Probability without Equations: Concepts for Clinicians
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Instead, the psychiatrist states his probability based on his knowledge of the natural history of disease and the available literature regarding signs and symptoms in schizophrenia and positive family history. From this knowledge, the psychiatrist concludes that his belief in the diagnosis of schizophrenia in that particular patient is as strong as his belief in picking a black ball from a box containing 10 white and 90 black balls.
The probability in this case is certainly subjective probability. Let us consider another example: A year-old married female patient who suffered from severe abdominal pain is referred to a hospital. She is also having amenorrhea for the past 4 months. The pain is located in the left lower abdomen. As before, we ask the gynecologist to explain on what basis the diagnosis of ectopic pregnancy is suspected.
So in this case also, the probability is a subjective probability which was based on an observed frequency. One might also argue that even this probability is not good enough. We might ask the gynecologist to base his belief on a group of patients who also had the same age, height, color of hair and social background; and in the end, the reference group would be so restrictive that even the experience from a very large study would not provide the necessary information. If we went even further and required that he must base his belief on patients who in all respects resembled this particular patient, the probabilistic problem would vanish as we will be dealing with a certainty rather than a probability.
Recorded experience is never the sole basis of clinical decision making. The two situations described above are relatively straightforward.
The physician observed a patient with a particular set of signs and symptoms and assessed the subjective probability about the diagnosis in each case. Such probabilities have been termed diagnostic probabilities Wulff, Pedersen and Rosenberg, In practice, however, clinicians make diagnosis in a more complex manner which they themselves may be unable to analyze logically. First a formal analysis may be attempted, and then we can return to everyday clinical thinking.
The frequential probability which the doctor found in the literature may be written in the statistical notation as follows:.
However, such probabilities are of little clinical relevance. We of course do not suggest that clinicians should always make calculations of this sort when confronted with a diagnostic dilemma, but they must in an intuitive way think along these lines. Clinical knowledge is to a large extent based on textbook knowledge, and ordinary textbooks do not tell the reader much about the probabilities of different diseases given different symptoms.
The practical significance of this point is illustrated by the European doctor who accepted a position at a hospital in tropical Africa. In order to prepare himself for the new job, he bought himself a large textbook of tropical medicine and studied in great detail the clinical pictures of a large number of exotic diseases. However, for several months after his arrival at the tropical hospital, his diagnostic performance was very poor, as he knew nothing about the relative frequency of all these diseases.
The same thing happens on a smaller scale when a doctor trained at a university hospital establishes himself in general practice. At the beginning, he will suspect his patients of all sorts of rare diseases which are common at the university hospital , but after a while he will learn to assess correctly the frequency of different diseases in the general population.
Besides predictions on individual patients, the doctor is also concerned in generalizations to the population at large or the target population.
Put in other words, the test statistic does not eliminate uncertainty as many tend to believe ; it only quantifies our uncertainty. It will be evident that the choice is a difficult one, as both hypotheses, each in its own way, may be said to be unlikely, but any clinician who reasons along these lines will choose that hypothesis which is least unacceptable: Amazon Inspire Digital Educational Resources. Calculation of test statistic From the data contained in the sample, we compute a value of the test statistic and compare it with the rejection and non-rejection regions, which have to be specified in advance. Please try again later. There's a problem loading this menu right now.
We may say that probably there may have been life at Mars. These probabilities are again subjective probabilities rather than frequential probabilities. It simply means that our belief in the truth of the statement is the same as our belief in picking up a red ball from a box containing 95 red balls and 5 white balls. It means that we are, however, almost not totally convinced that the average recovery time during treatment with a particular antidepressant is shorter than during placebo treatment.
The purpose of hypothesis testing is to aid the clinician in reaching a conclusion concerning the universe by examining a sample from that universe. A hypothesis may be defined as a presumption or statement about the truth in the universe. It is frequently concerned about the parameters in the population about which the presumption or statement is made. It is the basis for motivating the research project. There are two types of hypotheses, research hypothesis and statistical hypothesis Daniel, ; Guyatt et al.
Hypothesis may be generated by deduction from anatomical, physiological facts or from clinical observations. Statistical hypotheses are hypotheses that are stated in such a way that they may be evaluated by appropriate statistical techniques. The types of data that form the basis of hypothesis testing procedures must be understood, since these dictate the choice of statistical test. These presumptions are the normality of the population distribution, equality of the standard deviations, random samples.
There are 2 statistical hypotheses involved in hypothesis testing. These should be stated a priori and explicitly. The null hypothesis is the hypothesis to be tested. It is denoted by the symbol H 0. It is also known as the hypothesis of no difference. The null hypothesis is set up with the sole purpose of efforts to knock it down. In the testing of hypothesis, the null hypothesis is either rejected knocked down or not rejected upheld. If the null hypothesis is not rejected, the interpretation is that the data is not sufficient evidence to cause rejection.
If the testing process rejects the null hypothesis, the inference is that the data available to us is not compatible with the null hypothesis and by default we accept the alternative hypothesis , which in most cases is the research hypothesis. The alternative hypothesis is designated with the symbol H A.
WHAT IS PROBABILITY?
Neither hypothesis testing nor statistical tests lead to proof. It merely indicates whether the hypothesis is supported or not supported by the available data. When we reject a null hypothesis, we do not mean it is not true but that it may be true. By default when we do not reject the null hypothesis, we should have this limitation in mind and should not convey the impression that this implies proof. The test statistic is the statistic that is derived from the data from the sample. Evidently, many possible values of the test statistic can be computed depending on the particular sample selected.
The test statistic serves as a decision maker, nothing more, nothing less, rather than proof or lack of it. The decision to reject or not to reject the null hypothesis depends on the magnitude of the test statistic. When we reject a null hypothesis, there is always the risk howsoever small it may be of committing a type I error, i. On the other hand, whenever we fail to reject a null hypothesis, the risk of failing to reject a false null hypothesis, or committing a type II error, will always be present. Put in other words, the test statistic does not eliminate uncertainty as many tend to believe ; it only quantifies our uncertainty.
From the data contained in the sample, we compute a value of the test statistic and compare it with the rejection and non-rejection regions, which have to be specified in advance.
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The statistical decision consists of rejecting or of not rejecting the null hypothesis. It is rejected if the computed value of the test statistic falls in the rejection region, and it is not rejected if the value falls in the non-rejection region. If H 0 is rejected, we conclude that H A is true. If H 0 is not rejected, we conclude that H 0 may be true. The P value is a number that tells us how unlikely our sample values are, given that the null hypothesis is true.
A P value indicating that the sample results are not likely to have occurred, if the null hypothesis is true, provides reason for doubting the truth of the null hypothesis. We must remember that, when the null hypothesis is not rejected, one should not say the null hypothesis is accepted. Since, frequently, the probability of committing error can be quite high particularly with small sample sizes , we should not commit ourselves to accepting the null hypothesis.
Probability without Equations: Concepts for Clinicians: Medicine & Health Science Books @ bahana-line.com Editorial Reviews. Review. "A good primer for the initiated or those requiring a refresher. Probability without Equations: Concepts for Clinicians 1st Edition, Kindle Edition. by.
With the above discussion on probability, clinical decision making and hypothesis testing in mind, let us reconsider the meaning of P values. The statement that there is difference between the cure rates of two treatments is a general one, and we have already discussed that the probability of the truth of a general statement hypothesis is subjective , whereas the probabilities which are calculated by statisticians are frequential ones.
The hypothesis that one treatment is better than the other is either true or false and cannot be interpreted in frequential terms. In this case, there are two possibilities, either the null hypothesis is true, which means that the two treatments are equally effective and the observed difference arose by chance; or the null hypothesis is not true and we accept the alternative hypothesis by default , which means that one treatment is better than the other.
The clinician wants to make up his mind to what extent he believes in the truth of the alternative hypothesis or the falsehood of the null hypothesis. To resolve this issue, he needs the aid of statistical analysis. However, it is essential to note that the P value does not provide a direct answer. In other words, the statistician asks us to assume that the null hypothesis is true and to imagine that we do a large number of trials. In order to elucidate the implications of the correct statistical definition of the P value, let us imagine that the patients who took part in the above trial suffered from depression, and that drug A was gentamycin, while drug B was a placebo.
Our theoretical knowledge gives us no grounds for believing that gentamycin has any affect whatsoever in the cure of depression. For this reason, our prior confidence in the truth of the null hypothesis is immense say, We must take these prior probabilities into account when we assess the result of the trial.
We have the following choice.
Probability, clinical decision making and hypothesis testing
It will be evident that the choice is a difficult one, as both hypotheses, each in its own way, may be said to be unlikely, but any clinician who reasons along these lines will choose that hypothesis which is least unacceptable: He will accept the null hypothesis and claim that the difference between the cure rates arose by chance however small it may be , as he does not feel that the evidence from this single trial is sufficient to shake his prior belief in the null hypothesis. Misinterpretation of P values is extremely common. One of the reasons may be that those who teach research methods do not themselves appreciate the problem.
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There was a problem filtering reviews right now. Please try again later. I think this is the only book I have come across which explains the meaning of "alpha levels" so clearly. The author's example of flipping a two-headed coin without revealing to his students that it is two-headed , observing their reactions as "the number of heads keep going up" and finally explaining that "different students had different alpha levels" could'nt have brought out the meaning of this term in a more better way!
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