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Owing to the very short half-life of lsO (Г 1/2 = 2 min) buy discount avapro 150 mg online, the radioactivity level in the brain reaches an equilibrium after about 10 min cheap avapro 150 mg with amex. Measurement of oxygen metabolism [3 discount avapro 150 mg with mastercard, 4] In the next step, 150 labelled oxygen gas with constant concentration is supplied continuously to the subject. It is calculated from the tracer concentrations in the brain tissue and in a blood sample. In this study, it is important to correct for dispersion of the arterial input curve . Recently, several excellent radiopharmaceuticals have become available commercially. However, owing to the low photon energy of 133Xe, the spatial resolution of the image is poor. First pass extraction fraction of C B F tracers and its effect on the C B F image One of the most important properties of flow tracers is the first pass extraction fraction, i. Diagram illustrating the blood flow, oxygen metabolism and perfusion pressure relationship. This is luxury perfusion, a term that indi cates excessive blood perfusion to the ischaemically damaged tissue . Perfusion pressure-blood flow-oxygen metabolism relationship and compensatory mechanisms preventing ischaemic tissue damage The brain tissue is well protected from a decrease of perfusion pressure [2, 35]. As described above, the compensatory mechanism to prevent ischaemic tissue damage for pressure reduction is comprised of two serial mechanisms (Fig. Clinical study of patients with acute ischaemia It is important clinically to analyse the pathophysiological state described above. The angiograms disclosed occlusion of the right cervical internal carotid artery and severe stenosis of the left internal carotid syphon. According to this analysis, both frontal lobes are structurally almost normal, but are considered to be haemodynamically at risk. In patients with unilateral infarc tion of the carotid arterial territory, the most commonly seen flow/metabolism reduc tions are found in the contralateral cerebellum, which has been called ‘crossed cerebellar diaschisis’ , and in the ipsilateral thalamus. Relationship between O E F and cerebrovascular response rates to (a) hypercapnea and (b) hypertension load . A similar effect can be observed in patients with a brain tumour, intracerebral haematoma and other localized lesions of the cerebrum. The remote effect will be mediated not only by neuronal deactivation (diaschisis), but also by degeneration of fibre tracts and by microscopic neuronal loss. The ‘crossed cerebellar diaschisis’ has been interpreted as a neuronal disconnection through the cortico-ponto-cerebellar tract. However, none of these has provided direct information on neuron specific damage after ischaemic damage. In this study, it was found that the 123I-iomazenyl uptake was decreased in the areas surrounding the infarction, and that normal and decreased binding of the tracer were distinguished in the hypoperfused normodensity tissue. However, the method has a limitation in not being sensitive in the central grey matter, white matter and the brain stem owing to lower distribution of the receptor to those areas. Usually, the primary sensory and motor cortices, the basal ganglia, the thalamus and cerebellum are relatively spared [49, 50]. Epilepsy In 1933, Penfield [55, 56] presented the first systemic evidence of blood flow changes associated with focal seizure, acquired using intraoperative observation of the pial vessels. In the immediate post-ictal period, up to 2 min after the end of the seizure, there was hyperperfusion of the mesial temporal cortex with hypoperfusion of the lateral cortex. Up to 15 min after the end of the seizure, hypoperfusion alone, which again might be localized at the temporal lobe or be more widespread, was seen. The phenomenon of reduction of benzodiazepine receptor binding in epileptic foci is very interesting . It is anticipated that the ligand will soon be applied widely in clinical practice. The clinical value of these studies depends in part on their clinical efficacy and their cost effectiveness. Description of the method and its compa rison with the Cl50 2 continuous inhalation method, J. The lumped constants and rate constants for [F-18]fluorodeoxy-glucose and [C-ll]deoxyglucose, J. Theory, procedure and normal values in a conscious and anesthetized albino rat, J. Eighty-five patients with three different types of brain lesions were included in the study. Calculation of early delayed uptake and the retention index showed high early late uptake with low retention index in high grade astrocytoma versus a low mean value of early and delayed uptake with a high retention index in low grade glioma. Also, crossed cerebellar diaschiasis was seen in 50% of each group and ‘luxury’ perfusion in 30% of the subacute phase. Additional lesions with signs of cerebral atrophy in 75% of acute and 50% of subacute phases were noted. Such lipophilic compounds cross the normal blood brain barrier and localize in normal brain cells by passive transport proportional to the blood flow, with an extraction efficiency of around 60%. They have many applications in the field of epilepsy, cerebrovascular strokes, traumatic lesions, dementia and brain death . On the other hand, 20lTl-chloride has been shown to reflect viable malignant glioma, as its uptake is related to the pumping effect of potassium, blood brain barrier dysfunction and increased regional blood flow. Group 1 consisted of 15 patients imaged within two weeks following surgery to detect residual tumours. Group 2 consisted of ten patients with possible recurrence or post-radiation gliosis. Twenty-five out of the 30 patients (83%) were uncontrolled by medical treat ment. A 64 x 64 projection with 30 s per view was obtained with the camera rotated 360°. Tomographic slices were recon structed using filtered back projection with a Shepp-Logan filter and a power of 0. Regions of interest were drawn on the slice with the greatest tumour activity and on the contralateral scalp for calculation of the early and delayed uptake and retention index. Post-operative residual A higher mean value of early and delayed 201T1 uptake of 2. There was a significant differ ence with a low retention index of 9 ± 2% in high grade glioma versus a high reten tion index of 32 ± 1% in low grade tumours (P < 0. Tumour recurrence versus gliosis A higher mean value for early and delayed 201T1 uptake of 2. Figures 1(a)- 1(b) show a case of astrocytoma with a residual viable tumour with a high uptake of 2. Epilepsy Thirty patients ranging in age from 15 to 34 years, with a mean age of 24. They had a history of epileptic fits ranging from 4 months to 20 years which were controlled through medical treatment. Cerebrovascular stroke Thirty patients, ranging in age from 40 to 65 years, with different types of cerebrovascular strokes were included in the study. There was no evidence of other lesions, cerebellar diaschiasis or signs of cerebral atrophy. The accumulation of 210T1 in malignant tumours may be related to changes in the blood brain barrier, regional blood flow and/or increased pumping of this potas sium analogue by the Na+-K + adenosine triphosphate pump . In this study, a significant correlation between tumour grade and retention index (r = 0. Recurrent tumours or post-radiation gliosis Following radical dose of radiation therapy, it is critical to differentiate between post-radiation necrosis, which requires conservative measures, and recurrent tumours, which may need resurgery or adjuvant therapy in order to improve the quality of life and the survival rate . In this work, 8 out of 10 patients (80%) were shown as having recurrent tumours in view of the high early, late 201T1 uptake and retention index. In this work, interictal evaluation for the detection of epileptic focus showed a sensitivity of 80, 73. However, differences in sensitivity between structural and functional imaging modalities disappear within 72 h . This is a common finding accompanying cortical strokes because of cortico-pontine-cerebellar linkages which lead to reduced perfu sion as a secondary phenomenon following cerebral ischaemia . Luxury perfusion was usually evident 5 to 20 d after the attack; however, its cause was not fully understood . Twenty-one patients were studied: 14 females and 7 males, ranging in age from 11 to 74 years (x = 37 years).
How well a relationship helps us to predict the different Y scores is the extent that it “explains” or “accounts” for the variance in Y scores purchase 300mg avapro free shipping. However cheap avapro 150mg with visa, the rela- tionship with list length tends to group similar scores together order 300mg avapro otc. Therefore, we know when participants score around 3 (when they recall a 5-item list) and when they pro- duce a different score of, say, 9 (when they recall a 15-item list). By considering list length, our predictions seem very close to each person’s actual score, so we seem to be close to predicting many of the differences among the nine scores. Therefore, in our lingo, we would say that the variable of list length seems to “account for” a sizable portion of the variance in recall scores. However, we still have some error in our pre- dictions because not everyone scored exactly the score we’d predict. Therefore, some differences among scores are not predicted, so we say that some of the variance in re- call scores is not accounted for. On the other hand, consider when a relationship is weaker, such as the relationship between someone’s gender and his or her height. We would predict the average man’s height for any man and the average woman’s height for any woman. However, there is a wide range of women’s and men’s heights, so our predictions each time may not be very close to someone’s actual height. Therefore, this relationship is not all that much help in predicting someone’s exact height, and so it would be described as accounting for little of the variance in height. As these examples illustrate, more consistent relationships account for a greater amount of the variance. Chapters 8 and 12 discuss ways to precisely measure the amount of variance accounted for. For example, recall that the symbol for the sample mean is M, so in a report of our list-length study, you might see this: “The fewest errors were produced when recalling 5-item lists (M 3. With this information, you are largely finished with descriptive statistics because you know the important characteristics of the sample data and you’ll be ready to draw inferences about the corresponding population. Later we will compute the mean and standard deviation in each con- dition of an experiment as part of performing inferential statistics. Measures of variability describe how much the scores differ from each other, or how much the distribution is spread out. The variance is used with the mean to describe a normal distribution of interval or ratio scores. The standard deviation is also used with the mean to describe a normal distribution of interval/ratio scores. It can be thought of as somewhat like the “average” amount that scores deviate from the mean. Transforming scores by adding or subtracting a constant does not alter the standard deviation. Transforming scores by multiplying or dividing by a constant alters the standard deviation by the same amount as if we had multiplied or divided the original standard deviation by the constant. There are three versions of the formula for variance:S2 describes how far the sam- X ple scores are spread out around X, σ2 describes how far the population of scores X is spread out around , and s2 is computed using sample data but is the X inferential, unbiased estimate of how far the scores in the population are spread out around. The formulas for the descriptive measures of variability (for S2 and S ) use N as X X the final denominator. On a normal distribution, approximately 34% of the scores are between the mean and the score that is a distance of one standard deviation from the mean. There- fore, approximately 68% of the distribution lies between the two scores that are plus and minus one standard deviation from the mean. We summarize an experiment usually by computing the mean and standard devia- tion in each condition. When the standard deviations are relatively small, the scores in the conditions are similar, and so a more consistent—stronger—relation- ship is present. When we predict that participants obtained the mean score, our error in predic- tions is determined by the variability in the scores. In this context the variance and standard deviation measure the differences between the participants’ actual scores 1X2 and the score we predict for them 1X2, so we are computing an answer that is somewhat like the “average” error in our predictions. The amount that a relationship with X helps us to predict the different Y scores in the data is the extent that X accounts for the variance in scores. What do measures of variability communicate about (a) the size of differences among the scores in a distribution? Why are your estimates of the population variance and standard deviation always larger than the corresponding values that describe a sample from that population? In a condition of an experiment, a researcher obtains the following creativity scores: 3 In terms of creativity, interpret the variability of these data using the following: (a) the range, (b) the variance, and (c) the standard deviation. If you could test the entire population in question 11, what would you expect each of the following to be? As part of studying the relationship between mental and physical health, you obtain the following heart rates: 73 72 67 74 78 84 79 71 76 76 79 81 75 80 78 76 78 In terms of differences in heart rates, interpret these data using the following: (a) the range, (b) the variance, and (c) the standard deviation. If you could test the population in question 14, what would you expect each of the following to be? Indicate whether by knowing someone’s score on the first variable, the relationship accounts for a large or small amount of the variance in the second variable. Consider the results of this experiment: Condition A Condition B Condition C 12 33 47 11 33 48 11 34 49 10 31 48 (a) What “measures” should you compute to summarize the experiment? Compute the appropriate descriptive statistics and summarize the relationship in the sample data. Consider these ratio scores from an experiment: Condition 1 Condition 2 Condition 3 18 8 3 13 11 9 9 6 5 (a) What should you do to summarize the experiment? Comparing the results in questions 19 and 22, which experiment produced the stronger relationship? What are the three major pieces of information we need in order to summarize the scores in any data? What is the difference between what a measure of central tendency tells us and what a measure of variability tells us? For each of the following, identify the conditions of the independent variable, the dependent variable, their scales of measurement, which measure of central tendency and variability to compute and which scores you would use in the com- putations. For each experiment in question 28, indicate the type of graph you would create, and how you would label the X and Y axes. The computational formula for estimating the population variance is Range highest score lowest score 1©X22 ©X2 2 2. The computational formula for the sample N s2 5 variance is X N 2 1 1©X22 ©X2 2 5. Your goals in this chapter are to learn ■ What a z-score is and what it tells you about a raw score’s relative standing. The techniques discussed in the preceding chapters for graphing, measuring central tendency, and measuring variability comprise the descriptive procedures used in most behavioral research. In this chapter, we’ll combine these procedures to answer another question about data: How does any one particular score compare to the other scores in a sample or population? In the following sections, we discuss (1) the logic of z-scores and their simple com- putation, (2) how z-scores are used to describe individual scores, and (3) how z-scores are used to describe sample means. The size of a number, regardless of its sign, is the absolute value of the number. When we do not ignore the sign, you’ll encounter the symbol ;, which means “plus or minus. Saying “the scores between ;1,” means all possible scores from 21, through 0, up to and including 11. Recall that we transform raw scores to make different variables comparable and to make scores within the same distribution easier to interpret. The “z-transformation” is the Rolls-Royce of transformations because with it we can compare and interpret scores from virtually any normal distribution of interval or ratio scores. Because researchers usually don’t know how to inter- pret someone’s raw score: Usually, we won’t know whether, in nature, a score should be considered high or low, good, bad, or what. Instead, the best we can do is compare a score to the other scores in the distribution, describing the score’s relative standing.
Your goals in this chapter are to learn ■ What measures of central tendency tell us about data 300mg avapro sale. The frequency distributions discussed in the previous chapter are important because the shape of a distribution is an important characteristic of data for us to know generic 150 mg avapro with amex. Therefore discount avapro 150mg fast delivery, the first step in any statistical analysis is to determine the distribution’s shape. Then, however, we compute individual numbers—statistics—that each describe an important characteristic of the data. This chapter discusses statistics that describe the important characteristic called central tendency. The following sections present (1) the concept of central tendency, (2) the three ways to compute central tendency, and (3) how we use them to summarize and interpret data. It is used in conjunction with a symbol for scores, so you will see such no- tations as ©X. In words, ©X is pronounced sum of X and literally means to find the sum of the X scores. Recall that descriptive statistics tell us the obvious things we would ask about a sample of scores. So think about what questions you ask your professor about the grades after you’ve taken an exam. Your first question is how did you do, but your second question is how did everyone else do? Central tendency is important because it answers this most basic question about data: Are the scores gen- erally high scores or low scores? You need this information to understand both how the class performed and how you performed relative to everyone else. But it is difficult to do this by looking at the individual scores or at the frequency distribution. Instead, it is much better if you know something like the class average; an average on the exam of 80 versus 30 is very understandable. Therefore, in virtually all research, we first com- pute a statistic that shrinks the data down into one number that summarizes everyone’s score. To understand central tendency, first change your perspective of what a score indicates. For example, if I am 70 inches tall, don’t think of this as indicating that I have 70 inches of height. Instead, think of any variable as an infinite continuum—a straight line—and think of a score as indicating a participant’s location on that line. If my brother is 60 inches tall, then he is located at the point marked 60 on the height variable. The idea is not so much that he is 10 inches shorter than I am, but rather that we are separated by a distance of 10 units— in this case, 10 “inch” units. In statistics, scores are locations, and the difference between any two scores is the distance between them. In our parking lot view of the normal curve, partici- pants’ scores determine where they stand. A high score puts them on the right side of the lot, a low score puts them on the left side, and a middle score puts them in a crowd in the middle. Further, if we have two distributions containing different scores, then the distributions have different locations on the variable. Thus, a measure of central tendency is a number that is a summary that you can think of as indicating where on the variable most scores are located; or the score that everyone scored around; or the typical score; or the score that serves as the address for the distribution as a whole. Notice that the above example again illustrates how to use descriptive statistics to envision the important aspects of the distribution without looking at every individual score. If a researcher told you only that one normal distribution is centered at 60 and the other is centered at 70, you could envision Figure 4. Thus, although you’ll see other statistics that add to this mental picture, measures of central tendency are at the core of sum- marizing data. The trick is to com- pute the correct one so that you accurately envision where most scores in the data are located. The scale of measurement used so that the summary makes sense given the nature of the scores. The shape of the frequency distribution the scores produce so that the measure accurately summarizes the distribution. In the following sections, we first discuss the mode, then the median, and finally the mean. The score of 4 is the mode because it occurs more frequently than any other score. Also, notice that the scores form a roughly normal curve, with the highest point at the mode. When a polygon has one hump, such as on the normal curve, the distribution is called unimodal, indicating that one score qualifies as the mode. For example, consider the scores 2, 3, 4, 5, 5, 5, 6, 7, 8, 9, 9, 9, 10, 11, and 12. Describing this distribution as bimodal and identifying the two modes does summarize where most of the scores tend to be located—most are either around 5 or around 9. The way to summarize such data would be to indicate the most frequently occurring category: Reporting that the mode was a preference for “Goopy Chocolate” is very in- formative. Also, you have the option of reporting the mode along with other measures of central tendency when describing other scales of measurement because it’s always informative to know the “modal score. First, the distribution may contain many scores that are all tied at the same highest frequency. In the most extreme case, we might obtain a rectangular distribution such as 4, 4, 5, 5, 6, 6, 7, and 7. A sec- ond problem is that the mode does not take into account any scores other than the most frequent score(s), so it may not accurately summarize where most scores in the distri- bution are located. For example, say that we obtain the skewed distribution containing 7, 7, 7, 20, 20, 21, 22, 22, 23, and 24. Because of these limitations, we usually rely on one of the other measures of central tendency when we have ordinal, interval, or ratio scores. Recall that 50% of a distribution is at or below the score at the 50th percentile. As we discussed in the previous chapter, when researchers are dealing with a large distribution they may ignore the relatively few scores at a percentile, so they may say that 50% of the scores are below the median and 50% are above it. To visualize this, re- call that a score’s percentile equals the proportion of the area under the curve that is to the left of—below—the score. Therefore, the 50th percentile is the score that separates the lower 50% of the distribution from the upper 50%. Because 50% of the area under the curve is to the left of the line, the score at the line is the 50th percentile, so that score is the median. In fact, the median is the score below which 50% of the area of any polygon is lo- cated. When scores form a perfect normal distribution, the median is also the most frequent score, so it is the same score as the mode. When scores are approximately normally distributed, the median will be close to the mode. When data are not at all normally distributed, however, there is no easy way to deter- mine the point below which. Also, recall that using the area under the curve is not accurate with a small sample. With an odd number of scores, the score in the middle position is the ap- proximate median. For example, for the nine scores 1, 2, 3, 3, 4, 7, 9, 10, and 11, the score in the middle position is the fifth score, so the median is the score of 4. On the other hand, if N is an even number, the average of the two scores in the middle is the approximate median. For example, for the ten scores 3, 8, 11, 11, 12, 13, 24, 35, 46, and 48, the middle scores are at position 5 (the score of 12) and position 6 (the score of 13). To precisely calculate the median, consult an advanced textbook for the formula, or as in Appendix B.
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