Блог Анкара

In This Chapter

^ Concentrating on the most important concepts ^ Listing key kinds of calculations

^ Breaking down exam questions into their component parts

M Curing the course of the AP exam, you’ll be asked to answer a variety of types of chem-V^^istry questions. Some of these questions will be explicit and straightforward; in other words, you’ll know for certain just what you’re being asked. Other questions will be implicit and indirect; in other words, you’ll have to unpack the question to determine just what you’re being asked. Whether explicit or implicit, no matter what clothes they wear, the questions will fall into one or another of a limited number of categories. Here’s an overview of those categories.

Periodic Table

Knowledge of the patterns of the periodic table is essential to do well on the AP chemistry exam; both explicitly and implicitly, questions will require you to refer to this basic chemical knowledge. Here are some of the contexts in which you might be called to consult the table:

What is the subatomic composition of a particular atom?

What is the ground state or excited electronic structure of an atom?

What kind of compound, with what formula, will be formed if two elements react?

Is a particular chemical species likely or unlikely?

Will two compounds react or not?

What kind of bond forms between the atoms of two elements? Is a particular atom likely to form an ion and if so, which ion? How many covalent bonds will a particular atom form?

Composition and Structure

Knowing the rules by which atoms assemble into compounds is key. Know how to do the following:

Determine a percent composition for a compound, given the compound’s formula

Determine a compound’s empirical formula, given its percent composition (and a molecular formula, given the compound’s molar mass)

Move easily between compound names and formulas

Given a compound’s formula, be able to

• Determine whether the compound is ionic or molecular

• Propose a likely covalent structure for a molecular compound, including possible double or triple bonds, and draw its Lewis dot structure

• Propose a likely molecular shape, especially by using VSEPR principles

• Explain the polarity of a molecule with respect to molecular shape and bond polarity

Solubility and Colligative Properties

Solubility is important because it can control the phases of reactants or products, and even determine whether a given reaction is possible. Almost all soutions on the AP exam have water as the solvent. Whether or not a substance dissolves in a given solvent is intimately connected to the structure and properties of both the substance and the solvent. In other words, be familiar with the following:

I How molecular structure, especially polarity, controls solubility and miscibility in different solvents

I How temperature affects the solubility of solid and gaseous solutes I How pressure affects the solubility of gaseous solutes

Different chemistry problems require you to use different units of concentration. Some problems require you to convert between different units. So, you must be familiar with these different units, when it is appropriate to use each unit, and how to calculate dilutions:

Molarity: Moles solute per liter solution — by far the most used

Molality: Moles solute particles per kilogram solvent

• To be used in colligative properties calculations

Partial pressure of an ideal gas: Equals the mole fraction of the gas multiplied by the total pressure

Percent solution: Mass percent, ppm, ppb, and volume percent — relatively less common

Colligative properties, the properties of a solution that depend on the number of solute particles, vary with molality. Molality can be used to calculate three key properties with which you should be familiar:

I Boiling point elevation

Freezing point depression I Molar mass of a solute

In addition, you should be able to describe the effects of added nonvolatile solute on the vapor pressure of solvent over a solution.

Gas Behavior and Phase Behavior

Don’t enter the exam without knowing ideal gas behavior thoroughly and effortlessly. Here are the key relationships that may crop up in questions:

Charateristics of an ideal gas: For instance, molecules have no volume, molecules are in random motion, molecules neither attract nor repel each other, molecules collide elastically

I Meaning of gas temperature: As the temperature of a gas increases, the distribution of kinetic energies of the particles gets broader, and the average kinetic energy increases.

Ideal Gas Law: PV = NRT, The most complete statement of ideal gas behavior — forget this one at your peril.

Combined Gas Law: P1V1/T1 = P2V2/T2, A useful combination of other laws that allows you to calculate responses to changes in pressure, volume, and temperature

• Boyle’s Law: PV = K, Which leads to P1V1= P2V2

• Charles’s Law: V/T = k, which leads to V1/T1= V2/T2

• Gay-Lussac’s Law: P/T = k, which leads to P1/T1= P2/T2

Dalton’s Law: Ptotal=P1+P2…+Pn

I Graham’s Law: The ratio of the square roots of the molar masses equals the inverse of the rates of effusion or diffusion

The same concepts of kinetic energy and particle motion (in other words, kinetic molecular theory) that inform our model of gas behavior can also be used to help explain the movement of substances between gas, liquid, and solid phases. Be comfortable with the following:

I The microscopic description of solid, liquid, and gas phases, especially as it relates to particle motions and kinetic energy

I How the microscopic details of each phase correspond to macroscopic properties such as density, viscosity, and heat capacity

I How molecular structure and interparticle forces (like dipole-dipole and dispersion forces) factor into phase behavior, especially in condensed phases

Stoichiometry and Titration

Knowing the numerical relationships between reactants and products is the starting point for countless questions. So, be sure you can do the following:

I Balance reaction equations

Use balanced reaction equations to construct conversion factors

I Move easily between units of moles and other units (mass, volume, and particles)

Apply balanced reaction equations to determine the identity of a limiting reagent and calculate the theoretical, actual, and percent yield of a reaction

Apply knowledge of stoichiometry to acid-base reactions, especially in accounting for acid/base equivalents within titration reactions

Make predictions about whether a given titration reaction is at its equivalence point (equal amonts of acid and base reaction according to H+ + OH- H2O)

Move easily between molar concentrations of acid or base and related quantities of pH, pOH, Ka, Kb, And Kw

Understand the concept of a buffered solution, when buffered solutions are effective, and be able to use the Henderson-Hasselbach equation

Equilibrium

The concept of equilibrium is core to understanding how chemical systems respond to change, and it figures prominently in a large percentage of questions. Here are some of the ways in which equilibrium might rear its head:

Determine the direction in which a given reaction will shift, in response to the following

• increasing or decreasing the concentration of a reactant

• increasing or decreasing the concentration of a product

• increasing or decreasing temperature

• increasing or decreasing pressure or volume

Given concentrations of reactants or products, calculate an equilibrium constant and vice versa

Using an equilibrium constant or a reaction quotient and the concentrations of reac-tants or products to

• Determine whether a system is at equilibrium

• Determine the direction in which a nonequilibrium system will proceed

Manipulate equilibrium constant expressions and values for coupled equilibria and for forward versus reverse reactions

Apply equilibrium concepts to questions of solubility and acid-base behavior, especially with respect to Ksp, Ka, Kb And Kw

Thermodynamics and Thermochemistry

Thermodynamics deals quantitatively with differences in energy between reactants and products and states of substances, and thermochemistry deals specifically with thermal energy transfer as heat during chemical reactions. Reaction equilibrium can be predicted from knowledge of thermodynamic parameters enthalpy and entropy. Both of these topics are fundamental to chemical change. Have a solid grasp on the concepts and calculations associated with them.

Move easily between equilibrium concentrations and the free energy change for a reaction by using AG° = – RT ln Keq. and for nonequilibrium conditions using AG = AG°-RT Ln Q.

Understand the interrelationships of free energy, enthalpy, entropy, and temperature in determining the spontaneity of a chemical reaction

• Know and be able to use the Gibbs equation, AG = AH - TAS

• Be able to connect the concepts of enthalpy and entropy with behavior at the atomic and molecular level such as bonding and motion

Understand and be able to differentiate the concepts of heat capacity, molar heat capacity, and specific heat capacity

Be able to apply the concept of heat capacity and calorimetry to reactions in which heat is released or absorbed, especially by using Q = MCAT

Apply Hess’s Law to coupled systems of chemical reactions and determine a missing quantity from a Hess’s Law cycle

Kinetics

Just as a grasp of thermodynamics is key to understanding spontaneity, having a grasp of kinetics is key to understanding the rates of reactions. Knowing one concept without the other is like walking on one stilt — you go nowhere and you fall down a lot.

Understand the concept of reaction rate and how questions of rate differ from questions of equilibrium

Given a set of experimental data, be able to formulate and use rate laws and understand the distinct roles of

• Rate constants

• Reactant concentrations

• Reaction orders

Be able to apply the concepts of molecularity, elementary steps, and rate-determining steps to the mechanism of a chemical reaction

Interpret reaction energy diagrams with regard to the kinetics and mechanism of a reaction

Understand the concept of activation energy, Ea, And be able to apply it to questions of rate, especially by using the Arrhenius equation

Redox and Electrochemistry

Charges can change during chemical reactions, and when they do, they become critical players, altering the stoichiometry and energetics of the reaction. Oxidation-reduction reactions and electrochemistry are must-know categories for the exam, especially with respect to the following skills:

Determining the oxidation number of all atoms in a balanced reacton equation and using those numbers to determine

• Whether or not a given reaction involves redox

• The identity of both oxidizing and reducing agents

Decomposing redox reactions into oxidation and reduction half-reactions

Using half-reactions to balance overall redox reaction equations (under acidic and basic conditions)

Applying redox chemistry to electrochemical and electrolytic cells in order to

• Determine the identity of anodes, cathodes

• Determine the direction in which electrons and ions flow

• Determine if and and at which electrode electroplating occurs

• Calculate standard cell potentials, especially with regard to standard reduction potentials of half-reactions, electrical current and the Faraday, and free energy changes under standard conditions

• Calculate cell potential under nonstandard conditions from concentrations and the standard cell potential by using the Nernst equation

Descriptive and Organic Chemistry

These topics are sometimes given short shrift in general Chemistry classes, but that doesn’t mean they’ll be absent from the AP exam — up to one-sixth of the material will test this information directly or indirectly. Be sure to focus on these items:

Given the reactants, make reasonable predictions about the products of the most common kinds of reactions, to include

• Single and double replacement/displacement

• Synthesis/combination and decomposition

• Combustion Be familiar with scenarios most likely to result in

• Precipitation

• Gas release

• Redox

• Formation of a colored compound

Be able to move easily between the names for organic compounds and their structures, to include

• Alkanes, alkenes, and alkynes

• Cyclic and aromatic compounds, including existence of isomers and resonance structures

• Geometric isomers

• Compounds with functional groups, including halides, alcohols, ethers, and carboxylic acids

Be able to make reasonable predictions about the properties of simple organic compounds (such as solubility, volatility, and reactivity)

Be familiar with common organic reaction types, to include substitution, condensation, hydrolysis, addition, and elimination

In This Chapter

^ Going for certain qualities

^ Understanding how these qualities can help your therapy

/f you are thinking of going to visit a hypnotherapist you want to know that you are going to see someone who is doing their utmost to help get you through whatever issue it is that you are seeing them for. Unfortunately, out there in the big wide world there are many charlatans purporting to be hypnotherapists but who are, in fact, just after your money. Fortunately, there are many others who are professional, well trained, and who offer an exemplary service (and we like to include ourselves in this category!).

Here is a list (in no particular order) of some of the qualities to look for in

Your hypnotherapist. By taking these into consideration when searching for

Your therapist, you can separate the wheat from the chaff.

Confidentiality

What is said to your therapist stays with your therapist. In other words, your therapist does not go around telling all and sundry about what went on in the

Therapy room during your sessions. If your therapist does need to talk to

Others about your case she’ll do so in such a fashion that your identity remains protected.

So, how do you know that your therapist is confidential? A legitimate therapist will be a member of a bona fide ethical organisation and subscribe to the organisation’s ethical code of conduct. Ask to see your therapist’s ethical

Code of conduct (check the Appendix for a sample). If she doesn’t have one, or subscribe to one that doesn’t emphasise confidentiality, then say ‘Thanks, but no thanks!’

Honesty

Honesty is the cornerstone on which trust is built. Before you can do therapeutic work, both the therapist and patient need to feel that their communication is open and truthful. Both parties need to feel okay about each other for effective change to occur.

Also, from another angle, honesty is important when understanding the qualifications and experience of your hypnotherapist. Beware of those who claim

To hold professional qualifications that they don’t really have. Your hypnotherapist should be honest and upfront about her training, experience, and your therapy.

If you have any concerns about what your therapist is saying or claiming, contact her training institution or professional body, and check her out. If

Your therapist won’t let you know the contact details then just say goodbye

And seek out a more reputable one.

Well-Trained

Make sure that your therapist is appropriately trained. That means that she has attended a prolonged classroom-based training, balancing theory with practise. Beware the therapist who learned their profession through correspondence courses, or through a single weekend of training, or a similar short course. After all, would you let a doctor loose on your body who had trained in this manner?

Don’t be afraid to ask your potential therapist about their training. If they

Are not forthcoming then beware. Any therapist worth their salt lets you know about it (after all, they are proud of their own achievement) and are more than happy to furnish you with details of their training institution so that you can check them out.

Empathy

Your therapist should be able to understand what you are experiencing with

Regard to your problem. That means she understands your experience and

Your feelings and always offers you a professional service reflecting this

Understanding. Of course, your therapist is not you and only you fully understand your experience. However, through empathy your therapist is able to show a genuine positive regard for you and whatever issue you are seeing them for.

Ethics

Your therapist should always work in an ethical way. That means that their

Conduct is always appropriate. Your therapist should:

^ Tell you their fee and availability in advance. ^ Explain the process of therapy to you. ^ Answer your questions honestly. ^ Not prolong therapy unnecessarily.

^ Ensure that you are as comfortable as possible during the therapy process.

^ Show a professional regard towards other therapists and therapies.

^ Work within their own level of competence.

^ Ensure the confidentiality of anything that you may tell them.

On top of this, they will always keep their relationship with you at a professional level. In other words, they should neither become friend nor lover! If

This happens, then stop seeing them for therapy. What you do afterwards is entirely up to you.

As we repeat throughout this book, all responsible hypnotherapists subscribe to a professional code of ethics, as determined by a professional body or training institution. If you want to know what your therapist’s ethical code of conduct is, just ask to see it. The Appendix has a sample code of ethics from the British Society of Clinical Hypnosis.

Experience

How experienced in general is your therapist? How long have they been in practice? How much experience have they had treating your particular symptom? These are all questions you may want to ask. However, length of time in

Practice on its own does not a good therapist make. You should also find out about their experience of training (see the previous ‘Well-Trained’ section), what their experience of clinical supervision is and, wherever possible, the

Experience of other patients. The last point can only be done through talking

To someone you know who has been to see your particular therapist. (As a

Matter of confidentiality your therapist NEVER gives you details of others

Who have been to see them!).

All helping professionals (counsellors, hypnotherapists, psychotherapists,

And the like) undergo Clinical supervision, Which involves going to see

Another professional in order to discuss cases.

Professionals need to be supported and receive new perspectives on the work they do with their patients. Clinical supervision also ensures that the

Therapist continues to improve their clinical work to provide the best treatments possible for patients. No matter how experienced a professional, your hypnotherapist should be involved in regular supervision. It’s okay to ask if

They are.

You may be thinking that it is better to see a seasoned therapist than to see

A newly qualified one. Well, that is not necessarily the case. If your therapist

Has been trained properly, then there will be little difference. However, do take into consideration everything else in this chapter.

Tidiness

Your therapist should be of a smart appearance and keep a tidy therapy room. By doing so, they help you feel comfortable, confident, and at ease,

Both with them and the process of therapy. Not feeling comfortable in your surroundings results in an adverse effect on your ability to go into trance and

Enjoy good therapy.

Punctuality

Your hypnotherapist should be punctual for appointments (and that goes for you too!). Obviously, for one reason or another there may be an occasional

Slight delay to your appointment – we have to be realistic here. But on the

Whole, you should be able to see your hypnotherapist at the time you have booked. If they are constantly late in starting your appointments, then perhaps question the professional regard they have for you.

Oh, and if you are late for an appointment then don’t be surprised if you only get the remaining time allocated for therapy. Don’t expect your therapist to

Delay another patient on your behalf.

Non-Judgemental

Your therapist is not there to judge you! No matter how embarrassing you think your symptom is your therapist has heard it all before. A good therapist listens to what you have to say with genuine empathy (see the previous

‘Empathy’ section). After all, she is there to help you.

Active Listening

Listening may seem to be an obvious quality to look for in your therapist, as

You are talking and your therapist should be listening. However, it is something

That is worth highlighting. When listening to what you have to say your therapist should be doing so in an active manner. In other words, she will look as if

She is paying attention to you rather than picking her nails or gazing off into space! At the same time, she will be encouraging you to talk further by asking

Appropriate questions and acknowledging your replies.

Beware the therapist who just loves to talk about herself. Obviously, a little

Bit of personal banter and history is important and may be relevant, but if

She keeps on and on about how wonderful she is and that stunning holiday

She just had in Mauritius, then she is not focusing on you and that means that your therapy is more than likely to be less effective.

In This Chapter

^ Checking out the trainers ^ Looking at the support available ^ Deciding on the right course for you ^ Following up on your training

^ Recognising what is good training and what to avoid like the plague

Erhaps you have been for hypnotherapy and your experience has so inspired you that you now want to become a hypnotherapist yourself. Or perhaps you are reading this book because you want to find out about

This thing called hypnotherapy before you commit yourself to some training.

Either way, this chapter is for you.

If you are thinking of becoming a hypnotherapist, it is important that you choose the right institution to train you. The following list will give you important pointers in helping to make the right decision. After all, you will be parting

With your hard-earned money and time, and will want to invest them wisely!

Making Sure the Institution Is Accredited

The institution you are thinking of training with should be accredited by an outside body. Accreditation means that the institution meets a certain standard in training that follows established guidelines.

The sponsorship of some programmes is obvious – for instance, those that fall within the university or government system. Others may be more obscure, but offer genuine and valid accreditation. Whilst others will be bogus, simply taking money so that any Tom, Dick, or Harry can get their

Course Validated.

Don’t be afraid to investigate what the accrediting body is all about by phoning them up, looking them up on the internet, and so on.

Training for Clinical Hypnosis, NOT Stage Hypnosis!

Remember, you want to train as a clinical hypnotherapist Not A stage hypnotist. Question the validity of any course that teaches this obnoxious

Branch of hypnosis. You want to train to help people, not to have others laugh at them!

Of course, many institutions explain the ins and outs of stage hypnosis because you will have to be able to explain it to your patients.

Looking at Length of Training

Find out how long the training takes. If the claim is that you’ll be a fully qualified therapist after only one or two weekends, you’re wasting your money if

You sign on for such a programme. Most bona fide institutions offer training that takes at least a couple of years to reach full qualification.

If you are feeling a little disheartened reading this, don’t be. The ‘quick route to becoming a therapist’ schools are only interested in your money, not in your integrity as a professional therapist. Ask yourself this question: ‘Would I be

Happy seeing a doctor who had only learnt medicine over a couple of weekends?’ If your answer is no, then don’t go anywhere near these institutions. If your answer is yes, then we think that perhaps you need to pay a visit to a

Hypnotherapist (a properly trained one at that!).

Going through the Interview Procedure

The institution should interview you before accepting you for training. This is to ensure that you are the right type of person to become a therapist (in other words, not barking mad or a serial killer!). Be upfront about any personal issues you may have, because the interviewer also ensures that training is safe for you. Very few issues would prevent you from training – your interviewer will be able to go over these with you.

Don’t forget that the interview is also an opportunity for you to interview your prospective training institution. You need to make sure that the institution’s approach is the right one for you. Many institutions allow you to sit in on a lecture to get the feel of the course that you’re considering attending.

If this courtesy isn’t offered, don’t be shy about asking for it.

Watch out for those institutions that make wild claims that you can be earning thousands a week by the time you finish training. This is just a ploy to

Get you to part with your money. The only one making thousands will be the

Institution! Building a practice takes time and effort, as any reputable training organisation will point out.

Sitting Still for Classroom-Based Training

Correspondence courses are anathema to all genuine therapists! Your training must be classroom based. That means that by far the majority of your training is through lectures and practical sessions, held in a classroom environment by professional therapists and lecturers. Classroom training allows you to question and understand the theory whilst practising in a very safe

Environment.

Of course, you’re also given homework in the form of assignments and

Required or recommended reading. This is to give you a wider insight and understanding of the material and techniques taught in the classroom.

Checking the Experience, Background, and Variety of Lecturers

Your lecturers are your most important source of knowledge. Find out about their backgrounds and experience as therapists. Most institutions only employ active therapists (and rightly so), as they will be able not only to teach you the theory and techniques, but also give you a wide variety of case examples

That put things into context for you.

Having a range of lecturers is also useful, because each therapist has their own

Individual approach to the way they do therapy. Being taught by different people exposes you to varying styles, helping you to develop as a therapist in your own right.

Getting Help from Tutorials

A very useful addition to any training is the tutorial system, in which you meet

Up with a tutor outside the classroom to go over course material in order to

Make sure that you understand it. A session with a tutor also gives you a

Chance to practise the variety of techniques you have been taught so far.

Tutorials offer a very personal addition to your training, and give you an opportunity to cover aspects of your learning experience that may not be appropriate, or possible, to do in class. Many institutions now have tutorials as a compulsory part of the course curriculum.

Talking to Previous and

Current Students

If you want to, your institution should allow you to get in contact with their students or graduates, so that you can get an unbiased opinion of the course you are considering undertaking.

Offering Continuing Professional Development

Look at the training opportunities your prospective training institution offers, for after you have qualified. Continuing professional development is very important, because it allows you to remain fresh and informed throughout your career as a hypnotherapist.

Make sure that the institution you choose offers short courses that allow you to keep abreast of developments in hypnotherapy, or courses that allow you

To examine aspects of hypnotherapy in much greater detail.

Supporting You After Training

A respectable institution provides support for its graduates through telephone, Web sites, or clinical supervision. That means that you can always

Access help on hand to guide you through every difficult case that you have in your therapy room – no matter how long it was since your graduation.

In This Chapter

^ Understanding the development of hypnosis ^ Meeting the originators of modern hypnosis

^ Realising how some ‘wrong’ ideas also contributed to modern hypnosis

/t is difficult to say exactly Who Started hypnosis. Most researchers and historians agree that all cultures have induced trance in some form since humans began communicating.

Especially popular is the idea that hypnosis has always had a connection with religion, as it was possible through hypnosis to create a sensation of religious ecstasy through suggestion. In these cases, the aim was not about giving up smoking or losing weight, but rather to be filled with spiritual bliss!

Hypnosis techniques can be observed in many modern day religious and political practices with particularly enthusiastic or charismatic speakers. After reading this book, you will be an astute observer of trance induction, and capable of spotting when and how a speaker induces a trance within an

Audience. This style was employed by early practitioners, especially Franz Mesmer, who was very ‘showbiz’ in his style.

This chapter concentrates on ten prominent individuals who influenced hypnotherapy as we apply it today in clinical/therapeutic applications. Many of the early contributions involved legitimising hypnosis – removing its occult or entertainment associations – and making it more acceptable to a scientific

Community. So it’s no surprise that most of the people in this list are doctors or psychologists.

Franz Mesmer (1734-1815)

Frederick (Franz) Anton Mesmer was an Austrian physician who, in 1766, wrote ‘The Influence of the Stars and Planets on the Human Body’. This essay developed the concept of Animal magnetism - a belief that the planets, stars,

And the moon affect not only the tides of the earth’s waters but the predominantly liquid substance in humans, and in all plants and animals, through an invisible, magnetic energy.

The terms Mesmerism And Mesmerise, Which refer to the act or condition of being enchanted or fascinated, come into the language through Franz Mesmer.

Mesmer believed that placing magnets directly on a person provided his many medical successes. His technique also involved stroking the patient’s entire body until the ‘animal magnetism’ was transferred from the ‘operator’

To the ‘subject’, sometimes using a wand to release the energy. Mesmer actually hypnotised people through direct suggestions to heal themselves.

People would easily go into trance given Mesmer’s over-the-top, flamboyant

Style – a bit like fainting to escape an overwhelming experience. Due to his crowd-pleasing act and his success in healing, Mesmer became

Very popular with patients. Needless to say, this bizarre new type of healing was not as popular with the medical professionals of the day, and in 1778 he was struck off the medical register and run out of Vienna. However, he moved

To Paris, where he became even more famous and even received the patronage of Marie Antoinette.

James Braid (1796-1860)

James Braid initiated the legitimisation of hypnosis with the British and European medical professions. Braid was a surgeon who, like most of his medical colleagues, was initially a sceptic of mesmerism. He accidentally discovered that, by getting patients to fix their view on a single point, he could induce a hypnotic trance. He later achieved trance by asking his patients to

Stare at his shiny scalpel case. He would move the shiny case in all directions

Before the patient’s eyes, while insisting the client keep his head still and follow the case with his eyes only. This method of inducing hypnosis through fixed focal concentration is still in use today.

As Braid began to understand his accidental discovery of hypnotic trance

Induction, he came to the conclusion that mesmerism was not a valid concept. He published attacks on Mesmer’s ideas about animal magnetism energies having curative powers. Braid wanted to give his understanding of this healing process a more scientific basis.

In 1842, Braid invented the word Hypnotism In a paper he wrote to discredit

Mesmerism and animal magnetism (see the earlier section on Franz Mesmer).

However, his paper, titled ‘Practical Essay on the Curative Agency of Neuro-Hypnotism’, was rejected by the British Medical Association. He nevertheless

Persisted to present his ideas in the form of a series of lectures and public demonstrations.

In 1843, Braid published Neurypnology, or the Rationale of Nervous Sleep. In this book he proposed that the phenomenon be called Neurohypnotism Rather than mesmerising. He also mistakenly referred to hypnosis as a ‘condition of nervous sleep’. This is actually inaccurate as hypnosis is not the same condition as sleep, producing different types of brain waves. However, Braid’s most

Important contribution was that he moved the world away from practice of

Animal magnetism and towards hypnosis.

Hippolyte Bernheim (1837-1919)

Bernheim, a French physician, incorrectly viewed hypnosis as a special form

Of sleeping, in which the patient focused on the suggestions made by the hypnotist. His important contribution is that he emphasised the psychological

Nature of hypnosis, thereby moving it away from its occult and magic associations and more towards a psychological and medical model – a crucial step in

The legitimisation of hypnosis.

James Esdaile (1808-59)

Esdaile, a Scottish physician with the East India Company, was the first to

Document the use of hypnosis as a surgical anaesthetic in 1845. As the head

Of the Native Hospital in Hooghly, Bengal, he performed hundreds of surgical operations using hypnosis as the sole anaesthetic. Many of the surgical procedures were quite serious, including amputations and the removal of large tumours. His method of induction would last anywhere from two to eight hours. Sadly, this property of hypnosis fell into disuse and was forgotten with the invention of modern anaesthetic drugs.

Jean-Martin Charcot (1825-93)

Charcot, a brilliant French physician and neurologist, was named as the

Superintendent of Salpetriere Hospital in 1862, then the largest hospice in Europe with a population of over 5,000 ‘incurables’. He raised the profile of hypnosis within the medical profession by his extensive clinical work in neurology

At the hospital. He hypnotised his patients in order to deliberately develop hysteria within them and thus document the treatability and psychological nature of the illness. However, he also got it badly wrong. He thought hypnosis was a symptom of a mental illness, which he termed Hysteria. Freud hung out at his

Psychiatric hospital for a while and learned a limited form of hypnosis from observing Charcot’s work.

Pierre Janet (1859-1947)

French philosopher, physician, and psychologist Pierre Janet was personally

Selected by Charcot (see the preceding section) to serve as Director of the

Laboratory of Pathological Psychology at the hospital at Salpetriere. He later

Served as Professor of Experimental and Comparative Psychology at the

College of France.

Janet made important discoveries and contributions in the study of hysterical neuroses with the use of hypnosis. He viewed hypnosis as a helpful investigative and therapeutic tool in helping his patients with dissociative conditions. He thought hypnosis itself was a form of dissociation. He found that patients who could retrieve troublesome memories of their past were often freed of the negative effects associated with the actual event.

Unlike Freud, who gave up on hypnosis after only a few years, Janet believed in it strongly and promoted its benefits during his entire career. He was one of the

First to point out the enormous role of suggested beliefs in hysteria. His work

Led to the theory of neurosis and psychosis by the subconscious persistence of

Emotional trauma. Janet is also the founder of the analytic tradition in psychology that greatly influenced Freud’s psychoanalytic ideas (see the next section).

Janet also contributed significantly to the work of Sigmund Freud. Janet and Freud developed Freud’s post-hypnosis ideas. In particular, after Freud

Abandoned hypnosis, he developed – with Janet’s help – his Big Idea, which

Became known as ‘free association’. This technique involved invoking a dream-like state in hysterical patients to allow them to speak directly from

Their unconscious about whatever came to their minds – especially in relation to their psychological problems. Although this technique is usually attributed to Freud, Janet’s influence was considerable.

Sigmund Freud (1856-1939)

Sigmund Freud is best known for developing psychoanalysis. He placed the

Concept of Dual consciousness - the idea that each person has conscious and unconscious minds – into modern Western thought and thereby made an

Important contribution to the field of hypnosis.

Before Freud developed his theory of psychoanalysis, he visited a clinic in

Nancy, France, to watch experimental treatments using hypnosis being conducted on psychiatric patients who had been diagnosed as hysterical – mostly women. (Interestingly, the term ‘hysteria’ is no longer used by psychiatrists.)

Freud was greatly impressed by the fact that hypnosis could help difficult patients access powerfully repressed emotions they otherwise would not have been aware of, or able, to articulate. Freud observed that by recalling

Some forgotten traumatic experience under hypnosis, many patients seemed to be cured of the emotional problems associated with the experience. In

1895 he and another doctor, Josef Breuer, wrote a book about hypnosis called Studies in Hysteria.

At this stage Freud was very keen on hypnosis, but he later abandoned the practice. By his own admission Freud was not very good as a hypnotist. He simply gave up when he had a few failures and was unable to get clients to

Talk about traumatic events. He didn’t have access to the techniques that

Most hypnotherapists use today to build rapport and make a patient feel safe

Before recalling – let alone discussing – traumatic events from the past. Freud also realised that simply recalling forgotten memories connected to a current problem did not necessarily remove the patient’s problem.

He chose to abandon hypnosis and focus on the patient’s avoidance of pain

And study how the mind represses difficult feelings. He did this by developing

The more active approach of talking to patients that is common in counselling

And psychotherapy today. Freud’s preference of psychoanalysis over hypnosis dealt a temporary blow to hypnosis. . . at least in Europe.

Clark L. Hull (1884-1952)

Meanwhile, in America, psychologist Clark Hull was conducting extensive

Experiments in hypnosis in the 1920s and 1930s. Hull greatly de-mystified hypnosis and described it as a normal part of human nature. Hull viewed trance states as a natural part of normal consciousness, no different from daydreaming or reverie. Hull wrote that the patient’s imagination played an important role in invoking the trance state. He put forward the idea that some people were more responsive to hypnosis than others. Hull’s writings were a major influence on the godfather of modern hypnosis, Milton Erickson.

Milton Erickson (1901-80)

Milton Erickson resurrected and reinvented modern hypnosis after Freud buried it. He is considered the founder of modern hypnotherapy.

Erickson is a fascinating figure, both in his life story as well as the hypnothera-peutic advances he singly developed. He grew up in a rural Midwest American community, partially disabled from polio. He hypnotised himself to overcome the intense pain he experienced as a result of the disease. He also devoured

Dictionaries (not literally!) and learned the nuances of words.

He later trained as a psychiatrist, but his love of language helped him to

Develop a conversational style of hypnosis – termed the Permissive style -

That was the antithesis of the old-fashioned authoritarian hypnosis.

Erickson found it easy to hypnotise his patients by letting them talk first

About their lives and interests. An expert listener with strong observational skills, Erickson noticed the content and style of speech of his patient and

Could induce trance simply by adopting a similar style of speech. His therapy

Sometimes included made-up stories or metaphors that he invented based on the patient’s interests.

Erickson was a kindly figure, but he was also very versatile with an extremely

Unconventional approach to hypnosis. He used authoritarian techniques if

That is what the patient could most benefit from. (Don’t forget that, like Freud,

Erickson was also a psychiatrist, and many people during Erickson’s day

Expected Their medical men to dominate them.)

Erickson is essentially the cornerstone for the study of modern hypnosis. It

Would be difficult to meet a hypnotherapist today who was not in some way

Influenced by Erickson’s writings, teachings, audio/video recordings, and

Methods.

Ernest Rossi (1933-present)

Rossi is an American psychotherapist and teacher who focuses on the mind -

Body connection in healing. Rossi worked closely with Erickson on several

Publications.

He is also a widely published author of books and scientific papers on hypnotherapy and healing. His ideas are pioneering in terms of how hypnosis can

Influence the body even at a cellular level.

In This Chapter

^ Debunking the magical, mystical illusions ^ Realising that hypnosis is safe and easy ^ Understanding that you’re in control

Ur experience as hypnotherapists and trainers tells us that people often have similar types of misconceptions about hypnosis. Some may sense that their beliefs about hypnosis are inaccurate, but a small part of them still believes in the misconceptions. Typically, we hear something like, ‘I know it sounds ridiculous but. . . (fill in your misconception here)’.

These inaccurate beliefs may prevent people who could actually benefit from

Hypnotherapy from seeking help. Perhaps some of these misunderstandings

Play a part in holding you back from seeking hypnotherapy.

Understanding misconceptions about hypnosis can alleviate your fears about being hypnotised, so in this chapter we list the misconceptions that we have come across most frequently, in no particular order.

Hypnosis Is Magical and Mystical

Throughout history, hypnosis has often been connected with the occult. The concept of hypnosis having an occult connection has often been the image

Perpetuated by some of the earliest known practitioners, the Egyptian priesthood, who entranced religious followers.

Magic and hypnotism were often linked by people who wanted to invoke a fearful sense of power and control over others. Hollywood movies and lowbrow fiction also contributed to the idea of the hypnotic bogeyman. Often the underlying implication is that the public should be afraid – be very afraid – of anyone who wielded the evil ‘hypnotic eye’.

Consequently, even today people erroneously believe that hypnotherapists

Have a power that allows them to manipulate others, but this is simply not

True!

The reality is that trance is a natural state of mind. Hypnosis is any technique

That brings about trance. In actual practice, all hypnosis is self-hypnosis – you can’t be hypnotised unless you are willing. Hypnotherapy is simply a way

Of using trance to help with problems. Nothing mystical involved at all.

Of course, the results of good clinical hypnotherapy may Seem Like magic

Once you are rapidly relieved of your problem, or achieve your goal with ease!

You’re Under the Power of the Hypnotherapist

This misconception is related to the one that says hypnosis is magical and

Mystical. The idea is probably influenced by stage hypnotists who Appear To have power over those they hypnotise. Just keep in mind that people in stage hypnosis acts are willing participants. Hypnosis is really just self-hypnosis and the participants in a stage hypnosis show choose to join in – even if they

Appear not to.

It is simply not true that a hypnotist has any control over you. No hypnotherapist can make you do anything that you don’t want to do, or anything that is

Not in character.

Hypnosis Is Dangerous

Hypnosis in itself is not dangerous. You are particularly safe when working with qualified hypnotherapists. You are always in control and can come out of trance whenever you want.

One caveat we offer is to avoid personal involvement with unqualified hypnotherapists and stage hypnotists. Unscrupulous people, who have had only minimal instruction in trance induction, often set themselves up as hypnotists without understanding the complexities of psychological problems. This is not the type of practitioner you want to seek help from. (See Chapter 12 for tips on choosing a qualified hypnotherapist.) A qualified hypnotherapist will

Ensure that you are taken care of emotionally and will treat you with care, dignity, and respect.

Hypnosis Makes You Cluck like a Chicken and Lose Control

Now is the time to draw distinctions between stage hypnosis and clinical hypnotherapy. Stage hypnosis is about entertainment and laughs. Clinical hypnotherapy is about helping you with problems, or achieving goals. A

Stage hypnotist simply uses hypnosis for a laugh. A clinical hypnotherapist is serious about working with Your Stated goals.

Keep in mind that the stage hypnotist carefully selects who comes up on stage. Usually compliant extrovert types are ideal for a stage hypnotist. The people chosen are willing to do any silly things suggested to them.

Stage hypnotists may vary in their qualifications and hypnosis experience.

Some may even be qualified hypnotherapists, but a stage hypnotist will never treat you with the individual respect and attention you get within the context of one-on-one clinical hypnotherapy.

You Have to Keep Your Eyes Closed and Stay Completely Still

Anyone can move while in a hypnotised state. You may need to scratch an itch, and that’s perfectly all right. It doesn’t break the trance state.

Although a lot of trance induction involves closing your eyes and being in a relaxed state, this is not always the case.

Athletes are often in trance while competing in sports. An athlete seeking hypnotherapy in order to enhance her sporting performance, will not be asked to close her eyes or to relax. A hypnotist works with such an athlete

By bringing about an Alert trance. This type of trance is more about recalling

Past peak performances while the eyes are open and movement is occurring. Relaxation and improved sporting performance are not compatible! Can you imagine running a race or playing any competitive sport in a super-relaxed

State? You need the ‘edge’ to perform well.

Similarly, children who come for hypnosis can go into trance even when their

Eyes are wide open and they’re moving around. (Chapter 9 is devoted to children and hypnotherapy).

Also, clients for whom eye closure or relaxation is a threatening occurrence, such as those who suffer panic attacks or have issues of severe trauma, may

Not be given suggestions to relax or close their eyes because this may invoke

The very state of fear that they are seeking treatment for.

Hypnosis Is Therapy

Hypnosis is not therapy, it is a therapeutic technique. Hypnosis can be used

As a tool, or a complement, to various types of therapy and counselling.

Hypnotherapy is the therapeutic aspect of hypnosis. Hypnotherapy can be

Combined to work very powerfully with a range of counselling approaches -

Even forms that are contradictory in their approach such as behavioural therapies, which don’t recognise the concept of the unconscious, and psychodynamic approaches, which do.

May Not Wake Up from Trance

What wakes you up in the morning? If you said ‘My alarm clock’, you’re missing the point. You always wake up from each night’s sleep – even when

Your alarm clock doesn’t ring. Similarly, you always awaken from trance. Remember, trance is not like being in a coma and is not sleep. Trance is a

Natural state that you enter several times a day while you daydream, exercise, or focus intently on a problem at work. You return to a ‘normal’ state

Of non-trance after each trance state. So, if you think about it, you have a

Daily practice of awakening from trance states – several times a day!

We admit that it’s a bit of a contradiction to use the word Awaken For a state that is not sleep. However, this is common terminology that hypnotherapists also use, even though all are aware that hypnosis isn’t the same state as sleep.

It’s just one of the widespread paradoxes that has become commonplace!

Likewise, you can come out of a hypnotic trance state at anytime that you wish. A qualified hypnotherapist will look after you and carefully bring you

Out of trance.

Don’t worry, your hypnotherapist won’t let you fall asleep. You remain quite aware of your surroundings, even in trance, and may even hear sounds both inside and outside the room you’re in – a fact that can help you feel safe and

Allow yourself to enter trance.

You may be surprised that you clearly recall what was said to you during the

Session.

Some People Can’t Be Hypnotised – Even if They Want to Be

Most people can be hypnotised – except those who really don’t want to be.

Sometimes fear and misconceptions about hypnosis can create an unconscious resistance. This is why a qualified hypnotherapist will take a lot of time, the first time you meet, to answer your questions and earn your trust before any hypnosis takes place.

The main thing we emphasise in this book is the need to work with a hypnotherapist before trying self-hypnosis. Even then we would not wholeheartedly recommend – as other books do – that you practise hypnotherapy on

Yourself.

You Go to Sleep during a Hypnosis Session

You You

It is practically impossible to work on your own unconscious problems unaided. Even experienced hypnotherapists seek help from others to work on their deeper psychological issues.

However, once you experience hypnosis with a hypnotherapist, you are in a

Stronger position to decide when, and when not, to apply self-hypnosis. (For more information on self-hypnosis, turn to Chapter 14.)

In This Chapter

^ Translating a word problem into a statistics problem ^ Picking out the necessary info

Any students miss out on the fact that the most important and difficult skill they need to develop in statistics is the ability to attack a problem correctly, especially real-world problems. This skill requires identifying what the problem is really asking, figuring out what the underlying statistical question is, and determining which statistical technique will do the job. Because professors give course exams usually over small chunks of information in certain chapters of a textbook, the synthesis process is underdeveloped. Then comes the final exam, where you’re supposed to magically be able to put it all together, which can spell disaster.

In this chapter, you discover the important skill of attacking problems correctly and with confidence — a skill that can no doubt help you to be successful not only in your statistics course, but also in the workplace and everyday life. I help you determine which statistical technique you need to solve each problem (I don’t actually solve the problems in this chapter but refer you to the appropriate chapters to get those details). The focus of this chapter is how to start a problem.

Comparing Means with One-Way ANOVA

The key to knowing you need to use ANOVA is that you have a group of populations that you want to compare according to some quantitative variable y. Suppose you have a population of consumers for each of the four brands of cereal, and you’re interested in seeing whether ages differ across any of the four populations. The response variable is age and the variable on which ages are being compared is the brand of cereal the population buys. Cereal

Brand is the variable on which Y Is being compared; cereal brand is called a Factor In this case. The fact that you have a response variable being compared according to different values of a factor tips you off that one-way ANOVA is to be used in this situation; you have a quantitative response variable whose means are compared on some categorical variable called a factor.

If your were to compare two populations, you’d use a hypothesis test for two population means. If you have more than two means to compare, you must go in the direction of ANOVA (see Chapter 9 for the big ideas of ANOVA). The only factor to include in the model is cereal brand, because that variable is the only one on which you’re making comparisons. So, you use a one-way ANOVA versus a two-way ANOVA (see Chapter 9).

ANOVA first tests to see whether there’s an overall difference between population means, using the F-test. If you reject Ho: The population means are equal, you can conclude Ha: At least two of the population means are different. The ANOVA table for comparing data from four brands of cereal is shown in Table 22-1. Because a condition of ANOVA is that the populations are independent, you take a random sample of ten boxes of each type of cereal, for a total of 40 observations. (Table 22-1 gives you the general setup of the ANOVA table; you can determine the sums of squares from the particular data in the problem.)

Doing Multiple Comparisons

When comparing multiple population means on some factor (such as brand of cereal), you first conduct a one-way ANOVA (see Chapter 9) to determine whether any differences at all are in the means. If you determine that at least two population means are different (in other words, Ho is rejected in the ANOVA procedure), your next step is to find out which ones are different and how they compare to the others. This situation is where multiple comparison procedures enter the picture (see Chapter 10). (If you can’t say the means are different, you have no reason to proceed further.)

While many multiple comparison procedures exist, in this book I discuss LSD (least significant differences) and Tukey’s (not Turkeys) Procedure. LSD compares all the pairs of N Different means while keeping an overall eye on the chance of making an error due to chance. Tukey uses pairs of confidence intervals and looks for overlap and groups the means in order of magnitude. (Each procedure has its pluses and minuses, but most statisticians use Tukey or LSD. See Chapter 10 for full details on multiple comparison procedures.)

Sometimes, this process of answering questions is flipped around. Instead of asking you a question that you use computer output to answer, your professor may give you computer output and ask you to determine what question was answered by the analysis. To do this, you look for clues that tell you what type of analysis was done, and fill in the details using what you already know about that particular type of analysis.

For example, your prof gives you computer output comparing the ages of ten consumers of each of the four cereal brands, labeled C1-C4 (see Figure 22-1). On the analysis, you can see the mean consumer ages for the four cereals being compared to each other, and the confidence intervals for the averages are also shown and compared. Seeing confidence intervals being compared tells you that you’re dealing with a multiple comparison procedure.

Remember you’re looking to see whether the confidence intervals for each cereal group overlap; if they don’t, those cereals have different average ages of consumers. If they do overlap, those cereals have mean ages that can’t be declared different. From Figure 22-1, you can see that cereals one and two aren’t significantly different, but for cereal three, consumers have a higher average age than cereals one and two, while cereal four has a significantly higher age then the three others. Now after the multiple comparison procedure, you know which cereals are different and how they compare to the others.

Figure 22-1:

Multiple comparison results for cereal example.

Level

C1

C2

C3

C4

N 10 10 10

Mean 8.800 11.800 36.500

StDev 1.687 1.033 7.735

10 55.400 10.309

Individual 95% CIs For Mean Based on Pooled StDev

——–1———–1———–1———–1—

(–*–) (–*–)

Looking at Two Factors with Two-Way ANOVA

You use two-way ANOVA when you want to compare the means of N Populations that are classified according to two different categorical variables (factors). For example, suppose you want to see how four brands of detergent (brands A, B, C, and D) and water temperature (cold, warm, hot) work together to affect the whiteness of clothes being washed. Product-testing groups can use this information as well as the detergent companies to investigate or advertise how it measures up according to its competitors. The only way I can think of to measure whiteness is on some sort of scale from least white (say 1) to most white (say 10).

It makes sense that you would want to test different combinations of detergents and water temperatures to see how they affect the mean whiteness of the clothes. Because this question involves two different factors and their affects on some numerical (quantitative) variable, you know that you need to do a two-way ANOVA. (For all the information on two-way ANOVA, see Chapter 11; I just discuss the overall setup here.)

You can’t assume that water temperature affects whiteness of clothes in the same way for each brand, so you need to include an interaction effect of brand and temperature in the two-way ANOVA model. Because brand of detergent has four possible types (or levels) and water temperature has three possible values (or levels), you have 4 * 3 = 12 different combinations to examine in terms of how brand and temperature interact. Those combinations are: brand A in cold water, brand A in warm water, brand A in hot water, brand B in cold water, brand B in warm water, brand B in hot water, and so on.

The resulting model looks like this: Y = Bi + WJ + Bwii + e, where B Represents the brand of detergent, W Represents the water temperature, Y Represents the whiteness of the clothes after washing, and bwij represents the interaction of brand I Of detergent (i = 1, 2, 3, and 4) and temperature J Of the water (J = 1, 2, 3). (e represents the amount of variation in the Y Values [whiteness] that isn’t explained by either brand or temperature.)

Suppose that your experiment involves four brands of detergents, three water temperatures, and ten data values for each combination (for a total of 4 *3 *10 = 120 data values). You can see the setup of the ANOVA table to analyze this data in Table 21-2. Now you’re off and running (hopefully not in two directions) with a two-way ANOVA!

Predicting a Quantitative Variable by Using Regression

You use regression when you have a response variable, Y, That’s quantitative, and you’re using another quantitative variable, X, To predict it. For example, suppose you’re trying to estimate how much a house is going to cost (on average). You may think of many different factors that could come into play when estimating house cost, such as house size, location, number of bedrooms, number of bathrooms, or the cost of other homes in the neighborhood.

Suppose you focus on only one variable: house size. Certainly house size is one of the factors that builders and realtors use to base house price. For example, suppose the typical price for a new house in Columbus, Ohio is approximately $100 per square foot. Then a home that has 2,000 square feet would cost approximately $200,000 on average.

By trying to put yourself into the shoes of the person who’s asking this question, you can get a much better idea of what the problem is really asking. Here, you have one variable — house price — and you’re trying to estimate that variable. That tells you that house price is a response (outcome) variable, because you’re using one variable (house size) to estimate house price. That means you’re treating house size as an explanatory (input) variable — the variable on the X-axis. Trying to use X (house size) to estimate Y (house price) is what you do in simple linear regression. And that technique is exactly what you need in order to answer this question.

If indeed house cost is based on a model of $100 per square foot, your data would be fit, using the straight line shown in Figure 22-2. (This figure shows a hypothetical data set of 22 homes.)

Figure 22-2:

House price = 100 * size of home (in square feet).

300000-

250000-

200000 -

150000-

100000-

1000

1500 2000 2500

Size of house (square feet)

3000

You can add more X Variables to the model to try to predict Y. This procedure is called Multiple regression. (For more information on simple linear regression, see Chapter 4; for multiple regression, see Chapter 5.)

Predicting a Probability with Logistic Regression

You use logistic regression when you use a quantitative variable to predict or guess the outcome of some categorical variable with only two outcomes (for example, using barometric pressure to predict whether or not it will rain).

Because you’re trying to use one variable (x) To make a prediction for another variable (y), You may think about using regression — and you would be right. However, you have many types of regression to choose from, and you need to determine what kind is most appropriate here. You need the type of regression that uses a quantitative variable (x) To predict the outcome of some categorical variable (y) That has only two outcomes (yes or no).

So being the good intermediate statistics student that you are, you go to your trusty list of statistical techniques, and you look under regression. You see simple linear regression. . . no, you use that when you have one quantitative variable predicting another. Multiple regression? No. . . that method just expands simple linear regression to add more X Variables. Nonlinear regression? Well no. . . that still works with two quantitative variables; it’s just that the data forms a curve, not a line.

But then you come across logistic regression, and. . . eureka! You see that logistic regression handles situations where the X Variable is numerical and the Y Variable is categorical with two possible categories. Just what you’re looking for! Logistic regression, in essence, estimates the probability of Y Being in one category or the other, based on the value of some quantitative variable, X. In the gender and height example, logistic regression predicts whether someone is a male (or female) based on his height. If a "1" indicates a male, then people who receive a probability of more than 0.5 of being male (based on their heights) are predicted to be male, and the people who receive a probability of less than 0.5 of being male (based on their heights) are predicted to be female. (For all the details on logistic regression, see Chapter 8.)

It may help at this point to sort out some situations that sound similar but have subtle differences that lead to very different analyses. You can use the following list to compare these subtle, but important, differences:

U If you want to compare three or more groups of numerical variables, use ANOVA (Chapter 10). (For only two groups use a /-test; see Chapters 3 and 9.)

U If you want to estimate one numerical variable from another, use simple linear regression (Chapter 4).

U If you want to estimate one numerical variable using many other numerical variables, use multiple regression (Chapter 5).

U If you want to estimate a categorical variable with two categories by using a numerical variable, you want to use logistic regression (Chapter 8.)

U If you want to compare two categorical variables to each other, head straight for a Chi-square test (Chapter 14).

Using Nonlinear Regression for Curved Data

Nonlinear regression takes the stage when you want to predict some quantitative variable (y) By using another quantitative variable (x), But the pattern you see in the data collected resembles not a straight line, but rather a curve.

Suppose a manager is considering the purchase of a new office management software but is hesitating. She wants to know how long it typically takes someone to get up to speed using the software (that’s what a learning curve shows — the decrease in time to do a task with more and more practice).

What is the statistical question here? She wants a model that shows what the learning curve looks like (on average). You have two variables — time to complete the task and trial number (for example, the first try is designated by 1, the second try by 2, and so on). Both of these variables are numerical, or quantitative, and you want to find a connection between two quantitative variables. At this point, you can start thinking regression.

A regression model produces a function (be it a line or otherwise) that describes a pattern or relationship. The relationship here is task time versus number of times the task is practiced. But what type of regression model do you use? After all, you can see four types in this book: simple linear regression, multiple regression, nonlinear regression, and logistic regression. You need more clues.

The word Curve In learning curve is a clue that the relationship being modeled here may not be linear. That word sends the signal that you’re talking about a nonlinear regression model (see Chapter 7). If you think about what a possible learning curve may look like, you can imagine task time on the y-axis, and the number of the trial on the x-axis. You may guess that, at first, the Y-values will be high, because the first couple of times you try a new task, it takes longer. Then, as the task is repeated, the task time decreases, but at some point, more practice doesn’t reduce task time much. So the relationship may be represented by some sort of curve, like the one I simulate in Figure 22-3 (which can be fit by using an exponential function).

Using Chi-Square to Test for Independence

When you read this section’s heading, you may notice one thing right off the bat: the word Independence. This word should remind you of the Chi-square test of independence. Don’t forget to take a second look at how many and what type of variables you’ve got (and be sure you do this for every problem before you start it).

Suppose you want to study two variables — eating breakfast (yes or no data) and gender (male or female). Each of these variables is categorical, or qualitative. Whenever you have two variables, X And Y, That are both qualitative, use a Chi-square test to see whether or not those variables are independent. Use Ho: X And Y Are independent, versus Ha: X And Y Are dependent. (See Chapter 14 for more on the Chi-square test.)

Table 22-3 shows how you would set up the table for the Chi-square test for this particular question. You would enter the data in the cells marked by xx.

Note that the Chi-square test for independence is equivalent to testing whether two population proportions are equal, in other words Ho: p1 = p2 versus Ha: p1 ^ p2. That is, if you took this same data and analyzed it using a two-sample test for proportions, you’d test to see whether the proportion of breakfast eaters (p) Is the same for males and females. If you reject Ho, that means breakfast eating is different for males and females. This result implies then that gender and eating breakfast are dependent. Similarly, if Ho isn’t rejected, you conclude you can’t find a difference in breakfast eating for males versus females, which tells you gender and breakfast eating may be independent.

Checking Specific Models with the Goodness-of-Fit Test

You can use the Chi-square goodness-of-fit test to check to see whether a specified model fits. A Specified model Is a model in which each possible value of the variable X Is listed, along with its associated probability according to the model. For example, suppose you want to know whether the colors of Skittles candy are evenly mixed (that is, you have an equal percentage of each color). Think about circumstances where you want to know whether a situation is even, or fair. You may be flipping a coin. You can assess fairness in this instance by testing whether the probability of heads equals K (using a one-sample test for proportions; see Statistics For Dummies [Wiley] or your intro stats textbook for more information).

But in this case, instead of heads and tails, you have five possible outcomes representing each color of Skittles (purple, orange, red, green, and yellow). You want to know whether the proportion of each color of Skittles is the same. In other words, you want to test Ho: p! = p2 = p3 = p4 = p5, where each P Represents the proportion of a different color of Skittles. In this case, each proportion would have to equal 0.20 to spread the Skittle colors evenly. This model is very specific. Which statistical technique requires your model to be very specific? (Hold that thought for just a second. You’re not quite done.)

You can find another clue by again looking at the number and type of variables you’re working with. You have one variable — Skittles color — and that variable is categorical. So you’re testing a model for one categorical variable and that model is very specific. You want to see whether that specific model fits. How do you do it? With a Chi-square goodness-of-fit test. (See Chapter!5 for all the information on the goodness-of-fit test.)

Estimating the Median with the Signed Rank Test

Many times when you hear the word Median, You think of the middle number in a data set. It’s true that the median is the middle number, when you order all the values from smallest to largest. But you may be more accustomed to finding the median of a sample, rather than estimating the median of an entire population. Estimating the median of a population is quite a bit different from finding the median of a sample.

If you want to estimate the mean cost of tuition per year, you would right away think of a confidence interval for the population mean, based on X, the sample mean, plus or minus a margin of error. You can’t use the same formula to answer the given question about the median, but you can use the general idea. You can’t know the median of a population any more than you can know the mean; populations are generally too large to measure every value, so you need to take a sample and calculate a confidence interval instead. That is, you need a sample statistic plus or minus a margin of error. (See Chapter 3 for the full breakdown on confidence intervals and the whole margin-of-error thing.) In this case, the sample statistic would be the sample median; it only makes sense. But what about the margin of error? Where do you turn for a formula for that?

Don’t forget the unsung hero: nonparametric statistics. Anytime you’re dealing with data that doesn’t meet the conditions of the "normal" procedures, pull out your nonparametric tools. Anytime you’re estimating or testing the median, the data at hand likely doesn’t come from a normal distribution either. The reason the data doesn’t come from a normal distribution is that in a normal distribution, the mean and the median are the same, and you can use the regular old (parametric) methods to estimate the median.

So far, you know that you need a confidence interval for the median that’s based on nonparametric statistics. The signed rank test handles just that situation because its sole purpose is to rank data from smallest to largest and figure out where the middle lies (see Chapter 17 for all the details). The biggest challenge is to remember that nonparametric statistics are available, and you need to use them when you can’t use parametric procedures. (Chapter 16 tells you what types of situations need nonparametric procedures.)

Checking Model Fit by Using R2

One of the most important ideas in intermediate statistics is using the right technique for the right data and to answer the right question. To know whether you have the right technique, you need to check the conditions for that technique, using your data, to make sure those conditions are being met in the population. (Each technique used in this book has a set of conditions presented along with it in its corresponding chapter and section.) Because most of these procedures are based on building a model from the data to make predictions, you also need to make sure that the final model you chose fits the data well, so you can sleep at night knowing you did the right thing.

Several different methods exist for checking the fit of models, and those methods differ according to the model you use, of course. However, one particular method is universal no matter what kind of model you fit. Always

Check the value of R2, the Coefficient of determination (also known as the Coefficient of extermination, Because it can kill off a model in a matter of seconds with a low number).

The coefficient of determination (R2) measures the amount to which the model (which contains the X Variable or variables) explains or accounts for the amount of variability in the Y Variable. The value of R2 Is a number between 0 and 1, and you can interpret it as a percentage. A high value of R2 (at least 0.70, but the higher, the better) indicates that the model fits well; a value of R2 Below 0.70 indicates the model doesn’t fit well (and the closer R2 Is to zero, the worse the model fits).

For example, say you want to conduct a regression analysis of exam score based on study time. Suppose you analyzed your data and got the computer output listed in Figure 22-4.

Figure 22-4:

Regression analysis for exam data.

You can see in Figure 22-4 that the value of R2 For this model is 98.2 percent. So study time in this case explains 98.2 percent of why those exam scores vary. Therefore, the model fits the data very well according to R2.

The most important use of R2 Is in choosing the best model if given a variety of possibilities. Typically you choose the model with the highest value of R2, Adjusting for the number of variables in the model. This variation of R2 Is called R2 Adjusted (in Figure 22-4, R2 Adjusted is 98.0 percent, which is very high). (For the full scoop on model fit, see Chapter 6, where you can find stepwise procedures to choose the best multiple regression model given a choice of many variables.)

7his Appendix includes commonly used tables for five important distributions for intermediate statistics: the /-distribution, the binomial distribution, the Chi-square distribution, the distribution for the rank sum test statistic, and the F-distribution.

T-Tabte

Table A-1 shows right-tail probabilities for the /-distribution (refer to Chapter 3). To use Table A-1, you need four pieces of information from the problem you’re working on:

The sample size (n)

The mean of X (the given normal distribution)

The standard deviation of your data (s)

The value of X For which you want the right-tail probability

After you have this information, transform your value of X To a /-statistic (or /-value) by taking your value of X, Subtracting the mean, and dividing by

I ii F /"ii ox i – ir i X _ U

The standard error (see Chapter 3) by using the formula /n _ l = —S—.

Then look up this value of / On Table A-1 by finding the row corresponding to the degrees of freedom for the /-statistic (n – 1). Go across that row until you find two values between which your /-statistic falls. Then go to the top of those columns and find the probabilities there. The probability that / Is beyond your value of X (the right-tail probability) is somewhere between these two probabilities. Note that the last line of the /-table shows df = <*>, which represents the values of the z-distribution because for large sample sizes / And Z Are close.

^-Distribution

T-distribution showing area to the right

T (p, df)

Table A-1

Binomial Table

Table A-2 shows probabilities for the binomial distribution (refer to Chapter 17). To use Table A-2, you need three pieces of information from the particular problem you’re working on:

The sample size, N

The probability of success, P

The value of X For which you want the cumulative probability

Find the portion of Table A-2 that’s devoted to your N, And look at the row for your X And the column for your P. Intersect that row and column, and you can see the probability for X. To get the probability of being strictly less than, greater than, greater than or equal to, or between two values of X, You sum the appropriate values of Table A-2, using the steps found in Chapter 16.

Table A-2

The Binomial Table

Numbers in the table represent the probabilities for values of XFrom 0 to N.

Binomial probabilities:

(continued)

P

Table A-2 (continued)

Binomial probabilities:

IX) - P’n~x

(continued)

P

Table A-2 (continued)

Binomial probabilities:

(x) - P’n~x

P

(continued)

Table A-2 (continued)

Binomial probabilities:

P

N

5

20

Chi-Square Table

Table A-3 shows right-tail probabilities for the Chi-square distribution (you can use Chapter 14 as a reference for the Chi-square test). To use Table A-3, you need three pieces of information from the particular problem you’re working on:

The sample size, N.

The value of %-squared, for which you want the right-tail probability.

If you’re working with a two-way table, you need R = number of rows and C = number of columns. If you’re working with a goodness-of-fit test, you need K - 1, where K Is the number of categories.

The degrees of freedom for the Chi-square test statistic is (r – 1) * (c – 1) if you’re testing for an association between two variables, where R And C Are the number of rows and columns in the two-way table, respectively. Or, the degrees of freedom is K - 1 in a goodness-of-fit test, where K Is the number of categories; see Chapter 15.

Go across the row for your degrees of freedom until you find the value in that row closest to your Chi-square test statistic. Look up at the number at the top of that column. That value is the area to the right (beyond) that particular Chi-square statistic.

Table A-3 The Chi-Square Table

Numbers in the table represent Chi-square values whose area to the right equals P.

Rank Sum Table

Table A-4 shows the critical values for the rank sum test where a is 0.05 for two-sided tests (equivalent to 0.025 for one-sided tests); see Chapter 18 for more on this test. To use Table A-4, you need two pieces of information from the particular problem you’re working on:

The rank sum statistic, T

The sample sizes of the two samples, n and n2

To find the critical value for your rank sum statistic using Table A-4, go to the column representing n and the row representing n2. Intersect the row and the column on Table A-4, and you find the lower and upper critical values (denoted TL and Ty) for the rank sum test.

Table A-4 Rank Sum Table

A = .025 One-Sided; A = .05 Two-Sided

(continued)

Table A-4 (continued)

A = .05 One-Sided; A = .10 Two-Sided

F-Tabte

Table A-5 shows the critical values on the F-distribution where a is equal to 0.05. (Critical values are those values that represent the boundary between rejecting Ho and not rejecting Ho; refer to Chapter 9.) To use Table A-5, you need three pieces of information from the particular problem you’re working on:

IU The sample size, N

IU The number of populations (or treatments being compared), K IU The value of FFor which you want the cumulative probability

To find the critical value for your F-test statistic using Table A-5, go to the column representing the degrees of freedom you need (k – 1, N - k). Intersect the column degrees of freedom (k – 1) with the row degrees of freedom (n – k), and you find the critical value on the F-distribution. For more on the F-test, see Chapter 9.

Table A-5

The F-Table

CD -i

CD

F (.05, dfl, df2>