------------------------------------------------------------------------------- Transformations: an introduction ------------------------------------------------------------------------------- In data analysis transformation is the replacement of a variable by a function of that variable: for example, replacing a variable x by the square root of x or the logarithm of x. In a stronger sense, a transformation is a replacement that changes the shape of a distribution or relationship. This help does not pretend to be comprehensive or even generous on literature citations. Various references that I have found helpful are sprinkled here and there. Two that have particularly shaped my understanding are Emerson and Stoto (1983) and Emerson (1983). Behind those articles lies the persistent emphasis placed on the value of transformations in the work of John Wilder Tukey (1915-2000). This help item covers the following topics. You can read in sequence or skim directly to each section. Starred sections are likely to appear more esoteric or more difficult than the others to those new to the subject. Reasons for using transformations Review of most common transformations Psychological comments - for the puzzled How to do transformations in Stata * Transformations for proportions and percents * Transformations as a family * Transformations for variables that are both positive and negative Typographical notes: ^ means raise to the power of whatever follows. _ means that whatever follows should be considered a subscript (written below the line). The Stata notation == for "is equal to" and != for "is not equal to" are used for tests of various true-or-false conditions. Reasons for using transformations There are many reasons for transformation. The list here is not comprehensive. 1. Convenience 2. Reducing skewness 3. Equal spreads 4. Linear relationships 5. Additive relationships If you are looking at just one variable, 1, 2 and 3 are relevant, while if you are looking at two or more variables, 4 and 5 are more important. However, transformations that achieve 4 and 5 very often achieve 2 and 3. 1. Convenience A transformed scale may be as natural as the original scale and more convenient for a specific purpose (e.g. percentages rather than original data, sines rather than degrees). One important example is standardisation , whereby values are adjusted for differing level and spread. In general value - level standardised value = -------------. spread Standardised values have level 0 and spread 1 and have no units: hence standardisation is useful for comparing variables expressed in different units. Most commonly a standard score is calculated using the mean and standard deviation (sd) of a variable: x - mean of x z = -------------. sd of x Standardisation makes no difference to the shape of a distribution. 2. Reducing skewness A transformation may be used to reduce skewness. A distribution that is symmetric or nearly so is often easier to handle and interpret than a skewed distribution. More specifically, a normal or Gaussian distribution is often regarded as ideal as it is assumed by many statistical methods. To reduce right skewness, take roots or logarithms or reciprocals (roots are weakest). This is the commonest problem in practice. To reduce left skewness, take squares or cubes or higher powers. 3. Equal spreads A transformation may be used to produce approximately equal spreads, despite marked variations in level, which again makes data easier to handle and interpret. Each data set or subset having about the same spread or variability is a condition called homoscedasticity : its opposite is called heteroscedasticity . (The spelling -sked- rather than -sced- is also used.) 4. Linear relationships When looking at relationships between variables, it is often far easier to think about patterns that are approximately linear than about patterns that are highly curved. This is vitally important when using linear regression, which amounts to fitting such patterns to data. (In Stata, regress is the basic command for regression.) For example, a plot of logarithms of a series of values against time has the property that periods with constant rates of change (growth or decline) plot as straight lines. 5. Additive relationships Relationships are often easier to analyse when additive rather than (say) multiplicative. So y = a + bx in which two terms a and bx are added is easier to deal with than y = ax^b in which two terms a and x^b are multiplied. Additivity is a vital issue in analysis of variance (in Stata, anova, oneway, etc.). In practice, a transformation often works, serendipitously, to do several of these at once, particularly to reduce skewness, to produce nearly equal spreads and to produce a nearly linear or additive relationship. But this is not guaranteed. Review of most common transformations The most useful transformations in introductory data analysis are the reciprocal, logarithm, cube root, square root, and square. In what follows, even when it is not emphasised, it is supposed that transformations are used only over ranges on which they yield (finite) real numbers as results. Reciprocal The reciprocal , x to 1/x, with its sibling the negative reciprocal , x to -1/x, is a very strong transformation with a drastic effect on distribution shape. It can not be applied to zero values. Although it can be applied to negative values, it is not useful unless all values are positive. The reciprocal of a ratio may often be interpreted as easily as the ratio itself: e.g. population density (people per unit area) becomes area per person; persons per doctor becomes doctors per person; rates of erosion become time to erode a unit depth. (In practice, we might want to multiply or divide the results of taking the reciprocal by some constant, such as 1000 or 10000, to get numbers that are easy to manage, but that itself has no effect on skewness or linearity.) The reciprocal reverses order among values of the same sign: largest becomes smallest, etc. The negative reciprocal preserves order among values of the same sign. Logarithm The logarithm , x to log base 10 of x, or x to log base e of x (ln x), or x to log base 2 of x, is a strong transformation with a major effect on distribution shape. It is commonly used for reducing right skewness and is often appropriate for measured variables. It can not be applied to zero or negative values. One unit on a logarithmic scale means a multiplication by the base of logarithms being used. Exponential growth or decline y = a exp(bx) is made linear by ln y = ln a + bx so that the response variable y should be logged. (Here exp() means raising to the power e, approximately 2.71828, that is the base of natural logarithms.) An aside on this exponential growth or decline equation: put x = 0, and y = a exp(0) = a, so that a is the amount or count when x = 0. If a and b 0, then y grows at a faster and faster rate (e.g. compound interest or unchecked population growth), whereas if a 0 and b 0, y declines at a slower and slower rate (e.g. radioactive decay). Power functions y = ax^b are made linear by log y = log a + b log x so that both variables y and x should be logged. An aside on such power functions : put x = 0, and for b 0, y = ax^b = 0, so the power function for positive b goes through the origin, which often makes physical or biological or economic sense. Think: does zero for x imply zero for y? This kind of power function is a shape that fits many data sets rather well. Consider ratios y = p / q where p and q are both positive in practice. Examples are males / females; dependants / workers; downstream length / downvalley length. Then y is somewhere between 0 and infinity, or in the last case, between 1 and infinity. If p = q, then y = 1. Such definitions often lead to skewed data, because there is a clear lower limit and no clear upper limit. The logarithm, however, namely log y = log p / q = log p - log q, is somewhere between -infinity and infinity and p = q means that log y = 0. Hence the logarithm of such a ratio is likely to be more symmetrically distributed. Cube root The cube root , x to x^(1/3). This is a fairly strong transformation with a substantial effect on distribution shape: it is weaker than the logarithm. It is also used for reducing right skewness, and has the advantage that it can be applied to zero and negative values. Note that the cube root of a volume has the units of a length. It is commonly applied to rainfall data. Applicability to negative values requires a special note. Consider (2)(2)(2) = 8 and (-2)(-2)(-2) = -8. These examples show that the cube root of a negative number has negative sign and the same absolute value as the cube root of the equivalent positive number. A similar property is possessed by any other root whose power is the reciprocal of an odd positive integer (powers 1/3, 1/5, 1/7, etc.). This property is a little delicate. For example, change the power just a smidgen from 1/3, and we can no longer define the result as a product of precisely three terms. However, the property is there to be exploited if useful. Square root The square root , x to x^(1/2) = sqrt(x), is a transformation with a moderate effect on distribution shape: it is weaker than the logarithm and the cube root. It is also used for reducing right skewness, and also has the advantage that it can be applied to zero values. Note that the square root of an area has the units of a length. It is commonly applied to counted data, especially if the values are mostly rather small. Square The square , x to x^2, has a moderate effect on distribution shape and it could be used to reduce left skewness. In practice, the main reason for using it is to fit a response by a quadratic function y = a + b x + c x^2. Quadratics have a turning point, either a maximum or a minimum, although the turning point in a function fitted to data might be far beyond the limits of the observations. The distance of a body from an origin is a quadratic if that body is moving under constant acceleration, which gives a very clear physical justification for using a quadratic. Otherwise quadratics are typically used solely because they can mimic a relationship within the data region. Outside that region they may behave very poorly, because they take on arbitrarily large values for extreme values of x, and unless the intercept a is constrained to be 0, they may behave unrealistically close to the origin. Squaring usually makes sense only if the variable concerned is zero or positive, given that (-x)^2 and x^2 are identical. Which transformation? The main criterion in choosing a transformation is: what works with the data? As examples above indicate, it is important to consider as well two questions. What makes physical (biological, economic, whatever) sense, for example in terms of limiting behaviour as values get very small or very large? This question often leads to the use of logarithms. Can we keep dimensions and units simple and convenient? If possible, we prefer measurement scales that are easy to think about. The cube root of a volume and the square root of an area both have the dimensions of length, so far from complicating matters, such transformations may simplify them. Reciprocals usually have simple units, as mentioned earlier. Often, however, somewhat complicated units are a sacrifice that has to be made. Psychological comments - for the puzzled The main motive for transformation is greater ease of description. Although transformed scales may seem less natural, this is largely a psychological objection. Greater experience with transformation tends to reduce this feeling, simply because transformation so often works so well. In fact, many familiar measured scales are really transformed scales: decibels, pH and the Richter scale of earthquake magnitude are all logarithmic. However, transformations cause debate even among experienced data analysts. Some use them routinely, others much less. Various views, extreme or not so extreme, are slightly caricatured here to stimulate reflection or discussion. For what it is worth, I consider all these views defensible, or at least understandable. "This seems like a kind of cheating. You don't like how the data are, so you decide to change them." "I see that this is a clever trick that works nicely. But how do I know when this trick will work with some other data, or if another trick is needed, or if no transformation is needed?" "Transformations are needed because there is no guarantee that the world works on the scales it happens to be measured on." "Transformations are most appropriate when they match a scientific view of how a variable behaves." Often it helps to transform results back again, using the reverse or inverse transformation: reciprocal t = 1 / x reciprocal x = 1 / t log base 10 t = log_10 x 10 to the power x = 10^t log base e t = log_e x = ln x e to the power x = exp(t) log base 2 t = log_2 x 2 to the power x = 2^t cube root t = x^(1/3) cube x = t^3 square root t = x^(1/2) square x = t^2 How to do transformations in Stata Basic first steps 1. Draw a graph of the data to see how far patterns in data match the simplest ideal patterns. Try dotplot or scatter as appropriate. 2. See what range the data cover. Transformations will have little effect if the range is small. 3. Think carefully about data sets including zero or negative values. Some transformations are not defined mathematically for some values, and often they make little or no scientific sense. For example, I would never transform temperatures in degrees Celsius or Fahrenheit for these reasons (unless to Kelvin). Standard scores (mean 0 and sd 1) in a new variable are obtained by . egen stdpopi = std(popi) whereas the basic transformations can all be put in new variables by generate: . gen recener = 1/energy . gen logeener = ln(energy) . gen l10ener = log10(energy) . gen curtener = energy^(1/3) . gen sqrtener = sqrt(energy) . gen sqener = energy^2 . gen logitp = logit(p) if p is a proportion . gen logitp = logit(p / 100) if p is a percent . gen frootp = sqrt(p) - sqrt(1-p) if p is a proportion . gen frootp = sqrt(p) - sqrt(100-p) if p is a percent Cube roots of negative numbers require special care. Stata uses a general routine to calculate powers and does not look for special cases of powers. Whenever negative values are present, a more general recipe for cube roots is sign(x) * (abs(x)^(1/3)) . Similar comments apply to fifth, seventh, roots etc. Note any messages about missing values carefully: unless you had missing values in the original variable, they indicate an attempt to apply a transformation when it is not defined. (Do you have zero or negative values, for example?) It is not always necessary to create a transformed variable before working with it. In particular, many graph commands allow the options yscale(log) and xscale(log) . This is very useful because the graph is labelled using the original values, but it does not leave behind a log-transformed variable in memory. Other commands Stata offers various other commands designed to help you choose a transformation. ladder, gladder and qladder try several transformations of a variable with the aim of showing how far they produce a more nearly normal (Gaussian) distribution. In practice such commands can be helpful, or they can be confusing at an introductory level: for examples, they can suggest a transform at odds with what your scientific knowledge would indicate. boxcox and lnskew0 are more advanced commands that should be used only after studying textbook explanations of what they do. Box and Cox (1964) is the key original reference. For some statistical people any debate about transformation is largely side-stepped by the advent of generalised linear models . In such models, estimation is carried out on a transformed scale using a specified link function, but results are reported on the original scale of the response. The Stata command is glm. Transformations for proportions and percents (more advanced) Data that are proportions (between 0 and 1) or percents (between 0 and 100) often benefit from special transformations. The most common is the logit (or logistic) transformation, which is logit p = log (p / (1 - p)) for proportions OR logit p = log (p / (100 - p)) for percents where p is a proportion or percent. This transformation treats very small and very large values symmetrically, pulling out the tails and pulling in the middle around 0.5 or 50%. The plot of p against logit p is thus a flattened S-shape. Strictly, logit p cannot be determined for the extreme values of 0 and 1 (100%): if they occur in data, there needs to be some adjustment. One justification for this logit transformation might be sketched in terms of a diffusion process such as the spread of literacy. The push from zero to a few percent might take a fair time; once literacy starts spreading its increase becomes more rapid and then in turn slows; and finally the last few percent may be very slow in converting to literacy, as we are left with the isolated and the awkward, who are the slowest to pick up any new thing. The resulting curve is thus a flattened S-shape against time, which in turn is made more nearly linear by taking logits of literacy. More formally, the same idea might be justified by imagining that adoption (infection, whatever) is proportional to the number of contacts between those who do and those who do not, which will rise and then fall quadratically. More generally, there are many relationships in which predicted values cannot logically be less than 0 or more than 1 (100%). Using logits is one way of ensuring this: otherwise models may produce absurd predictions. The logit (looking only at the case of proportions) logit p = log (p / (1 - p)) can be rewritten logit p = log p - log (1 - p) and in this form it can be seen as a member of a set of folded transformations transform of p = something done to p - something done to (1 - p). This way of writing it brings out the symmetrical way in which very high and very low values are treated. (If p is small, 1 - p is large, and vice versa.) The logit is occasionally called the folded log . The simplest other such transformation is the folded root (that means square root) folded root of p = root of p - root of (1 - p). As with square roots and logarithms generally, the folded root has the advantage that it can be applied without adjustment to data values of 0 and 1 (100%). The folded root is a weaker transformation than the logit. In practice it is used far less frequently. Two other transformations for proportions and percents met in the older literature (and still used occasionally) are the angular and the probit . The angular is arcsin(root of p) or the angle whose sine is the square root of p. In practice, it behaves very like p^0.41 - (1 - p)^0.41, which in turn is close to p^0.5 - (1 - p)^0.5, which is another way of writing the folded root (Tukey 1960). The probit is a transformation with a mathematical connection to the normal (Gaussian) distribution, which is not only very similar in behaviour to the logit, but also more awkward to work with. As a result, it is now less seen, except in more advanced applications, where it retains several advantages. Transformations as a family (more advanced) The main transformations mentioned previously, with the exception of the logarithm, namely the reciprocal, cube root, square root and square, are all powers. The powers concerned are reciprocal -1 cube root 1/3 square root 1/2 square 2 Note that the sequence of explanation was not capricious, but in numerical order of power. Therefore, these transformations are all members of a family. In addition, contrary to what may appear at first sight, the logarithm really belongs in the family too. Knowing this is important to appreciating that the transformations used in practice are not just a bag of tricks, but a series of tools of different sizes or strengths, like a set of screwdrivers or drill bits. We could thus fill out this sequence, the ladder of transformations as it is sometimes known, with more powers, as for example in reciprocal square -2 reciprocal -1 (yields one) 0 cube root 1/3 square root 1/2 identity 1 square 2 cube 3 fourth power 4 Among the additions here, the identity transformation, say x^1 = x, is the transformation that is, in a sense, no transformation. The graph of x against x is naturally a straight line and so the power of 1 divides transformations whose graph is convex upwards (powers less than 1) from transformations whose graph is concave upwards (powers greater than 1). Powers less than 1 squeeze high values together and stretch low values apart, and powers more than 1 do the opposite. The transformation x^0, on the other hand, is degenerate, as it always yields 1 as a result. However, we will now see that in a strong sense log x (meaning, strictly, the natural logarithm or ln x) really belongs in the family at the position of power 0. If you know calculus, you will know that the sequence of powers ..., x^-3, x^-2, x^-1, x^0, x^1, x^2, ... has as integrals, apart from additive constants, ..., -x^-2 / 2, -x^-1, ln x, x, x^2 / 2, x^3 / 3, ... and the mapping can be reversed by differentiation. So integrating x^(p - 1) yields x^p / p, unless p is 0, in which case it yields ln x. Thus we can define a family t_p(x) = x^p if p != 0, = ln x if p == 0. The notion of choosing from a family when we choose a power or logarithm is a key idea. It follows that we can usually choose a different member of the family if the transformation turns out to be too weak, or too strong, for our purpose and our data. Many discussions of transformations focus on slightly different families, for a variety of mathematical and statistical reasons. The canonical reference here is Box and Cox (1964), although note also earlier work by Tukey (1957). Most commonly, the definition is changed to t_p(x) = (x^p - 1) / p if p != 0, = ln x if p == 0. This t(x, p) has various properties which point up family resemblances. 1. ln x is the limit as p - 0 of (x^p - 1) / p. 2. At x = 1, t_p(x) = 0, for all p. 3. The first derivative (rate of change) of t_p(x) is x^(p - 1) if p != 0 and 1 / x if p == 0. At x = 1, this is always 1. 4. The second derivative of t_p(x) is (p - 1) x^(p - 2) if p != 0 and -1 / x^2 if p == 0. At x = 1, this is always (p - 1). Another small change of definition has some similar consequences, but also some other advantages. Consider t_p(x) = / p if p != 0, = ln(x + 1) if p == 0. This t(x, p) has various properties which also point up family resemblances. 1. If p = 1, t_p(x) = x. 2. At x = 0, t_p(x) = 0, for all p. So all curves start at the origin. 3. The first derivative (rate of change) of t_p(x) is (x + 1)^(p - 1) if p != 0 and 1 / (x + 1) if p == 0. At x = 0, this is always 1. So the curves have the same slope at the origin. 4. The second derivative of t_p(x) is (p - 1) (x + 1)^(p - 2) if p != 0 and -1 / (x + 1)^2 if p == 0. At x = 0, this is always (p - 1). The most useful consequence, however, is that this definition can be extended more easily to variables that can be both positive and negative, as will now be seen. Transformations for variables that are both positive and negative (more advance d) Most of the literature on transformations focuses on one or both of two related situations: the variable concerned is strictly positive; or it is zero or positive. If the first situation does not hold, some transformations do not yield real number results (notably, logarithms and reciprocals); if the second situation does not hold, then some other transformations do not yield real number results or more generally do not appear useful (notably, square roots or squares). However, in some situations response variables in particular can be both positive and negative. This is common whenever the response is a balance, change, difference or derivative. Although such variables are often skew, the most awkward property that may invite transformation is heavy (long or fat) tails, high kurtosis in one terminology. Zero usually has a strong substantive meaning, so that we wish to preserve the distinction between negative, zero and positive values. (Note that Celsius or Fahrenheit temperatures do not really qualify here, as their zero points are statistically arbitrary, for all the importance of whether water melts or freezes.) In these circumstances, experience with right-skewed and strictly positive variables might suggest looking for a transformation that behaves like ln x when x is positive and like -ln(-x) when x is negative. This still leaves the problem of what to do with zeros. In addition, it is clear from any sketch that (in Stata terms) cond(x = 0, -ln(-x), ln(x)) would be useless. One way forward is to use -ln(-x + 1) if x = 0, ln(x + 1) if x 0. This can also be written sign(x) ln(|x| + 1) where sign(x) is 1 if x 0, 0 if x == 0 and -1 if x 0. This function passes through the origin, behaves like x for small x, positive and negative, and like sign(x) ln(abs(x)) for large |x|. The gradient is steepest at 1 at x = 0, so the transformation pulls in extreme values relative to those near the origin. It has recently been dubbed the neglog transformation (Whittaker et al. 2005). An earlier reference is John and Draper (1980). In Stata language, this could be cond(x = 0, -ln(-x + 1), ln(x + 1)) or sign(x) * ln(abs(x) + 1) The inverse transformation is cond(t = 0, 1 - exp(-t), exp(t) - 1) A suitable generalisation of powers other than 0 is - / p if x = 0, / p if x 0. Transformations that affect skewness as well as heavy tails in variables that are both positive and negative were discussed by Yeo and Johnson (2000). Another possibility in this terrain is to apply the inverse hyperbolic function arsinh (also known as arg sinh, sinh^-1 and arcsinh). This is the inverse of the sinh function, which in turn is defined as sinh(x) = (exp(x) - exp(-x)) / 2. The sinh and arsinh functions can be computed in Mata as sinh(x) and asinh(x) and in Stata as (exp(x) - exp(-x))/2 and ln(x + sqrt(x^2 + 1)) . The arsinh function also too passes through the origin and is steepest at the origin. For large |x| it behaves like sign(x) ln(|2x|). So in practice neglog(x) and arsinh(x) have loosely similar effects. See also Johnson (1949). Acknowledgements Austin Nichols pointed out that cube roots are well defined for negative values. Author Nicholas J. Cox, Durham University n.j.cox@durham.ac.uk (last major revision 29 November 2005; corrections and minor revisions 8 November 2006, 25 July 2007) Postscript I came across the following in a text on calculus. Transformation of a function into a form in which it can readily be integrated can be effected by suitable algebraical substitutions in which the independent variable is changed. The forms these take will depend on the kind of function to be integrated and, in general, experience and experiment must guide the student. The general aim will be to simplify the function so that it may become easier to integrate. (Abbott 1940, p.184) Modulo some small changes in terminology, this applies here too. Either way, the advice that "experience and experiment must guide the student" is not much comfort to the beginner looking for guidance! References Abbott, P. 1940. Teach Yourself Calculus. London: English Universities Press. Box, G.E.P. and D.R. Cox. 1964. An analysis of transformations. Journal of the Royal Statistical Society B 26: 211-252. Emerson, J.D. 1983. Mathematical aspects of transformation. In Hoaglin, D.C., F. Mosteller and J.W. Tukey (eds) Understanding Robust and Exploratory Data Analysis. New York: John Wiley, 247-282. Emerson, J.D. and M.A. Stoto. 1983. Transforming data. In Hoaglin, D.C., F. Mosteller and J.W. Tukey (eds) Understanding Robust and Exploratory Data Analysis. New York: John Wiley, 97-128. John, J.A. and N.R. Draper. 1980. An alternative family of transformations. Applied Statistics 29: 190-197. Johnson, N.L. 1949. Systems of frequency curves generated by methods of translation. Biometrika 36: 149-176. Tukey, J.W. 1957. On the comparative anatomy of transformations. Annals of Mathematical Statistics 28: 602-632. Tukey, J. W. 1960. The practical relationship between the common transformations of percentages or fractions and of amounts. Reprinted in Mallows, C.L. (ed.) 1990. The Collected Works of John W. Tukey. Volume VI: More Mathematical. Pacific Grove, CA: Wadsworth Brooks-Cole, 211-219. Whittaker, J., J. Whitehead and M. Somers. 2005. The neglog transformation and quantile regression for the analysis of a large credit scoring database. Applied Statistics 54: 863-878. Yeo, I. and R.A. Johnson. 2000. A new family of power transformations to improve normality or symmetry. Biometrika 87: 954-959. Also see On-line: generate, egen, graph
function Fun_A1(x) if cint(x)=1 then Fun_A1="1 、经常帮助 " elseif cint(x)=2 then Fun_A1="2 、有时帮助 " elseif cint(x)=3 then Fun_A1="3 、很少帮助 " elseif cint(x)=4 then Fun_A1="4 、从不帮助 " elseif cint(x)=5 then Fun_A1="5 、不评价 " else Fun_A1="5 、不评价 " end if end function function Fun_A2(x) if cint(x)=1 then Fun_A2="1 、经常 " elseif cint(x)=2 then Fun_A2="2 、有时 " elseif cint(x)=3 then Fun_A2="3 、很少 " elseif cint(x)=4 then Fun_A2="4 、从不 " elseif cint(x)=5 then Fun_A2="5 、不评价 " else Fun_A2="5 、不评价 " end if end function function Fun_A3(x) if cint(x)=1 then Fun_A3="1 、关心 " elseif cint(x)=2 then Fun_A3="2 、比较关心 " elseif cint(x)=3 then Fun_A3="3 、一般 " elseif cint(x)=4 then Fun_A3="4 、不太关心 " elseif cint(x)=5 then Fun_A3="5 、不关心 " elseif cint(x)=6 then Fun_A3="6 、不评价 " else Fun_A3="6 、不评价 " end if end function function Fun_A4(x) if cint(x)=1 then Fun_A4="1 、经常联系 " elseif cint(x)=2 then Fun_A4="2 、有时联系 " elseif cint(x)=3 then Fun_A4="3 、很少联系 " elseif cint(x)=4 then Fun_A4="4 、没有联系 " elseif cint(x)=5 then Fun_A4="5 、不评价 " else Fun_A4="5 、不评价 " end if end function function Fun_A5(x) if cint(x)=1 then Fun_A5="1 、满意 " elseif cint(x)=2 then Fun_A5="2 、较满意 " elseif cint(x)=3 then Fun_A5="3 、一般 " elseif cint(x)=4 then Fun_A5="4 、不太满意 " elseif cint(x)=5 then Fun_A5="5 、不满意 " elseif cint(x)=6 then Fun_A5="6 、不清楚 " elseif cint(x)=7 then Fun_A5="7 、不评价 " else Fun_A5="7 、不评价 " end if end function function Fun_B1(x) if cint(x)=1 then Fun_B1="1 、教学态度认真 " elseif cint(x)=2 then Fun_B1="2 、教学能力较强 " elseif cint(x)=3 then Fun_B1="3 、教学语言幽默 " elseif cint(x)=4 then Fun_B1="4 、师生关系亲密 " else Fun_B1="4 、师生关系亲密 " end if end function function Fun_B2(x) if cint(x)=1 then Fun_B2="1 、好 " elseif cint(x)=2 then Fun_B2="2 、比较好 " elseif cint(x)=3 then Fun_B2="3 、一般 " elseif cint(x)=4 then Fun_B2="4 、不太好 " elseif cint(x)=5 then Fun_B2="5 、不好 " elseif cint(x)=6 then Fun_B2="6 、不评价 " else Fun_B2="6 、不评价 " end if end function function Fun_B3(x) if cint(x)=1 then Fun_B3="1 、满意 " elseif cint(x)=2 then Fun_B3="2 、较满意 " elseif cint(x)=3 then Fun_B3="3 、一般 " elseif cint(x)=4 then Fun_B3="4 、不太满意 " elseif cint(x)=5 then Fun_B3="5 、不满意 " elseif cint(x)=6 then Fun_B3="6 、不评价 " else Fun_B3="6 、不评价 " end if end function function Fun_B4(x) if cint(x)=1 then Fun_B4="1 、好 " elseif cint(x)=2 then Fun_B4="2 、比较好 " elseif cint(x)=3 then Fun_B4="3 、一般 " elseif cint(x)=4 then Fun_B4="4 、不太好 " elseif cint(x)=5 then Fun_B4="5 、不好 " elseif cint(x)=6 then Fun_B4="6 、不评价 " else Fun_B4="6 、不评价 " end if end function function Fun_B5(x) if cint(x)=1 then Fun_B5="1 、好 " elseif cint(x)=2 then Fun_B5="2 、比较好 " elseif cint(x)=3 then Fun_B5="3 、一般 " elseif cint(x)=4 then Fun_B5="4 、不太好 " elseif cint(x)=5 then Fun_B5="5 、不好 " elseif cint(x)=6 then Fun_B5="6 、不清楚 " elseif cint(x)=7 then Fun_B5="7 、不评价 " else Fun_B5="7 、不评价 " end if end function function Fun_C1(x) if cint(x)=1 then Fun_C1="1 、好 " elseif cint(x)=2 then Fun_C1="2 、比较好 " elseif cint(x)=3 then Fun_C1="3 、一般 " elseif cint(x)=4 then Fun_C1="4 、不太好 " elseif cint(x)=5 then Fun_C1="5 、不好 " elseif cint(x)=6 then Fun_C1="6 、不评价 " else Fun_C1="6 、不评价 " end if end function function Fun_C2(x) if cint(x)=1 then Fun_C2="1 、好 " elseif cint(x)=2 then Fun_C2="2 、比较好 " elseif cint(x)=3 then Fun_C2="3 、一般 " elseif cint(x)=4 then Fun_C2="4 、不太好 " elseif cint(x)=5 then Fun_C2="5 、不好 " elseif cint(x)=6 then Fun_C2="6 、不评价 " else Fun_C2="6 、不评价 " end if end function function Fun_C3(x) if cint(x)=1 then Fun_C3="1 、重视 " elseif cint(x)=2 then Fun_C3="2 、较重视 " elseif cint(x)=3 then Fun_C3="3 、一般 " elseif cint(x)=4 then Fun_C3="4 、不太重视 " elseif cint(x)=5 then Fun_C3="5 、不重视 " elseif cint(x)=6 then Fun_C3="6 、不评价 " else Fun_C3="6 、不评价 " end if end function function Fun_C4(x) if cint(x)=1 then Fun_C4="1 、好 " elseif cint(x)=2 then Fun_C4="2 、比较好 " elseif cint(x)=3 then Fun_C4="3 、一般 " elseif cint(x)=4 then Fun_C4="4 、不太好 " elseif cint(x)=5 then Fun_C4="5 、不好 " elseif cint(x)=6 then Fun_C4="6 、不评价 " else Fun_C4="6 、不评价 " end if end function function Fun_C5(x) if cint(x)=1 then Fun_C5="1 、重视 " elseif cint(x)=2 then Fun_C5="2 、较重视 " elseif cint(x)=3 then Fun_C5="3 、一般 " elseif cint(x)=4 then Fun_C5="4 、不太重视 " elseif cint(x)=5 then Fun_C5="5 、不重视 " elseif cint(x)=6 then Fun_C5="6 、不评价 " else Fun_C5="6 、不评价 " end if end function function Fun_C6(x) if cint(x)=1 then Fun_C6="1 、好 " elseif cint(x)=2 then Fun_C6="2 、比较好 " elseif cint(x)=3 then Fun_C6="3 、一般 " elseif cint(x)=4 then Fun_C6="4 、不太好 " elseif cint(x)=5 then Fun_C6="5 、不好 " elseif cint(x)=6 then Fun_C6="6 、不评价 " else Fun_C6="6 、不评价 " end if end function function Fun_C7(x) if cint(x)=1 then Fun_C7="1 、好 " elseif cint(x)=2 then Fun_C7="2 、比较好 " elseif cint(x)=3 then Fun_C7="3 、一般 " elseif cint(x)=4 then Fun_C7="4 、不太好 " elseif cint(x)=5 then Fun_C7="5 、不好 " elseif cint(x)=6 then Fun_C7="6 、不评价 " else Fun_C7="6 、不评价 " end if end function function Fun_C8(x) if cint(x)=1 then Fun_C8="1 、满意 " elseif cint(x)=2 then Fun_C8="2 、较满意 " elseif cint(x)=3 then Fun_C8="3 、一般 " elseif cint(x)=4 then Fun_C8="4 、不太满意 " elseif cint(x)=5 then Fun_C8="5 、不满意 " elseif cint(x)=6 then Fun_C8="6 、不评价 " else Fun_C8="6 、不评价 " end if end function function Fun_A1(x) if cint(x)=1 then Fun_A1="1 、满意 " elseif cint(x)=2 then Fun_A1="2 、较满意 " elseif cint(x)=3 then Fun_A1="3 、一般 " elseif cint(x)=4 then Fun_A1="4 、不太满意 " elseif cint(x)=5 then Fun_A1="5 、不满意 " elseif cint(x)=6 then Fun_A1="6 、不评价 " else Fun_A1="6 、不评价 " end if end function function Fun_A2(x) if cint(x)=1 then Fun_A2="1 、强 " elseif cint(x)=2 then Fun_A2="2 、较强 " elseif cint(x)=3 then Fun_A2="3 、一般 " elseif cint(x)=4 then Fun_A2="4 、不太强 " elseif cint(x)=5 then Fun_A2="5 、不强 " elseif cint(x)=6 then Fun_A2="6 、不评价 " else Fun_A2="6 、不评价 " end if end function function Fun_A3(x) if cint(x)=1 then Fun_A3="1 、好 " elseif cint(x)=2 then Fun_A3="2 、比较好 " elseif cint(x)=3 then Fun_A3="3 、一般 " elseif cint(x)=4 then Fun_A3="4 、不太好 " elseif cint(x)=5 then Fun_A3="5 、不好 " elseif cint(x)=6 then Fun_A3="6 、不评价 " else Fun_A3="6 、不评价 " end if end function function Fun_A4(x) if cint(x)=1 then Fun_A4="1 、经常交流 " elseif cint(x)=2 then Fun_A4="2 、有时交流 " elseif cint(x)=3 then Fun_A4="3 、很少交流 " elseif cint(x)=4 then Fun_A4="4 、没有交流 " elseif cint(x)=5 then Fun_A4="5 、不评价 " else Fun_A4="5 、不评价 " end if end function function Fun_A5(x) if cint(x)=1 then Fun_A5="1 、经常 " elseif cint(x)=2 then Fun_A5="2 、偶尔 " elseif cint(x)=3 then Fun_A5="3 、很少 " elseif cint(x)=4 then Fun_A5="4 、没有 " elseif cint(x)=5 then Fun_A5="5 、不评价 " else Fun_A5="5 、不评价 " end if end function function Fun_A6(x) if cint(x)=1 then Fun_A6="1 、满意 " elseif cint(x)=2 then Fun_A6="2 、较满意 " elseif cint(x)=3 then Fun_A6="3 、一般 " elseif cint(x)=4 then Fun_A6="4 、不太满意 " elseif cint(x)=5 then Fun_A6="5 、不满意 " elseif cint(x)=6 then Fun_A6="6 、不评价 " else Fun_A6="6 、不评价 " end if end function function Fun_A7(x) if cint(x)=1 then Fun_A7="1 、满意 " elseif cint(x)=2 then Fun_A7="2 、较满意 " elseif cint(x)=3 then Fun_A7="3 、一般 " elseif cint(x)=4 then Fun_A7="4 、不太满意 " elseif cint(x)=5 then Fun_A7="5 、不满意 " elseif cint(x)=6 then Fun_A7="6 、不清楚 " elseif cint(x)=7 then Fun_A7="7 、不评价 " else Fun_A7="7 、不评价 " end if end function function Fun_B1(x) if cint(x)=1 then Fun_B1="1 、强 " elseif cint(x)=2 then Fun_B1="2 、较强 " elseif cint(x)=3 then Fun_B1="3 、一般 " elseif cint(x)=4 then Fun_B1="4 、不太强 " elseif cint(x)=5 then Fun_B1="5 、不强 " elseif cint(x)=6 then Fun_B1="6 、不评价 " else Fun_B1="6 、不评价 " end if end function function Fun_B2(x) if cint(x)=1 then Fun_B2="1 、满意 " elseif cint(x)=2 then Fun_B2="2 、较满意 " elseif cint(x)=3 then Fun_B2="3 、一般 " elseif cint(x)=4 then Fun_B2="4 、不太满意 " elseif cint(x)=5 then Fun_B2="5 、不满意 " elseif cint(x)=6 then Fun_B2="6 、不评价 " else Fun_B2="6 、不评价 " end if end function function Fun_B3(x) if cint(x)=1 then Fun_B3="1 、是 " elseif cint(x)=2 then Fun_B3="2 、否 " elseif cint(x)=3 then Fun_B3="3 、不清楚 " elseif cint(x)=4 then Fun_B3="4 、不评价 " else Fun_B3="4 、不评价 " end if end function function Fun_B4(x) if cint(x)=1 then Fun_B4="1 、满意 " elseif cint(x)=2 then Fun_B4="2 、较满意 " elseif cint(x)=3 then Fun_B4="3 、一般 " elseif cint(x)=4 then Fun_B4="4 、不太满意 " elseif cint(x)=5 then Fun_B4="5 、不满意 " elseif cint(x)=6 then Fun_B4="6 、不清楚 " elseif cint(x)=7 then Fun_B4="7 、不评价 " else Fun_B4="7 、不评价 " end if end function function Fun_B5(x) if cint(x)=1 then Fun_B5="1 、好 " elseif cint(x)=2 then Fun_B5="2 、比较好 " elseif cint(x)=3 then Fun_B5="3 、一般 " elseif cint(x)=4 then Fun_B5="4 、不太好 " elseif cint(x)=5 then Fun_B5="5 、不好 " elseif cint(x)=6 then Fun_B5="6 、不评价 " else Fun_B5="6 、不评价 " end if end function function Fun_C1(x) if cint(x)=1 then Fun_C1="1 、有明显进步 " elseif cint(x)=2 then Fun_C1="2 、进步较明显 " elseif cint(x)=3 then Fun_C1="3 、一般 " elseif cint(x)=4 then Fun_C1="4 、不太明显 " elseif cint(x)=5 then Fun_C1="5 、不明显 " elseif cint(x)=6 then Fun_C1="6 、不评价 " else Fun_C1="6 、不评价 " end if end function function Fun_C2(x) if cint(x)=1 then Fun_C2="1 、满意 " elseif cint(x)=2 then Fun_C2="2 、较满意 " elseif cint(x)=3 then Fun_C2="3 、一般 " elseif cint(x)=4 then Fun_C2="4 、不太满意 " elseif cint(x)=5 then Fun_C2="5 、不满意 " elseif cint(x)=6 then Fun_C2="6 、不清楚 " elseif cint(x)=7 then Fun_C2="7 、不评价 " else Fun_C2="7 、不评价 " end if end function function Fun_C3(x) if cint(x)=1 then Fun_C3="1 、好 " elseif cint(x)=2 then Fun_C3="2 、比较好 " elseif cint(x)=3 then Fun_C3="3 、一般 " elseif cint(x)=4 then Fun_C3="4 、不太好 " elseif cint(x)=5 then Fun_C3="5 、不好 " elseif cint(x)=6 then Fun_C3="6 、不评价 " else Fun_C3="6 、不评价 " end if end function function Fun_C4(x) if cint(x)=1 then Fun_C4="1 、好 " elseif cint(x)=2 then Fun_C4="2 、比较好 " elseif cint(x)=3 then Fun_C4="3 、一般 " elseif cint(x)=4 then Fun_C4="4 、不太好 " elseif cint(x)=5 then Fun_C4="5 、不好 " elseif cint(x)=6 then Fun_C4="6 、不评价 " else Fun_C4="6 、不评价 " end if end function function Fun_C5(x) if cint(x)=1 then Fun_C5="1 、满意 " elseif cint(x)=2 then Fun_C5="2 、较满意 " elseif cint(x)=3 then Fun_C5="3 、一般 " elseif cint(x)=4 then Fun_C5="4 、不太满意 " elseif cint(x)=5 then Fun_C5="5 、不满意 " elseif cint(x)=6 then Fun_C5="6 、不清楚 " elseif cint(x)=7 then Fun_C5="7 、不评价 " else Fun_C5="7 、不评价 " end if end function
function Fun_A1(x) if cint(x)=1 then Fun_A1="1、经常帮助" elseif cint(x)=2 then Fun_A1="2、有时帮助" elseif cint(x)=3 then Fun_A1="3、很少帮助" elseif cint(x)=4 then Fun_A1="4、从不帮助" elseif cint(x)=5 then Fun_A1="5、不评价" else Fun_A1="5、不评价" end if end function function Fun_A2(x) if cint(x)=1 then Fun_A2="1、经常" elseif cint(x)=2 then Fun_A2="2、有时" elseif cint(x)=3 then Fun_A2="3、很少" elseif cint(x)=4 then Fun_A2="4、从不" elseif cint(x)=5 then Fun_A2="5、不评价" else Fun_A2="5、不评价" end if end function function Fun_A3(x) if cint(x)=1 then Fun_A3="1、关心" elseif cint(x)=2 then Fun_A3="2、比较关心" elseif cint(x)=3 then Fun_A3="3、一般" elseif cint(x)=4 then Fun_A3="4、不太关心" elseif cint(x)=5 then Fun_A3="5、不关心" elseif cint(x)=6 then Fun_A3="6、不评价" else Fun_A3="6、不评价" end if end function function Fun_A4(x) if cint(x)=1 then Fun_A4="1、经常联系" elseif cint(x)=2 then Fun_A4="2、有时联系" elseif cint(x)=3 then Fun_A4="3、很少联系" elseif cint(x)=4 then Fun_A4="4、没有联系" elseif cint(x)=5 then Fun_A4="5、不评价" else Fun_A4="5、不评价" end if end function function Fun_A5(x) if cint(x)=1 then Fun_A5="1、满意" elseif cint(x)=2 then Fun_A5="2、较满意" elseif cint(x)=3 then Fun_A5="3、一般" elseif cint(x)=4 then Fun_A5="4、不太满意" elseif cint(x)=5 then Fun_A5="5、不满意" elseif cint(x)=6 then Fun_A5="6、不清楚" elseif cint(x)=7 then Fun_A5="7、不评价" else Fun_A5="7、不评价" end if end function function Fun_B1(x) if cint(x)=1 then Fun_B1="1、教学态度认真" elseif cint(x)=2 then Fun_B1="2、教学能力较强" elseif cint(x)=3 then Fun_B1="3、教学语言幽默" elseif cint(x)=4 then Fun_B1="4、师生关系亲密" else Fun_B1="4、师生关系亲密" end if end function function Fun_B2(x) if cint(x)=1 then Fun_B2="1、好" elseif cint(x)=2 then Fun_B2="2、比较好" elseif cint(x)=3 then Fun_B2="3、一般" elseif cint(x)=4 then Fun_B2="4、不太好" elseif cint(x)=5 then Fun_B2="5、不好" elseif cint(x)=6 then Fun_B2="6、不评价" else Fun_B2="6、不评价" end if end function function Fun_B3(x) if cint(x)=1 then Fun_B3="1、满意" elseif cint(x)=2 then Fun_B3="2、较满意" elseif cint(x)=3 then Fun_B3="3、一般" elseif cint(x)=4 then Fun_B3="4、不太满意" elseif cint(x)=5 then Fun_B3="5、不满意" elseif cint(x)=6 then Fun_B3="6、不评价" else Fun_B3="6、不评价" end if end function function Fun_B4(x) if cint(x)=1 then Fun_B4="1、好" elseif cint(x)=2 then Fun_B4="2、比较好" elseif cint(x)=3 then Fun_B4="3、一般" elseif cint(x)=4 then Fun_B4="4、不太好" elseif cint(x)=5 then Fun_B4="5、不好" elseif cint(x)=6 then Fun_B4="6、不评价" else Fun_B4="6、不评价" end if end function function Fun_B5(x) if cint(x)=1 then Fun_B5="1、好" elseif cint(x)=2 then Fun_B5="2、比较好" elseif cint(x)=3 then Fun_B5="3、一般" elseif cint(x)=4 then Fun_B5="4、不太好" elseif cint(x)=5 then Fun_B5="5、不好" elseif cint(x)=6 then Fun_B5="6、不清楚" elseif cint(x)=7 then Fun_B5="7、不评价" else Fun_B5="7、不评价" end if end function function Fun_C1(x) if cint(x)=1 then Fun_C1="1、好" elseif cint(x)=2 then Fun_C1="2、比较好" elseif cint(x)=3 then Fun_C1="3、一般" elseif cint(x)=4 then Fun_C1="4、不太好" elseif cint(x)=5 then Fun_C1="5、不好" elseif cint(x)=6 then Fun_C1="6、不评价" else Fun_C1="6、不评价" end if end function function Fun_C2(x) if cint(x)=1 then Fun_C2="1、好" elseif cint(x)=2 then Fun_C2="2、比较好" elseif cint(x)=3 then Fun_C2="3、一般" elseif cint(x)=4 then Fun_C2="4、不太好" elseif cint(x)=5 then Fun_C2="5、不好" elseif cint(x)=6 then Fun_C2="6、不评价" else Fun_C2="6、不评价" end if end function function Fun_C3(x) if cint(x)=1 then Fun_C3="1、重视" elseif cint(x)=2 then Fun_C3="2、较重视" elseif cint(x)=3 then Fun_C3="3、一般" elseif cint(x)=4 then Fun_C3="4、不太重视" elseif cint(x)=5 then Fun_C3="5、不重视" elseif cint(x)=6 then Fun_C3="6、不评价" else Fun_C3="6、不评价" end if end function function Fun_C4(x) if cint(x)=1 then Fun_C4="1、好" elseif cint(x)=2 then Fun_C4="2、比较好" elseif cint(x)=3 then Fun_C4="3、一般" elseif cint(x)=4 then Fun_C4="4、不太好" elseif cint(x)=5 then Fun_C4="5、不好" elseif cint(x)=6 then Fun_C4="6、不评价" else Fun_C4="6、不评价" end if end function function Fun_C5(x) if cint(x)=1 then Fun_C5="1、重视" elseif cint(x)=2 then Fun_C5="2、较重视" elseif cint(x)=3 then Fun_C5="3、一般" elseif cint(x)=4 then Fun_C5="4、不太重视" elseif cint(x)=5 then Fun_C5="5、不重视" elseif cint(x)=6 then Fun_C5="6、不评价" else Fun_C5="6、不评价" end if end function function Fun_C6(x) if cint(x)=1 then Fun_C6="1、好" elseif cint(x)=2 then Fun_C6="2、比较好" elseif cint(x)=3 then Fun_C6="3、一般" elseif cint(x)=4 then Fun_C6="4、不太好" elseif cint(x)=5 then Fun_C6="5、不好" elseif cint(x)=6 then Fun_C6="6、不评价" else Fun_C6="6、不评价" end if end function function Fun_C7(x) if cint(x)=1 then Fun_C7="1、好" elseif cint(x)=2 then Fun_C7="2、比较好" elseif cint(x)=3 then Fun_C7="3、一般" elseif cint(x)=4 then Fun_C7="4、不太好" elseif cint(x)=5 then Fun_C7="5、不好" elseif cint(x)=6 then Fun_C7="6、不评价" else Fun_C7="6、不评价" end if end function function Fun_C8(x) if cint(x)=1 then Fun_C8="1、满意" elseif cint(x)=2 then Fun_C8="2、较满意" elseif cint(x)=3 then Fun_C8="3、一般" elseif cint(x)=4 then Fun_C8="4、不太满意" elseif cint(x)=5 then Fun_C8="5、不满意" elseif cint(x)=6 then Fun_C8="6、不评价" else Fun_C8="6、不评价" end if end function function Fun_A1(x) if cint(x)=1 then Fun_A1="1、满意" elseif cint(x)=2 then Fun_A1="2、较满意" elseif cint(x)=3 then Fun_A1="3、一般" elseif cint(x)=4 then Fun_A1="4、不太满意" elseif cint(x)=5 then Fun_A1="5、不满意" elseif cint(x)=6 then Fun_A1="6、不评价" else Fun_A1="6、不评价" end if end function function Fun_A2(x) if cint(x)=1 then Fun_A2="1、强" elseif cint(x)=2 then Fun_A2="2、较强" elseif cint(x)=3 then Fun_A2="3、一般" elseif cint(x)=4 then Fun_A2="4、不太强" elseif cint(x)=5 then Fun_A2="5、不强" elseif cint(x)=6 then Fun_A2="6、不评价" else Fun_A2="6、不评价" end if end function function Fun_A3(x) if cint(x)=1 then Fun_A3="1、好" elseif cint(x)=2 then Fun_A3="2、比较好" elseif cint(x)=3 then Fun_A3="3、一般" elseif cint(x)=4 then Fun_A3="4、不太好" elseif cint(x)=5 then Fun_A3="5、不好" elseif cint(x)=6 then Fun_A3="6、不评价" else Fun_A3="6、不评价" end if end function function Fun_A4(x) if cint(x)=1 then Fun_A4="1、经常交流" elseif cint(x)=2 then Fun_A4="2、有时交流" elseif cint(x)=3 then Fun_A4="3、很少交流" elseif cint(x)=4 then Fun_A4="4、没有交流" elseif cint(x)=5 then Fun_A4="5、不评价" else Fun_A4="5、不评价" end if end function function Fun_A5(x) if cint(x)=1 then Fun_A5="1、经常" elseif cint(x)=2 then Fun_A5="2、偶尔" elseif cint(x)=3 then Fun_A5="3、很少" elseif cint(x)=4 then Fun_A5="4、没有" elseif cint(x)=5 then Fun_A5="5、不评价" else Fun_A5="5、不评价" end if end function function Fun_A6(x) if cint(x)=1 then Fun_A6="1、满意" elseif cint(x)=2 then Fun_A6="2、较满意" elseif cint(x)=3 then Fun_A6="3、一般" elseif cint(x)=4 then Fun_A6="4、不太满意" elseif cint(x)=5 then Fun_A6="5、不满意" elseif cint(x)=6 then Fun_A6="6、不评价" else Fun_A6="6、不评价" end if end function function Fun_A7(x) if cint(x)=1 then Fun_A7="1、满意" elseif cint(x)=2 then Fun_A7="2、较满意" elseif cint(x)=3 then Fun_A7="3、一般" elseif cint(x)=4 then Fun_A7="4、不太满意" elseif cint(x)=5 then Fun_A7="5、不满意" elseif cint(x)=6 then Fun_A7="6、不清楚" elseif cint(x)=7 then Fun_A7="7、不评价" else Fun_A7="7、不评价" end if end function function Fun_B1(x) if cint(x)=1 then Fun_B1="1、强" elseif cint(x)=2 then Fun_B1="2、较强" elseif cint(x)=3 then Fun_B1="3、一般" elseif cint(x)=4 then Fun_B1="4、不太强" elseif cint(x)=5 then Fun_B1="5、不强" elseif cint(x)=6 then Fun_B1="6、不评价" else Fun_B1="6、不评价" end if end function function Fun_B2(x) if cint(x)=1 then Fun_B2="1、满意" elseif cint(x)=2 then Fun_B2="2、较满意" elseif cint(x)=3 then Fun_B2="3、一般" elseif cint(x)=4 then Fun_B2="4、不太满意" elseif cint(x)=5 then Fun_B2="5、不满意" elseif cint(x)=6 then Fun_B2="6、不评价" else Fun_B2="6、不评价" end if end function function Fun_B3(x) if cint(x)=1 then Fun_B3="1、是" elseif cint(x)=2 then Fun_B3="2、否" elseif cint(x)=3 then Fun_B3="3、不清楚" elseif cint(x)=4 then Fun_B3="4、不评价" else Fun_B3="4、不评价" end if end function function Fun_B4(x) if cint(x)=1 then Fun_B4="1、满意" elseif cint(x)=2 then Fun_B4="2、较满意" elseif cint(x)=3 then Fun_B4="3、一般" elseif cint(x)=4 then Fun_B4="4、不太满意" elseif cint(x)=5 then Fun_B4="5、不满意" elseif cint(x)=6 then Fun_B4="6、不清楚" elseif cint(x)=7 then Fun_B4="7、不评价" else Fun_B4="7、不评价" end if end function function Fun_B5(x) if cint(x)=1 then Fun_B5="1、好" elseif cint(x)=2 then Fun_B5="2、比较好" elseif cint(x)=3 then Fun_B5="3、一般" elseif cint(x)=4 then Fun_B5="4、不太好" elseif cint(x)=5 then Fun_B5="5、不好" elseif cint(x)=6 then Fun_B5="6、不评价" else Fun_B5="6、不评价" end if end function function Fun_C1(x) if cint(x)=1 then Fun_C1="1、有明显进步" elseif cint(x)=2 then Fun_C1="2、进步较明显" elseif cint(x)=3 then Fun_C1="3、一般" elseif cint(x)=4 then Fun_C1="4、不太明显" elseif cint(x)=5 then Fun_C1="5、不明显" elseif cint(x)=6 then Fun_C1="6、不评价" else Fun_C1="6、不评价" end if end function function Fun_C2(x) if cint(x)=1 then Fun_C2="1、满意" elseif cint(x)=2 then Fun_C2="2、较满意" elseif cint(x)=3 then Fun_C2="3、一般" elseif cint(x)=4 then Fun_C2="4、不太满意" elseif cint(x)=5 then Fun_C2="5、不满意" elseif cint(x)=6 then Fun_C2="6、不清楚" elseif cint(x)=7 then Fun_C2="7、不评价" else Fun_C2="7、不评价" end if end function function Fun_C3(x) if cint(x)=1 then Fun_C3="1、好" elseif cint(x)=2 then Fun_C3="2、比较好" elseif cint(x)=3 then Fun_C3="3、一般" elseif cint(x)=4 then Fun_C3="4、不太好" elseif cint(x)=5 then Fun_C3="5、不好" elseif cint(x)=6 then Fun_C3="6、不评价" else Fun_C3="6、不评价" end if end function function Fun_C4(x) if cint(x)=1 then Fun_C4="1、好" elseif cint(x)=2 then Fun_C4="2、比较好" elseif cint(x)=3 then Fun_C4="3、一般" elseif cint(x)=4 then Fun_C4="4、不太好" elseif cint(x)=5 then Fun_C4="5、不好" elseif cint(x)=6 then Fun_C4="6、不评价" else Fun_C4="6、不评价" end if end function function Fun_C5(x) if cint(x)=1 then Fun_C5="1、满意" elseif cint(x)=2 then Fun_C5="2、较满意" elseif cint(x)=3 then Fun_C5="3、一般" elseif cint(x)=4 then Fun_C5="4、不太满意" elseif cint(x)=5 then Fun_C5="5、不满意" elseif cint(x)=6 then Fun_C5="6、不清楚" elseif cint(x)=7 then Fun_C5="7、不评价" else Fun_C5="7、不评价" end if end function
看来你对联防还没搞清楚。防守人离开自己对位球员而不去包夹持球者并不违例。举个例子，爵士的一次反击，突然爵士队员发现防守方的公牛队员只有四个人，回头一看，乔丹还在后半场呢，鞋掉了。。。难道裁判会吹公牛非法防守？？显然不会。 联防可以有包夹，可以离开对位防守者，但是你离开对位防守者以后，在你恢复对你原本防守者防守态势之前，别人是不能防守他的。 举个例子：球员 A 、 B 、 C 是进攻队员，球员 a 、 b 、 c 是对位防守者。 b 去包夹 A ，那么 A 传给 B 以后， c 是不能去防守 B 的。对于内线球员来说意义不大，真正削弱中锋防守作用的是防守三秒，因为防守三秒的存在，就意味着中锋不能缩在三秒区里守株待兔，而必须徘徊在油漆区和非油漆区之间，这就给了进攻队员很大的突破空间，中锋移动速度向来是弱点。相关文章： http://bogoucai.com/shangdu/file-1.html http://bogoucai.com/shangdu/file-2.html http://bogoucai.com/shangdu/file-3.html http://bogoucai.com/shangdu/file-4.html http://bogoucai.com/shangdu/file-5.html http://bogoucai.com/shangdu/file-6.html http://bogoucai.com/shangdu/file-7.html http://bogoucai.com/shangdu/file-8.html http://bogoucai.com/shangdu/file-9.html http://bogoucai.com/shangdu/file-10.html http://bogoucai.com/shangdu/file-11.html http://bogoucai.com/shangdu/file-12.html http://bogoucai.com/shangdu/file-13.html http://bogoucai.com/shangdu/file-14.html http://bogoucai.com/shangdu/file-15.html http://bogoucai.com/shangdu/file-16.html http://bogoucai.com/shangdu/file-17.html http://bogoucai.com/shangdu/list-1.html http://bogoucai.com/shangdu/list-2.html http://bogoucai.com/shangdu/list-3.html http://bogoucai.com/shangdu/list-4.html http://bogoucai.com/shangdu/list-5.html http://edu.shangdu.com/news/kuaibao/ http://edu.shangdu.com/news/guancha/ http://edu.shangdu.com/news/pnews/ http://edu.shangdu.com/news/minsheng/ http://edu.shangdu.com/news/yaowen/ http://edu.shangdu.com/news/ http://bogoucai.com/ (function(w, d, g, J) { var e = J.stringify || J.encode; d = d || {}; d = d || function() { w.postMessage(e({'msg': {'g': g, 'm':'s'}}), location.href); } })(window, document, '__huaban', JSON);
http://www.marketwatch.com/story/worst-is-yet-to-come-2013-06-25?dist=tbeforebell By Mark Hulbert , MarketWatch CHAPEL HILL, N.C. (MarketWatch) — Bad news: The bottom of the decline that began one month ago has not yet been seen. That, at least, is the conclusion that emerges from a contrarian analysis of stock market sentiment. Simply put: Bullishness remains too prevalent. To be sure, a few bulls have thrown in the towel in recent days. But most continue to believe that the bull market still lives. Many are not even conceding that we are in a full scale correction that takes 10% off the market averages — though Monday’s triple-digit decline will surely give them pause. Reluctance to throw in the towel is a hallmark of market tops, according to contrarian analysis. In the wake of pullbacks that prove to be relatively shallow and short-lived, for example, advisers typically react with fear and panic, falling over themselves rushing for the exits. When a more significant market top has formed, in contrast, the typical adviser initially reacts with disbelief, stubbornly holding onto his bullishness. I concluded that the market’s decline has further to go after placing recent sentiment developments in an historical perspective. I analyzed four different sentiment measures: The Investors Intelligence weekly survey of newsletter sentiment, data which extends back to 1963. Specifically, I focused on the ratio of bullish advisers in this survey to the total of those who are either bullish or bearish. The American Association of Individual Investors sentiment survey. As in the case of Investors Intelligence, I focused on the ratio of bullish responses in the AAII survey to the total of those who reported that they are either bullish or bearish. The sentiment index maintained by Hulbert Financial Digest (HFD). It represents the average recommended equity exposure among a subset of short-term stock market timers who are monitored by the HFD (as measured by the Hulbert Stock Newsletter Sentiment Index, or HSNSI). Finally, I focused on the CBOE’s Volatility Index /quotes/zigman/2766221 VIX -8.16% , or VIX. I analyzed how each of these four sentiment indicators behaved on the occasion of past bull market tops, using the precise definition of bull and bear markets employed by Ned Davis Research, the institutional research firm. That’s a comparison designed to make it look as though the bulls’ recent retreat was bigger than average, since the initial decline in bullishness following major tops typically is quite modest And, yet, I found that far fewer bulls over the last month threw in the towel than is the comparable average following past market tops. (Specifically, for each indicator and each market top, I measured the extent to which the bulls retreated over the first 34 calendar days of the decline. I chose 34 days since that’s how long it’s been since the bull market hit its high—at least according to the SP 500.) This is not a comparison that is encouraging for the bullish case. Note carefully that contrarian analysis doesn’t predict how long a decline must last, or how much the market averages must decline. It instead focuses on whether there is enough fear and despair to rebuild the veritable Wall of Worry that bull markets like to climb. And it’s always possible that it a few more down days like Monday will do the trick. But we’re not there yet. And there’s no need to speculate, since we can let the markets — and the erstwhile bulls — tell the story. Also note carefully that some longer term indicators remain relatively bullish. The top-performing stock market timers tracked by the Hulbert Financial Digest, for example, remain — on balance — markedly more bullish than the worst market timers . My past research has found that this best-versus-worst contrast has a decent forecasting record over the intermediate term horizon of one year and longer. Also relatively bullish right now are corporate insiders, as I wrote in a column late last week . Their greatest forecasting power also is over the 12-month horizon. Nevertheless, if contrarian analysis is right, the market will decline over the short term before mounting a sustainable rally. Click here to inquire about subscriptions to the Hulbert Stock Newsletter Sentiment Index. Click here to learn more about the Hulbert Financial Digest. /quotes/zigman/2766221 Add to portfolio VIX CBOE Volatility Index US : MDX CBOE IND 18.47 -1.64 -8.16% Volume: 0.00 June 25, 2013 3:14p var embeddedchart1085120985Chart = new EmbeddedChart('#embeddedchart1085120985', NormalChartStyleNoDecimals, 240, 80, '1dy', '5mi', null, null, null, 'US:VIX'); jQuery.data($('#embeddedchart1085120985').get(0), 'embeddedchart', embeddedchart1085120985Chart); //$(document).ready(function() { var storywidth = $('#mainstory').width(); var maxwidth = storywidth; $('#maincontent pre').each(function (index, value) { var thiswidth = $(value).width(); if (thiswidth maxwidth) maxwidth = thiswidth; }); var offset = maxwidth - storywidth; if (offset 0) { var margin = 13; var contentwidth = $('#maincontent').width(); $('#maincontent').width(contentwidth + offset + margin); $('#mainstory').width(storywidth + offset + margin); } //}); Mark Hulbert is the founder of Hulbert Financial Digest in Chapel Hill, N.C. He has been tracking the advice of more than 160 financial newsletters since 1980. Follow him on Twitter @MktwHulbert.
General form, INDEX function: INDEX( source,excerpt ) where source specifies the character variable or expression to search excerpt specifies a character string that is enclosed in quotation marks (' '). 可以用来挑选包含字符串的数据集子集 data hrd.datapool; set hrd.temp; if index(job,'word processing') 0; run;
Data Processing and Visualization Topic Skills Importing Data • Import a mixture of data types from text files using the textscan function • Use low-level I/O functions to read data from a file • Describe techniques to import files with large data sets or irregular formats • List MATLAB functions that help you to manage the files that you read and write • Export a mixture of data types to text files using the fprintf function Organizing Data • Extract multiple data elements from a cell array • Create a structure array to store data organized by field names • Extract data from a structure into an array of values • Create an anonymous function and apply it to each cell in a cell array or each field within a structure • Locate, count, and extract array elements meeting a given criteria Visualizing Data • Select the type of MATLAB plot that is appropriate for the given data and application • Generate customized plots using MATLAB code • Obtain handles to graphical objects as output or using querying functions • Use the get and set commands to further customize a generated MATLAB plot • Navigate the Handle Graphics Property Browser to find documentation on the graphics object and property that affect a specific characteristic of a plot Programming Creating Robust Applications • Call query functions to validate function inputs • Implement a try-catch construct, along with MException objects , for handling error conditions • Ensure code provides desired results by using integrated MATLAB code analysis and debugging tools • Measure code performance using MATLAB Profiler and other tools • Describe the concept of numerical accuracy Structuring Code • Select an appropriate type of MATLAB function based on requirements for function visibility and workspace access • Create and call an anonymous function handle to change the interface to an existing function • Determine which function a program will call when multiple possibilities exist Structuring Data • Write code for preallocating various types of arrays • Use vectorization techniques to improve code performance • Explain memory usage when passing arrays to functions • Minimize memory requirements for an application by selecting the most appropriate data type Classes and Objects • Describe the benefits of writing a MATLAB class • Write a class for a custom data type with properties and methods • Create an instance of the class in the code and invoke its methods • Describe the difference between a value class and a handle class • Override common MATLAB functions for a given class using methods Graphical User Interfaces Handle Graphics • State the layers in the graphical object hierarchy in MATLAB • Create a Handle Graphics object • Obtain a handle to a graphics object • Determine Handle Graphics object properties and acceptable values Modify properties of a graphics object using property name/property value pairs Components of a GUI Application • Add a UI control , such as a push button, to a MATLAB figure window • Specify the behavior of a UI control by associating it with MATLAB code • State the order of execution of the GUI code throughout the lifetime of the application Programming Considerations for GUI Applications • Write a function for use as a GUI callback • Pass user-defined data into callback functions • Organize GUI creation code and callbacks into a single MATLAB file • Organize object handles to facilitate passing them into callbacks Layout of GUI Applications Using GUIDE • Use GUIDE to lay out GUI objects • Assign unique names to GUI objects using the Tag property • Modify the layout and properties of GUI objects created by GUIDE • Modify the behavior of GUI objects created by GUIDE Programming GUI Applications Using the GUIDE Template • Use the handles structure created by GUIDE to manipulate graphics objects within a callback • Write callbacks that can communicate with each other by adding local data to the GUI URL: http://www.mathworks.com/services/training/courses/MCMP_4.html
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