Hypothesis TestingReference: http://www.ltcconline.net/greenl/courses/201/hyptest/index.htm
http://www.cas.lancs.ac.uk/glossary_v1.1/hyptest.html A statistical hypothesis test, or hypothesis test, is an algorithm to state the alternative (for or against the hypothesis) which minimizes certain risks. Procedures in Hypothesis Testing When we test a hypothesis we proceed as follows: Formulate the null and alternative hypothesis. Choose a level of significance. Determine the sample size. (Same as confidence intervals) Collect data. Calculate z (or t) score. Utilize the table to determine if the z score falls within the acceptance region. Decide to Reject the null hypothesis and therefore accept the alternative hypothesis or Fail to reject the null hypothesis and therefore state that there is not enough evidence to suggest the truth of the alternative hypothesis.
If the test statistic is outside the critical region, the only conclusion is that there is not enough evidence to reject the hypothesis. This is not the same as evidence in favor of the hypothesis. That we cannot obtain using these arguments, since lack of evidence against a hypothesis is not evidence for it. On this basis, statistical research progresses by eliminating error, not by finding the truth.
Setting up and testing hypotheses is an essential part of statistical inference. In order to formulate such a test, usually some theory has been put forward, either because it is believed to be true or because it is to be used as a basis for argument, but has not been proved, for example, claiming that a new drug is better than the current drug for treatment of the same symptoms. In each problem considered, the question of interest is simplified into two competing claims / hypotheses between which we have a choice; the null hypothesis, denoted H0, against the alternative hypothesis, denoted H1. These two competing claims / hypotheses are not however treated on an equal basis, special consideration is given to the null hypothesis. We have two common situations: 1. The experiment has been carried out in an attempt to disprove or reject a particular hypothesis, the null hypothesis, thus we give that one priority so it cannot be rejected unless the evidence against it is sufficiently strong. For example, H0: there is no difference in taste between coke and diet coke against H1: there is a difference. 2. If one of the two hypotheses is 'simpler' we give it priority so that a more 'complicated' theory is not adopted unless there is sufficient evidence against the simpler one. For example, it is 'simpler' to claim that there is no difference in flavour between coke and diet coke than it is to say that there is a difference. The hypotheses are often statements about population parameters like expected value and variance, for example H0 might be that the expected value of the height of ten year old boys in the Scottish population is not different from that of ten year old girls? A hypothesis might also be a statement about the distributional form of a characteristic of interest, for example that the height of ten year old boys is normally distributed within the Scottish population? The outcome of a hypothesis test test is 'reject H0' or 'do not reject H0'.
Null Hypothesis The null hypothesis or "Status Quo", H0 represents a theory that has been put forward, either because it is believed to be true or because it is to be used as a basis for argument, but has not been proved. For example, in a clinical trial of a new drug, the null hypothesis might be that the new drug is no better, on average, than the current drug. We would write H0: there is no difference between the two drugs on average. ********************* We give special consideration to the null hypothesis. This is due to the fact that the null hypothesis relates to the statement being tested, whereas the alternative hypothesis relates to the statement to be accepted if / when the null is rejected. The final conclusion once the test has been carried out is always given in terms of the null hypothesis. We either 'reject H0 in favour of H1' or 'do not reject H0'; we never conclude 'reject H1', or even 'accept H1'. If we conclude 'do not reject H0', this does not necessarily mean that the null hypothesis is true, it only suggests that there is not sufficient evidence against H0 in favour of H1; rejecting the null hypothesis then, suggests that the alternative hypothesis may be true.
Alternative Hypothesis The alternative (researched) hypothesis, H1, is a statement of what a statistical hypothesis test is set up to establish. For example, in a clinical trial of a new drug, the alternative hypothesis might be that the new drug has a different effect, on average, compared to that of the current drug. We would write H1: the two drugs have different effects, on average. The alternative hypothesis might also be that the new drug is better, on average, than the current drug. In this case we would write H1: the new drug is better than the current drug, on average. ********************* The final conclusion once the test has been carried out is always given in terms of the null hypothesis. We either 'reject H0 in favour of H1' or 'do not reject H0'; we never conclude 'reject H1', or even 'accept H1'. If we conclude 'do not reject H0', this does not necessarily mean that the null hypothesis is true, it only suggests that there is not sufficient evidence against H0 in favour of H1; rejecting the null hypothesis then, suggests that the alternative hypothesis may be true.
Errors in Hypothesis Tests We define a type I error as the event of rejecting the null hypothesis when the null hypothesis was true. The probability of a type I error (a) is called the significance level. We define a type II error (with probability b) as the event of failing to reject the null hypothesis when the null hypothesis was false. Example Suppose that you are a lawyer that is trying to establish that a company has been unfair to minorities with regard to salary increases. Suppose the mean salary increase per year is 8%. You set the null hypothesis to be H0: m = .08 H1: m < .08 Q. What is a type I error? A. We put sanctions on the company, when they were not being discriminatory. Q. What is a type II error? A. We allow the company to go about its discriminatory ways. Note: Larger a results in a smaller b, and smaller a results in a larger b.
Warren Buffett, financial market guruWarren Edward Buffett, a global financial market guru and head of Berkshire-Hathaway, puts it best when he says: 'It´s bad to go to bed at night thinking about the price of a stock. We think about the value of a company and the company results; the stock market is there to serve you, not instruct you.' A sound investor buys well-managed businesses, with strong earnings growth and significant barriers to entry that will provide long-term security. Warren Buffett was born on August 30, 1930, is an American stock investor, businessman and philanthropist Buffett has had an entrepreneurial spirit since his early years. He began working at his father's brokerage at the age of 11, and that same year made his first stock purchase, buying Cities Services preferred shares for $38 each. He sold them when the price reached $40, only to see them rocket to $200 a few years later. This taught him the importance of investing in good companies for the long term. He initially attended the Wharton School at the University of Pennsylvania, then transferred to the University of Nebraska. There he began his interest in investing after reading Benjamin Graham's The Intelligent Investor. He obtained a Master's degree in economics in 1951 at Columbia Business School, studying under Benjamin Graham, alongside other future value investors including Walter Schloss and Irving Kahn. Another influence on Buffett's investment philosophy was the well known investor and writer Philip Fisher. After receiving the only A+ Benjamin Graham ever handed out to a student in his security analysis class, Buffett wanted to work at Graham-Newman but was initially turned down. He went to work at his father's brokerage as a salesman until Graham offered him a position in 1954. Buffett returned to Omaha two years later, when Graham retired.
Buffett established Buffett Associates, Ltd., his first investment partnership, in 1956.[8] It was financed by $100 from Buffett, the general partner, and $105,000 from seven limited partners consisting of Buffett's family and friends. Buffett created several additional partnerships which were later consolidated as Buffett Partnership Limited. He ran the partnerships out of his bedroom, adhering closely to Graham's investment approach and compensation structure. These investments made in excess of 30% compounded annually between 1956 to 1969, in a market where 7% to 11% was the norm.
In June 2006, he made the commitment to give away 85% of his fortune, most of which would be going to the Bill and Melinda Gates Foundation. Buffett's donation was the largest act of charitable giving in United States history.
Flying High in a Competitive Industry Flying High in a Competitive Industry : cost-effective excellence at Singapore Airlines by Jochen Wirtz. Flying High in a Competitive Industry begins with an analysis of the airline industry and its key trends, moving on to a broad outline of SIA´s strategic drivers of success. Empirical research was conducted at SIA to gain a deeper understanding of its strategy, core competencies and internal organization, innovation processes, and human resource practices, in order to distill strategy lessons that can inform the strategies of any organization competing in intensely competitive industries.
Books on bankruptcy
Declaring bankruptcy is not an easy choice. But for individuals and businesses facing a dire financial situation, it can prove a welcome option. There are different types of bankruptcy. For instance, Chapter 7 bankruptcy is designed for individuals, while Chapter 11 deals with businesses. If you´d like to find more about bankruptcy and filing procedures, a couple of good books are available on the topic. Here are a few titles:
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" Personal Bankruptcy Simplified" by Daniel Sitarz offers insights on canceling major debt, dealing with creditors and deciding if Chapter 7 is the right option.
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" The Bankruptcy Kit" by John Ventura spotlights different types of bankruptcy and the filing processes involved.
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" How to File for Chapter 7 Bankruptcy" by Stephen Elias, Albin Renauer, Robin Leonard and Kathleen Michon explains how to file for bankruptcy, going to court and more, with forms and worksheets.
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" Bankruptcy Step By Step" by James John Jurinski covers Chapters 7, 11 and 13, starting the bankruptcy process and re-establishing credit, with helpful Q&As.
If you´re investing for a taxable account, index funds are a good idea. Most have low turnover, and they always stick to the same strategy so there´s no risk you´ll need to sell them because of manager or strategy change. Even when the market rebounded nicely in 2003, most funds were able to avoid big capital gains distributions because they had a lot of losses on the books.
Sun Tzu (The Art of War) was written by Sun Mo in The Spring and Autumn Period (B.C. 512), which is roughly the same period as Confucius. Sun Mo's father was a senior officer in the military establishment, which helped to develop his interest in tactical warfare at an early age and lead him to become an expert in the military field.
He was introduced to the emperor of Wu Kingdom by Wu Gi Xu to explain his art of war theories. Having successfully demonstrated the military strategies with the emperor's royal concubines at the emperor's request, the emperor eventually agreed to employ him as his General.
Applications of the Book
The strategies in the "The Art of War" were widely followed in Japan in medieval times (15th to 16th Century), and the Japanese military classic "Book of Five Rings", written by Miyamoto Musashi, a noted samurai (1645), contained many similarities to Sun Tzu's teachings.
The book has been translated into different languages such as, English, Japanese, German, French and Russian, which is highly valued in different countries especially as a reference book for various military academies around the globe.
Nowadays, the theories of the book are also widely employed in business approach, organization strategy and developing management skills.
Chapter 1 - Strategy / Considerations / Analyze
Analyze thoroughly before war solution
War is important to the country, either to win or ruin and as matter of life or death. This is the reason why thorough analysis is vital.
Appraise situation with five basic elements and enhance with seven vital answers
Five Basic elements:
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Politics: With total consent and complete harmony from the people.
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Weather: Signifies the effect of different weather condition, season, day or night, natural forces and also interact with the five elements such as metal, wood, water, fire and earth.
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Terrain: The safety of an army depends largely on the detail of geographical features. Factors to consider comprise distances, surrounding environment namely open ground or narrow passes, whether fit for either offensive or defensive tactics and always has plan for an escape route in case of retreat.
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Commander must have:
a. Wisdom
b. Sincerity
c. Benevolence
d. Courage
e. Strictness
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Discipline: State clearly and understand the marshalling of the army, the gradations of rank among the officers and their duties, maintenance of logistics, control of expenditure, rules and regulations.
Seven vital answers:
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Which country's sovereigns rules his people in harmony with Moral Law?
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Which sides General is more capable?
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Which sides terrain has the better advantages?
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Which side enforces rigorous discipline?
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Which army is stronger morally as well as physically?
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Which army is highly and disciplinal trained?
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Which army implements both reward and punishment?
One could forecast which side is having better chances to win after the above comprehensive analysis.
Addition to the above basic rules:
(1) General should listen to his counsel's advice and acting upon it will lead to success.
(2) Accept any avail and helpful circumstances over and beyond the ordinary rules.
(3) Plans should be modified along the line if an advantageous situation arises.
All warfare is partly based on deceptions:
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Seem unable when able to attack.
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Behave as inactive but are ready to use forces.
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Pretend the army is moving away from the war field but actually camped near the area.
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When far away, must make the opponent believe we are near.
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Use baits to allure the opponent.
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Feign disorder followed by attack.
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"Be prepared and stay low profile" if opponent is secure and strong.
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Pretend to be strong to cause the opponent to avoid you.
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Seek ways to irritate the opponent if they are having choleric temper.
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Pretend to be weak in order to provoke the opponent to grow arrogant.
(i.e. Like a cat plays with a mouse - a cat feigns weakness and immobility initially, then followed by sudden pouncing upon the mouse.)
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Give opponent no rest if they show ease.
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Separate the opponent if they are united.
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Attack the opponent when they are unprepared.
All the secrecy of the military devices must not be divulged.
Conclusion:
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He who employs thorough calculations/planning will win the battle.
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Compare the advantages and the disadvantages of different situations.
Should not enter into a war if disadvantages outweigh advantages.)
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Sticking only to devised strategy is sometime impossible since situations could be affected by any unforeseen factors.
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"Quick Decisions and Flexibility" are the important actions to take when the environment changes and to make good use of the situation swiftly in order to win the battle.
"Know yourself first, then know your opponent, and win thousand battles".
Applying to Business
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Analyze the nature of the business, strategy, products, marketing etc.
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Set up Company rules for employees to comply.
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Clearly state all the job description for each post.
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Introduce bonus scheme.
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Employ capable personnel.
"Speedy Decisions and Flexibility" are the major actions to take since external factors and unforeseen situations cannot be predicted, which will have a great effect on the business sector.
Chapter 2 - Waging War
Estimate all the expenditure before declaring War
Calculate the cost of the required equipment in a war operation, including all basic necessities together with salary to be dispatched to the army.
Disadvantages of a prolonged war
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Country's treasures will decrease.
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Mounting debts especially if the army has to come from a far.
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Blunt weapons.
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Depressed morale.
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The strength of the army will be extremely exhausted after attacking city.
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A chance for the chieftains of the neighboring places may spring up to take advantage to attack your country, in such a situation even a wise General will not be able to avert the consequences. "Distant water can not help to extinguish the near fire".
Speedy Victory is the solution:
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Haste in war may be stupid, but timing will save many costs.
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Detailed planning as mentioned in Chapter one is the vital factor for a speedy victory.
Understanding the evil of war first, will help to understand thoroughly the benefit the war will bring.
A wise General will do the following:
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Second levy of conscripts will never be called.
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The food supply-wagons would only be delivered twice.
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Army carry all the equipments from homeland.
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Forage on enemy land for the provisions especially food in order to reduce the burden to their own country's people.
Advantages:
(a) The price of the food in their own country will be maintained at acceptable level without draining away people's wealth and affect their routine life.
(b) Reduce cost of distant transportation and all related expenditure.
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In order to win the war, his army must be roused to anger in order to enhance their courage in overcoming the enemy.
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Conquer foe to augment one's strength
(a) Rewarding the army will boost the morale when capturing enemy's booty.
(b) The prisoners of war should be kindly treated and kept.
(c) Re-use captured equipment.
Therefore the leader of the armies is the arbiter of the people's fate, the nation's peace or peril will depend on him.
Conclusion
"Speedy Victory" is important for war.
Applying to Business
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Budget in detail before setting up any business.
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Reward workers with incentives will help to improve productivity.
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Equipment, systems, tactics, personnel, planning, targets etc have to be reviewed frequently in order to achieve better results.
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Utilize the local resources.
Chapter 3 - Attack by Stratagem
Capture the enemy's entire company and take the country as a whole and intact, breaking the enemy's resistance without fighting is considered to be of supreme excellence.
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Avoid Besieging walled cities - This is a lengthy and costly operation.
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Men will be killed if the impatient General orders attack.
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Subdue the enemy's troops without fighting.
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Capture cities without laying siege to them.
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Overthrow a country without prolonged operations.
Using troops:
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Surround the enemy if numbers are ten to one.
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Attack enemy if numbers are five to one.
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Divide enemy if numbers are two to one.
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Engage enemy with good plan if in equal number.
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Avoid engaging enemy if numbers are lower.
Therefore the General is the bulwark of the country, weakness or strength are all depending on his abilities.
Three ways for the Sovereign to bring misfortune upon the army:
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"Hindering the Army" - commanding the army to advance or retreat when both situations are impossible.
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Interference in the military affairs causes restlessness in the army.
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By employing officers of his army indiscriminately, through ignorance of military principles and how to adapt to different circumstances.
The above three ways will cause army to be restless, distrustful, confused and suspicious. The neighboring rulers will take advantage and attack.
Five elements to predict victory:
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Know when to fight and when not to fight.
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Know how to control both superior and inferior forces.
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Army should have equal high spirit throughout its ranks.
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Well prepared army will wait to take on unprepared enemy.
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The sovereign should never interfere with capable general.
Applying to Business:
Merger or takeover
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Collect and analyze all data and situations thoroughly.
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Calculate how much you will spend on such operation.
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Employ capable personnel.
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Announcements should be kept until the last minute.
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Keep Company intact.
Chapter 4 - Tactical Disposition
A Good General should know:
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Will win the war by knowing the possibility of defeat by others first, then waiting for a better chance to attack.
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Knows that avoiding defeat by the enemy lies in his own hands, but the chances to defeat the enemy are provided by the enemy.
A good General secures against defeat but cannot be certain to defeat the enemy.
Attack or Defense situation:
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Defense - Hide in the most secret place if the army does not have enough strength to conquer.
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Attack - When conditions are favorable, then attack with full force.
The clever General should win the war with ease, without mistake and not miss any chance to defeat the enemy.
Prepare before war:
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Know all the weak points of the enemy before the war begins.
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Analyze all the weak and delicate situations as well as plan any alternate methods.
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Implement moral law and discipline.
Five steps to win the battle:
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Measuring the size of the enemy's terrain will help to set up plan.
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Estimating the required resources according to the above measure.
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Calculating the required manpower according to the estimated resources.
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Comparing our army with the enemy - weighing up the chances.
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Victory will be assured according to the comparisons.
Applying to Business:
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Solid foundations and sound financial situations are the factors vital to planning any expansion of the Company.
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Do not advance when the situation is not favorable and keep the entire future expansion program in secret.
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Implement Company rules, systems and discipline on all levels.
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Before expansion, analyze the new project by using method of Measuring, Estimating, Calculating and Comparing in order to ensure victory
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