This one is real important to ask, especially if the data were not peer-reviewed. If the data come from a survey, for example, you want to know that the people who responded to the survey were selected at random. How many times have you seen news reports based on call-in polls or website surveys? Those can be fun (see my notes on the ladder of engagement in Chapter 8 but they aren't news that other publications should be reporting. These types of surveys simply reflect the views of what statisticians call a "self-selected sample." people who feel really passionately about one side or the other can flood the poll, skewing the results from what they would have been had you polled only a random. When this happens in online surveys, it's called "Freeping" the poll, after the website m, whose readers have become notorious over the years for doing this sort of thing to polls on other websites. Another problem with data is "cherry-picking." This is the social-science equivalent of gerrymandering, where you draw up a legislative district so that all the people who are going to vote for your candidate are included in your district and everyone else is scattered among. Be on the lookout for cherry-picking, for example, in epidemiological ( a fancy word for the study of disease that sometimes means: "We didn't go out and collect any data ourselves.
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Which brings us to the next question: have the data been peer-reviewed? Major studies that appear in journals like the. New England journal of Medicine paper undergo a process called "peer review" before they are published. That means that professionals — doctors, statisticians, etc. — have looked at the study before it was published and concluded that the study's authors followed the rules of good scientific research and didn't torture their data like a middle ages infidel to make the numbers conform to their conclusions. Always ask if research was formally peer reviewed. If it was, you know that the data you'll be looking at are at least minimally reliable. And if it wasn't peer-reviewed, ask why. It might be that the research just wasn't interesting to enough people to warrant peer review. Or it could mean that the research had as much chance of standing up mapping to professional scrutiny as a 500 mobile home has of standing up in a tornado. How were the data collected?
You always want to know who did the research that created the data you're going to write about. You'd be surprised — sometimes it turns out that the person who is feeding you a bunch of numbers can't tell you where they came from. That should be your roles first hint that you need to be very skeptical about what you are being told. Even if your data have an identifiable source, you still want to know what. You might have some extra questions about a medical study on the effects of secondhand smoking if you were to learn that it came from researchers employed by a tobacco company instead of from, say, a team of research physicians from a major medical school. You might question a study about water safety that came from a political interest group that had been lobbying Congress for a ban on pesticides. Just because a report comes from a group with a vested interest in its results doesn't guarantee the report is a sham. But you should always be skeptical when looking at research generated by people with a political agenda. At the very least, they have plenty of incentive not to tell you about data they found that contradict their organization's position.
You wouldn't buy a car or a house without asking some questions about it first. So don't go buying into literature someone else's data without asking questions, either. But with data there are no tires to kick, no doors to slam, no basement walls to check for water damage. Just numbers, graphs and other scary statistical things that are causing you to have bad flashbacks to your last income tax return. What the heck can you ask parts about data? Here are a few standard questions you should ask any human beings who slap a pile of data in front of you and ask you write about. Where did the data come from? Always ask this one first.
Regression, prediction and shrinkage. Series b, 45, 311354. wilkinson,., dallal,. Tests of significance in forward selection regression with an F-to enter stopping rule. The impact of model selection on inference in linear regression. American Statistician 44: 214217. Prediction error and its estimation for subset—selected models.
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(1998) "An introduction to the bootstrap Chapman hall/crc boxBehnken designs from a handbook on engineering statistics at nist efroymson, ma (1960) "Multiple regression analysis." In Ralston,. And Wilf, hs, editors, mathematical Methods for Digital the Computers. foster, dean., george, edward. The risk Inflation Criterion for Multiple regression. Annals of Statistics, 22 (4). Doi :.1214/aos/ Donoho, david., johnstone, jain. Ideal spatial adaptation by wavelet shrinkage.
Biometrika, 81 (3 425455. Doi :.1093/biomet/81.3.425 mark, jonathan, goldberg, michael. Multiple regression analysis and mass assessment: A review of the issues. The Appraisal journal, jan., 89109. The development of numerical credit evaluation systems. Journal of the American Statistical Association, 58 (303; Sept 799806. Inflation of r in Best Subset Regression.
Especially the practice of fitting the final selected model as if no model selection had taken place and reporting of estimates and confidence intervals as if least-squares theory were valid for them, has been described as a scandal. 7 Widespread incorrect usage and the availability of alternatives such as ensemble learning, leaving all variables in the model, or using expert judgement to identify relevant variables have led to calls to totally avoid stepwise model selection. 5 see also edit references edit efroymson,. (1960) "Multiple regression analysis mathematical Methods for Digital Computers, ralston. (1976) "The Analysis and Selection of Variables in Linear Regression biometrics,. (1981) Applied Regression Analysis, 2d Edition, new York: John Wiley sons, Inc.
(1989) sas/stat user's guide, version 6, fourth Edition, volume 2, cary, nc: sas institute Inc. a b Flom,. (2007) "Stopping stepwise: Why stepwise and similar selection methods are bad, and what you should use nesug 2007. (2001) "Regression modeling strategies: With applications to linear models, logistic regression, and survival analysis Springer-Verlag, new York. a b Chatfield,. (1995) "Model uncertainty, data mining and statistical inference. A 158, part 3,.
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Several points of criticism have been made. The tests themselves are biased, since they are based on the same data. 15 16 Wilkinson and Dallal (1981) 17 computed percentage points of the multiple correlation coefficient by simulation and showed that a final regression obtained by forward selection, said by the f-procedure to be significant.1, was in fact only significant. When estimating the degrees of freedom, the number of the candidate independent variables from the best fit selected may be smaller than the total number of final model variables, causing the fit to appear better than it is when adjusting the r 2 value for. It is important to consider how many degrees of freedom have been used in the entire model, not just count the number of independent variables in the resulting fit. 18 Models that are created may be over-simplifications of the real models of the data. 19 Such criticisms, based upon limitations first of the relationship between a model and procedure and data set used to fit it, are usually addressed by verifying the model on an independent data set, as in the press procedure. Critics regard the procedure as a paradigmatic example of data dredging, intense computation often being an inadequate substitute for subject area expertise. Additionally, the results of stepwise regression are often used incorrectly without adjusting them for the occurrence of model selection.
If we look at the risk of different cutoffs, then using this bound will be within a 2log p factor of the best possible risk. Any other cutoff will end up having a larger such risk inflation. 11 12 Model accuracy edit main article: Cross-validation (statistics) A way to test for errors in models created by step-wise regression, is to not rely on the model's f -statistic, significance, or multiple r, but instead assess the model against a set of data that. 13 This is often done by building a model based on a sample of the dataset available (e.g., 70) the training set and use the remainder of the dataset (e.g., 30) as a validation set to assess the accuracy of the model. Accuracy is then often measured as the actual standard writing error (se mape, or mean error between the predicted value and the actual value in the hold-out sample. 14 This method is particularly valuable when data are collected in different settings (e.g., different times, social. Solitary situations) or when models are assumed to be generalizable. Criticism edit Stepwise regression procedures are used in data mining, but are controversial.
(locally) maximized, or when the available improvement falls below some critical value. One of the main issues with stepwise regression is that it searches a large space of possible models. Hence it is prone to overfitting the data. In other words, stepwise regression will often fit much better in sample than it does on new out-of-sample data. This problem can be mitigated if the criterion for adding (or deleting) a variable is stiff enough. The key line in the sand is at what can be thought of as the bonferroni point: namely how significant the best spurious variable should be based on chance alone. On a t -statistic scale, this occurs at about 2logpdisplaystyle sqrt 2log p, where p is the number of predictors. Unfortunately, this means that many variables which actually carry signal will not be included. This fence turns out to be the right trade-off between over-fitting and missing signal.
There are more efficient designs, requiring fewer runs, even for k 16. Contents main approaches edit The main approaches are: Forward selection, which involves starting with no variables in the model, testing the addition of each variable using a chosen roles model fit criterion, adding the variable (if any) whose inclusion gives the most statistically significant improvement. Backward elimination, which involves starting with all candidate variables, testing the deletion of each variable using a chosen model fit criterion, deleting the variable (if any) whose loss gives the most statistically insignificant deterioration of the model fit, and repeating this process until no further. Bidirectional elimination, a combination of the above, testing at each step for variables to be included or excluded. Selection criterion edit further information: Model selection A widely used algorithm was first proposed by Efroymson (1960). 10 This is an automatic procedure for statistical model selection in cases where there is a large number of potential explanatory variables, and no underlying theory on which to base the model selection. The procedure is used primarily in regression analysis, though the basic approach is applicable in many forms of model selection. This is a variation on forward selection.
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In statistics, stepwise regression is a method of fitting regression models in which business the choice of predictive variables is carried out by an automatic procedure. 1 2 3 4, in each step, a variable is considered for addition to or subtraction from the set of explanatory variables based on some prespecified criterion. Usually, this takes the form of a sequence. F -tests or t -tests, but other techniques are possible, such as adjusted, r 2, akaike information criterion, bayesian information criterion, mallows's, cp, press, or false discovery rate. The frequent practice of fitting the final selected model followed by reporting estimates and confidence intervals without adjusting them to take the model building process into account has led to calls to stop using stepwise model building altogether 5 6 or to at least make. 7 8, in this example from engineering, necessity and sufficiency are usually determined. For additional consideration, when planning an experiment, computer simulation, or scientific survey to collect data for this model, one must keep in mind the number of parameters, p, to estimate and adjust the sample size accordingly. For k variables, p 1(Start) K (Stage I) ( K 2 k 2(Stage II) 3 K (Stage III).5 K.5 K. For k efficient design of experiments exists for this type of model, a boxBehnken design, 9 augmented with positive and negative axial points of length min(2, (int(1.5 K /4)1/2 plus point(s) at the origin.