Deal or Ne Deal: How to beat the banker and other uses of probability

Probability is used to predict the possible outcomes of any given group. In any given situation where there is the possibility of many different outcomes, probability can be used to estimate the likelihood of any outcome, by defining the outcomes as a fraction (Gravetter & Wallnau, 2009);

Probability of A =     number of outcomes classified as A

                                           Total number of possible outcomes

In order for probability to be accurate, the outcomes have to be random (Gravetter & Wallnau, 2009).

Probability is used throughout psychological testing as well as being applied to real-life situations. Probability in inferential statistics is used to predict the kind of samples that can be obtained from a population, and is usually expressed as a decimal, fraction or a percentage. Conclusions which are drawn from probability are accurate only if random sampling is used. This is achieved by; ensuring each individual has the same chance of being selected and probabilities stay constant when more than one individual is selected (by using sampling with replacement).

Probability is a good way to evaluate treatment effect. Values which are unlikely to be found in the target population show treatment effect when compared to a normal distribution. Probability forms a direct link between samples and original populations. This link forms the basis of inferential statistics.

 Probability can also be used in Game Shows to enhance opportunities of winning. Deal or no deal is a simple game of chance and by using the principles of probability we can beat the banker. In this game one person has the opportunity to win £250,000 simply by opening 22 boxes. Each box is chosen at random by the contestant ending in an array of possible outcomes.  Playing this risk/ reward game has attracted the attention of many day-time TV lovers as they follow the highs and lows of each contestants game. You can to put your statistical knowledge to the test by playing deal or no deal. After the trick on how to beat the banker is revealed…

Imagine you have 5 boxes left containing; £100, £200, £50,000, £1000 and £250,000. The banker offers you £80,000 to leave the game; Deal or No deal? By using probability we are able to predict the possible outcomes of this game ensuring we beat the banker.

Now this is where a calculator comes in handy. By using probability, take the mean based on the number of boxes left in the game.  (£60,260) – Accepting a deal that is lower than the mean is a poor decision to make.  However, later in the game, if a contestant was able to entice an amount from the banker that is higher than the mean, such as the example above, the contestant should utter the small word “deal”, with the recognition that they have beaten the banker. By using this method, your ultimate aim is to beat the mean at every stage of the game.

Probability is a statistical method that can be widely applied throughout many situations, both within psychology and the real-word.

The Helsinki Convention and 3 basic ethical principles

“We do not know what our nature permits us to be. – Jean-Jacques Rousseau” When a science or discipline deals directly with humans should you experiment on them? The answer is simply yes. Whether it’s for medical purposes or for consumer value, everything eventually has been tested on humans. How humans work and what affects our minds and bodies is a question which has tried to be answered by many western philosophers such as Rousseau and is still being studied today. During the 18^th century surgeons used to publically dissect the bodies of executed criminal or would actively snatch bodies from their graves, in order to see how the body worked; most would hopefully agree that this is totally unethical. Nowadays there is an array of guidelines to be followed when studying humans which are outlined by the WMA (World Medical Alliance) in order to prevent unethical research on humans which also apply to psychological research.

The main ethical principles for consideration are;

 

• Patients have the right to self-determination and the right to make informed decisions.

http://www.youtube.com/watch?v=x2XuGIB-E2w

Most if not all field experiments require the participants to be observed in their natural environment. Although this method is high in ecological validity, researchers are unable to gain informed consent from participants. Without informed consent is a study ethical? Although the study by Piliavin et al (1969) wasn’t able to get consent from participants it has benefited our understanding of the bystander effect. However, due to what detriment? If a participant is not able to consent they are unable to prepare themselves for any potential psychological harm. Do the benefits outweigh the costs?

 

• The physician must take into consideration the well-being of the patient at all times.

http://www.youtube.com/watch?v=XpIzju84v24

Does a study into obedience really have consideration for the well- being of its participants? This basic principle is in place to protect participants from any psychological harm or distress. Milgram’s (study although detrimental to refining and enhancing psychological theory’s on conformity, was it really necessary to put participants though unnecessary stress? In hind sight I personally feel that yes so long as it is for the sole benefit of psychological research and the participants are fully debriefed.

 

• It should be recognised that when the participant is incompetent, physically or mentally incapable of giving consent, or is a minor, consent should be taken from a parent or guardian who is acting in the subject’s best interest.

http://www.youtube.com/watch?v=lCETgT_Xfzg

In regards to psychological research, Bandura (1977) conducted a study on the social learning theory. Although this research has proved beneficial, do the benefits of studying children in this particular area outweigh the costs? The Helsinki convention is there to protect all human subjects including children (even though those aren’t the ones who primarily consent.)

 

Although ethics can sometimes hinder an experimental process, the introduction of the Helsinki convention doctrine has benefited psychology. Participants are always put first, meaning the research cannot push for the results they want when the outcome isn’t natural. For further information on the Helsinki Convention and the many other principles outlined by the WMA click the link below.

 

http://www.wma.net/en/20activities/10ethics/10helsinki/draft_historical_contemporary_perspectives.pdf

 

*Videos courtesy of Youtube.com

Do you need statistics to understand your data?

The true meaning of data without the use of statistical testing, such as the use of ANOVA’s and covariance in my opinion is meaningless. Through statistics we are able to interpret any kind of quantitative data using two methods: inferential and/or descriptive statistics.

 Imagine you’re the proprietor of a cake shop. Running your own business requires calculations of projections and sales. For example, considering your sales numbers for the past week (see table below), answer the question, which cake sells more on an average day: a classic sponge or an indulgent chocolate fudge cake?

	Classic Victoria Sponge	Chocolate fudge cake
Monday	12	27
Tuesday	19	3
Wednesday	23	67
Thursday	8	21
Friday	34	47
Saturday	12	56
Sunday	16	21

 By conducting a simple statistical equation we are able to answer this question. Using the mean is the easiest way to estimate the projection of sales on an average day. From the data inserted above we can conclude that the classic victoria sponge (M= 17.71) sells less than the indulgent chocolate cake (M= 34.57).

This working example of descriptive statistics provides an easy summary of the data gathered. From looking at the raw data we are able to work out measures of central tendencies such as the mean, median and mode to see if there are any patterns in our data.

 Granted statistics is not always as simple as the example outlined above. However, as a discipline, psychology shouldn’t, in my opinion be separated from statistics. Statistics (inferential statistics) on the whole, allows us to assess if the conclusions drawn from empirical research are not only reliable, but also whether they are valid and, how much up to a certain level is due to chance. Based on a probability of outcomes, a p value is used to see whether there is a significant difference between two groups/ variables.

 However, the main problem with statistics is that even though an effect can be seen, a causal link is unable to be made. The cause and effect of stimuli on behaviours are fundamental to the mechanics of psychology. Whether it’s to do with how people react differently to the same situation, or what kind of upbringing correlates to a certain personality trait(s). An absence of cause and effect is often seen in observational studies like Bandura’s Bobo Doll study. (http://library.nhsggc.org.uk/mediaAssets/Mental%20Health%20Partnership/Paper%201%206th%20November%20Bandura%20Film-1.pdf)

 A real life example of how cause and effect can not be inferred from statistics (http://www.youtube.com/watch?v=4RyhFzTnvRs )                                                                                                     

 Although we may not be able to infer cause and effect from data, by using statistics, we are able to test the significance of our findings. These are just as important. Without knowing if psychological data is simply due to chance, there are no requirements for any further understanding of behaviour, as theories wouldn’t be falsifiable. Therefore, there’s a strong and necessary use for statistics not only in psychology but all other forms of empirical research.

* Video Courtesy of Youtube.com