxon Signed-Rank statistic) is the lower of the (positive/negative) sum of the ranks, hence $13.5$.

We need to find the critical value of $W$, $Wcrit$, as there are only 7 samples, so that a z-score will be highly inaccurate. We do this by referring to a table for a two-tailed test at 5% level, and obtain $Wcrit=2$. As $W$ is greater than $Wcrit$, the result is not significant.

Even though the z-score will be inaccurate (on SciStatCalc, if the number of samples exceeds 25, the z-score is considered accurate enough, and the $Wcrit$ value is no longer used, to limit the size of the table storing $Wcrit$), it is nevertheless worth evaluating this as an exercise. The z-score is given by equation
$\Large \frac{W-\mu}{\sigma}$

where $\mu$ is the mean and $\sigma$ is the standard deviation.

The $\mu$ value is $\frac{Nr\times (N_r+1)}{4}$, and so will be $7\times 8\times 0.25 = 14$ for our example.

The $\sigma$ is given by $\sqrt{\frac{N_r(N_r+1)(2N_r+1)}{24}}$, and will be $\sqrt{7\times 8 \times 15 \times (1/24)}=5.9169$.

The z-score is thus $(13.5 - 14)/5.9169=-0.084515$, resulting in a p-value of 0.93, which is considerably larger than  the critical 0.05 value. The result is not significant by quite some margin.

Below is a screenshot of SciStatCalc with the results of the Wilcoxon signed rank test.

Wilcoxon Signed Rank test ios iphone app SciStatCalc


  

23 comments:

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    Replies
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  3. HELLO everyone! Still don’t know the right words to express my Gratitude to the Great DR.Imoudu After been diagnosed with the #herpes for the passed 1 years, i was given so many health prescription and advice with no improvement, I totally lost hope, until i found many testimonies of Great DR.Imoudu in an online research Like anybody would be, i advice anyone that is living with herpes can also contact him today, because he has the cure to any virus problem contact him on WhatsApp +2348109609753..
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    ReplyDelete
  7. Am Here To Give My Testimony About A Doctor Who Helped Me In My Life. I Was Infected With HERPES SIMPLEX VIRUS In 2019, I Went To Many Hospitals For Cure But There Was No Solution, So I Was Thinking How Can I Get A Solution Out So That My Body Can Be Okay. One Day I Was In The River Side Thinking Where I Can Go To Get Solution. So A Lady Walked To Me Telling Me Why Am I So Sad And I Open Up All To Her Telling Her My Problem, She Told Me That She Can Help Me Out, She Introduce Me To A Doctor Who Uses Herbal Medication To Cure HERPES SIMPLEX VIRUS And Gave Me His Email, So I Mail Him. He Told Me All The Things I Need To Do And Also Give Me Instructions To Take, Which I Followed Properly. Before I Knew What Is Happening After Two Weeks The HERPES SIMPLEX VIRUS That Was In My Body Got Vanished . So If You Are Also Heart Broken And Also Need A Help, You Can Also contact Him Through Dr. Oyagu reach him oyaguherbalhome@gmail.com visit his website https://oyaguspellcaster.wixsite.com/oyaguherbalhome Or whatsapp him via +2348101755322

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  8. DR OYAGU herbal medicine is a good remedy for herpes simplex virus cure. My name is MIGNON WRIGHT , am from USA,I am here to give my testimony about DR OYAGU who helped me in my life, i want to inform the public how i was cured from (HERPES SIMPLEX VIRUS) by DR OYAGU, i visited different hospital but they gave me list of drugs like Familiar, Zovirax, and Valtrex which is very expensive to treat the symptoms and never cured me. I was browsing through the Internet searching for remedy on HERPES and i saw comment of people talking about how DR OYAGU cured them, when i contacted him he gave me hope and send a Herbal medicine to me that i took and it seriously worked for me, am a free person now without any problem, my HERPES result came out negative, I pray to God to never let me and my family forget you in our life, am now cured permanently, you can also get your self cured my friends if you really need this doctor help, you can reach him on his website ;https://oyaguspellcaster.wixsite.com/oyaguherbalhome Email: oyaguherbalhome@gmail.com or via whatsapp +2348101755322

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  9. TESTIMONY ON HOW I GOT CURED TOTALLY FROM HERPES VIRUS BY DR ISHIAKU HERBS

    I want to inform the public how I was cured of herpes  Virus by a Doctor called Dr ISHIAKU. I visited different hospitals but they gave me a list of drugs like Famvir, Zovirax, and Valtrex which are very expensive to treat the symptoms and never cured me. I was browsing through the Internet searching for remedies on Herpes and I saw comments of people talking about how Doctor ishiaku cured them. I Was scared because I never believed in the Internet but I was convinced to give him a try because I had no hope of being cured of herpes so I decided to contact him on his email, i searched his email on the net and I saw a lot of people testifying about his goodness. When I contacted him he gave me hope and sent a Herbal medicine to me that I took and it seriously worked for me, am a free person now without any problems, my HERPES result came out negative. You can contact him on his email: (ishiakuherbalcure@yahoo.com)or what - sapp him via (+2348180828544) and get all your problems solved.

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  10. Hello everyone. Dr Ishiaku herbs is a good remedy for herpes Virus , I was a carrier of herpes virus and I saw a testimony on how Dr. Ishiaku cure Herpes Virus, I decided to contact him, I contacted him and he guided me. I asked him for solutions and he started the remedies for my health. After he finish he sent me the herbs which i took for 2 weeks before asking me to go for a check up and getting there i could not believe that i was confirm HSV 2 Negative after the test, Today i am so happy because I'm free from herpes disease with the help of Dr. Ishiaku . Thank God now everything is fine, I'm cured by Dr. Ishiaku herbal medicine, I'm very thankful to God for making it possible. you can reach him on his email, i strongly recommend him to any one out here looking for a cure to herpes or any other deadly disease...Contact Dr ishiaku via email: ishiakuherbalcure@yahoo.com or whats-app +2348180828544

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  11. It's a pleasure for me to write this testimony about this wonderful thing that happened to me last week on how i got my HIV aids cured, i have been reading so-many post of some people who were cured of HIV, but i never believed them, I was hurt and depressed so I was too curious and wanted to try dr.odoma then i contacted him on his email on drodomasolutionhome20@gmail.com when i contact him, he assured me 100% that he will heal me, i pleaded with him to help me out, it's a great success that he healed just as he promised, he told me that in three days time that i should go and check on my HIV status, I was floored that when i went to the hospital to check of my status that i was HIV negative, i never thought possible that dr.odoma can do miracles, i never really believed in magic but I played along with a little hope and faith and after everything but dr odoma changed my life and made me a true believer you can contact him drodomasolutionhome20@gmail.com or whatsapp Number: +2348100649947..visit his website:
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    ReplyDelete
  12. God is Good! I promised God that I would share my testimony on this blog. I had all the signs of STD Virus but I was not too sure as to which one. I did a lot of online research and scared myself straight for a whole week before going to see the nurse. She took one look at my genital part and first said that it could just be the anatomy of my body, then she said it looked like genital warts and that I may have herpes. I was devastated. She gave me some medicine for the herpes and some cream for the warts. I was also tested for every single STD including herpes. I went home and cried searching the web for all sorts of cures for herpes and awaiting my results. I saw a post whereby Dr. Oyagu cured Herpes and other diseases, I copied his contacts out and added him on whats app via (+2348101755322). The next day my test result was ready and i confirmed Herpes positive. I told Dr.Oyagu about my health problems and he assured me of cure. He prepared his herbal medicine and sent it to me. I took it for 14 days (2 weeks). Before the completion of the 14 days in which I completed the dose, the Blisters and Warts that were on my body was cleared. I went back for check-up and I was told I'm free from the virus. Dr. Oyagu cures all types of diseases and viruses with the help of his herbal medicine. You can reach Dr. Oyagu via his email address on (oyahuherbalhome@gmail.com) or WhatsApp him on (+2348101755322) Visit His website on https://oyaguspellcaster.wixsite.com/oyaguherbalhome

    ReplyDelete
  13. Are you battling with any health related issues or infection is not the end of your life, why not contact a herbal practitioner for cure Dr Oyagu has herbal remedies and permanent solution for all your health related problems. recommend him to you today only because i have also used his herbal medicine and it worked perfectly on my health problem, you can actually save yourself from giving your hard earned money to Scammers if only you can contact Dr Oyagu today for genuine and Permanent cure herbal products . Pls help share this post to save yourself and your love ones. Dr Oyagu is specialize in these areas, Permanent herbal supplements for anxiety and depression, HIV/AIDS, Diabetes, Epilepsy, Blood, Cancer, HPV, ALS, herpes etc. Email: oyaguherbalhome@gmail.com or visit his website https://oyaguspellcaster.wixsite.com/oyaguherbalhome Or Cell Whatsapp Number +2348101755322 thank you

    ReplyDelete
  14. It’s obvious some patient with HERPES are been enslaved to the antiviral and other supplementary Orthodox medicine just to help suppress the virus and not a cure. I have been with the virus since 2020 until I was introduce by a blogger who also narrated Her story online on how she was cured of Herpes after using Dr ISHIAKU Herbal Medicine. This is a year and 2 weeks since I was delivered from Herpes. All thanks to God for using this Great herbalist to heal me. I have promise to keep telling good about this. Please fill free to share Your problems with him. Thanks. Write him via call or whatsapp him on +2348180828544 or email ishiakuherbalcure@yahoo.com   thank you once again sir

    ReplyDelete
  15. Greatest thanks to Dr Oyagu for his herbal medicine that he prepared for me and when I start using it in just 2weeks I was completely cured and that ended my HERPES SIMPLEX 1&2 DISEASE i am so happy and grateful to Dr Oyagu . after reading about him on a testimony of Jason Cash on a blogger. I knew suddenly Dr Oyagu was the right Doctor to cure my HERPES SIMPLEX 1&2 DISEASE. I discuss with Dr Oyagu and he prepared a herbal medicine for me and when it got sent to me in south Korean . I used the herbal medicine in 2weeks and i went for check up again. after 15years of suffering from HERPES SIMPLEX 1&2 at last i am smiling once again. Dr Oyagu also has remedy to others disease like COLD SORES,HIV/AIDS,DIABETES.CANCER,HIGH BLOOD PRESSURE AND MANY MORE. I oblige everyone to contact this powerful herbalist Dr Oyagu and be free from your suffering. contact his WhatsApp line: +2348101755322 or visit his Website https://oyaguspellcaster.wixsite.com/oyaguherbalhome Email:Oyaguherbalhome@gmail.com

    ReplyDelete
  16. I got diagnose of herpes virus last year, and i was taking some drugs prescribed for me by my family doc the drugs could not work and the herpes in my system was very terrifying that i was so depressed the good news is that i never gave up in searching for natural cure for herpes virus ,cause i believe so much in herbal medication.. One faithful morning i read a comment from a lady called Destiny Hudson on how she was cured with natural herbs made by DR.OYAGU from somewhere is West Africa, i immediately copied out his contact email via oyaguherbalhome@gmail.com and explain all my herpes problem to him via his email. the big truth is that it took just two week for his herbal medication to cure me completely without side affect. Till date am herpes virus free and all thanks to Dr OYAGU for his good deeds for me, Once again am very happy to share this great testimony of DR OYAGU cure hurry up now and contact him via his email address (oyaguherbalhome@gmail.com Call & WhatsApp him on (+2348101755322 ) and see what he can do

    ReplyDelete
  17. Dear friends online My name is Destiny Hudson And I live in the USA, Dominica I am here today to appreciate the good work of Dr Oyagu, for helping me curing my HSV 1&2 Disease, I contacted the virus from my Partner, i found out he was cheating on me, so i broke up with him, 2 month later i went to test myself in the hospital when i was seeing sore on my mouth and Private areas, i was diagnosed of HSV 1&2. i tried using the acyclovir medicine but it didn't help in curing it, i went on a search and found out Dr Oyagu curing people illness, and so i got his email and i was told how i can get his herbal cure, 3 days later i received his medicine after using it for 2 weeks i was tested again and was confirm negative, today i am totally free. If you are over there looking for solution email: oyaguherbalhome@gmail.com or contact him on whatsapp +2348101755322 or visit his website https://oyaguspellcaster.wixsite.com/oyaguherbalhome today and share your own testimony. And He also has herbal cure for the Following DISEASES, eczema, urethra wart, chronic problems. Herpes, Cancer, Als, Hepatitis, Diabetes, HPV ,Infections, ulcer ETC

    ReplyDelete

  18. Hi, this is real testimony of a spell doctor who helped me bring back my finance, who left i and the kids for 9 month. i had lost all hope about my finance coming back home again. if you're going through a tough time in your marriage or relationship, or want back your Ex. contact him on email address: drozoeyspellhome@gmail.com or WhatsApp him ‪+2349056460552‬

    ReplyDelete
  19. I am here to give my testimony about a doctor who saved my life. i was infected with HERPES for more than 2 years, I tried different doctors over a period of time but no one work, but when i came on the Internet i saw great testimony about DR Enato how he was able to cure someone from HERPES virus with the help of herbal medicine I contacted him and he promised to cure my herpes virus.well i decided to give him a try, DR Enato put his best in it and gave me good and effective result just as he has promised. Well after taking all the treatment sent to me by Dr Enato i went back to the Hospital for check up, and now i have been confirmed HERPES Negative. You can contact him if you have any kind of sickness like, HERPES, HIV, CANCER, PILE, HEPATITIS, DIABETES, and alot more you can contact him ON WhatsApp (+2348071351544) or Email dr.enatoherbalcure@gmail.com His website is https://drenatoherbalcure.simdif.com

    ReplyDelete