Transposing data

Data transposition is the process of changing the orientation of the data from a normalized structure to a non-normalized structure or vice versa. There are many definitions of normalization of data, and you should learn about normal forms and normalization. Here, in brief, normalization of data means the process of taking information out of the variable definitions and turning that information into row definitions/keys in order to reduce the overall number of variables. Normalized data may also be described as stacked, vertical, or tall and skinny, while non-normalized data are often called flat, wide, or short and fat.  

Graphically, the process of data transposition from normalized to non-normalized data looks like this  

Typically, clinical data come to you in a shape that is dictated by the underlying CRF design and the clinical data management system. Most clinical data management systems use a relational data structure that is normalized and optimized for data management. Much of the time these normalized data are in a structure that is perfectly acceptable for analysis in SAS. However, sometimes the data need to be denormalized for proper analysis in SAS. 

A problem occurs when end users of the data cannot conceptualize how to handle normalized data. These users go out of their way to denormalize any normalized data that they see. I have seen entire databases denormalized so that a user could work with the data, and in some cases the user unknowingly renormalizes the data so that he or she can then analyze it properly. This type of user needs to be coached as to when denormalization is needed. 

Denormalization of data is needed when a statistical procedure requires that the information to be analyzed must be on the same observation. Procedures in SAS that perform data modeling are often the ones that require denormalized data, as they require that the dependent variable be present on the same observation as the independent variables. For example, imagine that you are trying to determine a mathematical model that predicts under what conditions a therapy is successful. That model might look like this  

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To determine the deterioration in component performance and efficiency, the values must be corrected to a reference plane. These corrected measurements will be referenced to different reference planes depending upon the point, which is being investigated. Corrected values can further be adjusted to a transposed design value to properly evaluate the deterioration of any given component. Transposed data points are very dependent on the characteristics of the components performance curves. To determine the characteristics of these curves, raw data points must be corrected and then plotted against representative nondimensional parameters. It is for this reason that we must evaluate the turbine train while its characteristics have not been altered due to component deterioration. If component data were available from the manufacturer, the task would be greatly reduced. 

The first Fourier transformation of the FID yields a complex function of frequency with real (cosine) and imaginary (sine) coefficients. Each FID therefore has a real half and an imaginary half, and when subjected to the first Fourier transformation the resulting spectrum will also have real and imaginary data points. When these real and imaginary data points are arranged behind one another, vertical columns result. This transposed data... 

Key Concepts for Creating Analysis Data Sets 84 Defining Variables Once 84 Defining Study Populations 85 Defining Baseline Observations 85 Last Observation Carried Forward (LOCF) 86 Defining Study Day 89 Windowing Data 91 Transposing Data 94... 

Program 4.5 Transposing Data with PROC TRANSPOSE... 

TRANSPOSE THE NORMALIZED SBP VALUES TO A FLAT STRUCTURE. proc transpose data = sbp out = sbpflat prefix = VISIT by subject id visit var sbp ... 

There may be times when a DATA step with arrays is a better means to transpose data. This is true when the data to be transposed have more than one record per BY group variable or when there is a need to have the resulting data set include data that are not in the source data set. In clinical trials missing data is a very common issue. Let s look at a derivation of the previous systolic blood pressure transposition problem where visit 2 is always missing. 

Program 4.7 Transposing Data with the DATA Step... 

TRANSPOSE AGE DESCRIPTIVE STATISTICS INTO COLUMNS. proc transpose data = age out = age prefix = col ... 

TRANSPOSE THE GENDER SUMMARY STATISTICS. proc transpose data = gender... 

TRANSPOSE THE RACE SUMMARY STATISTICS proc transpose data = race... 

It becomes apparent that to transpose data from different humidities, temperatures, thicknesses and varying stages of approach to equilibrium can be very involved and therefore subject to local, empirical rules. Further, whilst the transport relationships apply to the uptake of fluid, the effect of a fluid on properties at times below equilibrium can never be simple because the concentration varies with thickness. 

For both PCR and PLS it is, of course, possible to transpose data, and this can be useful if there are a large number of wavelengths, but both the jc block and the c block must be transposed. These facilities are not restricted to predicting concentrations in spectra of mixtures and can be used for any purpose, such as QSAR or sensory statistics. 

Methods of - cluster analysis are applied to the variables, on the so-called Q-mode data matrix, i.e. on the transposed data matrix. Once cluster analysis has been performed, one variable for each cluster is retained as representative of all the variables within that cluster. Which and how many are the retained/excluded variables depends on the chosen cluster analysis method. 

Representative values for the coefficients will be given in the following sections, with emphasis on standard values. Then, succeeding sections will review the effects of varying physical features, such as bends, flow unsteadiness, etc. There will be obviously some overlaps, as reported data does not always clarify which physical features are present. This, in fact, is one of the dangers in transposing data from one site to another. 

This process creates L blocks of new free induction decays. These free induction decays contain the time-domain information from the evolution period. Figure 6 shows the transposed data blocks corresponding to the finequency-domain data in Fig. 5. 

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