TO ERR IS STATISTICS Sarjinder Singh Department of Mathematics, Texas A&M University-Kingsville Kingsville, TX 78363, USA. E-mail:
[email protected] Statistics is very close to human beings in making errors. When an error occurs in our daily lives, a natural question arises? Why this error is made by the decision maker? A decision maker is dependent upon evidences and evidences make statistics. Thus decision making human beings are dependent upon statistics, which could do errors. Statistics is produced by decision makers who are humans. Thus conclusion is: “To Err is Human: To Err is Statistics.” Recall that there are three possibilities: rejection of a null hypothesis when it is true is called a Type-I error; acceptance of a null hypothesis when it is false is called a Type-II error; and otherwise it is called a correct decision or no error. Read the following five different settings and make your mind if these make sense or not, but remember that you are also a human being and may make an error!!! ORDER-ORDER: LAW IS BLIND Assume it is true that Mr. Kidder kidnapped Miss Kiddy. Later on Miss Kiddy’s uncle, Mr. Detective, suspects on Mr. Kidder and goes to court to find the Miss Kiddy’s kidnapper. The judge in the court sets the null hypothesis: H 0 : Mr. Kidder is not Miss Kiddy’s kidnapper against the alternative hypothesis: Fig.1. Kidnapper Blind Justice H a : Mr. Kidder is Miss Kiddy’s kidnapper On the basis of the evidence provided by the lawyers of Mr. Kidder and Mr. Detective, the judge makes a decision that Mr. Kidder is not guilty in the Miss Kiddy’s kidnapping case. Which error has the judge committed? Explain. OPTIONAL: OCCASIONALLY MOON COULD BE SEEN DURING DAY LIGHT Mr. Detective was confident that Mr. Kidder is the kidnapper. Outside the court Mr. Detective found a chance to punch Mr. Kidder, and Mr. Kidder immediately released Miss Kiddy. Which error has Mr. Detective committed? Was his approach correct? Explain.
Punching Miss Kiddy Waving Fig.2. Might is right.
BURGLARY IS A CRIME Assume Mr. Robby is involved in a bank robbery. A detective Mr. Doggy reported to a police officer that Mr. Robby is a robber. On the basis of the information provided by Mr. Doggy, the police officer sets the null hypothesis: H 0 : Mr. Robby is a robber against the alternative hypothesis:
Mr. Robby
Police Officer Fig. 3. Crime Stoppers.
Mr. Doggy
Mr. Robby is not a robber Based on the Mr. Doggy’s complaint, the police officer arrested and investigated Mr. Robby. On the basis of his investigation, the police officer concludes that Mr. Robby is not the robber. Which error has the police officer committed? Explain. Ha :
2
Too Err is Statistics
NEVER, NEVER GIVE UP Later on Mr. Doggy found that Mr. Robby is squandering his money gambling at a casino, without any gambling history. Mr. Doggy called the police officer and on a reinvestigation it is concluded that Mr. Robby committed the robbery. Which error has Mr. Doggy committed? Was his approach correct? Explain Fig 4. Gambling
WAR BEHIND THE BARS Assume Mr. Naïve is an innocent person, but unfortunately his name appeared in a murder case, and he is supposed to stay behind bars until a court makes a final decision about him. By looking at his case, a judge Mr. Critic sets the nullhypothesis: H 0 : Mr. Naïve should be hanged. against the alternative hypothesis: Fig. 5. Mr. Naïve and his lawyer: Blind justice hurts. H a : Mr. Naïve should not be hanged. Based on the evidence provided by Mr. Naïve and his lawyer Mr. Brief, the judge Mr. Critic makes the decision that Mr. Naïve should be hanged. Which error has the judge Mr. Critic committed? Is it a very serious error? If so, explain why? References
Singh, Sarjinder (2008). Highlights of the book, “Thinking Statistically: Elephants Go to School.” Kendall/Hunt Publishing Co. Presented at the Joint Statistical Meeting, American Statistical Association, Denver, USA.
