Types of Statistical Analysis

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Statistical analysis of the measurements is an increasingly complex procedure. Involvement with statisticians at an early stage in study design and analysis is advisable. Failure to be aware of statistical pitfalls can lead to embarrassing rejections by journal referees; sometimes re-analysis can address the problems, but sometimes data collection is fatally flawed. In this section the basic concepts relevant to statistical analysis of MR data are summarized; however for full treatment the reader should go to the books listed in Table 2.2. A short treatment of some relevant concepts is also given by Haacke et al. (1999) and Hendee and Ritenour (2oo2) contains a chapter on probability and statistics (see Table 1.1). Suitable software packages, favoured by professional statisticians, are SAS and STATA. These give a transparent description of the formulae used, good documentation, are programmable, have a range of techniques that is evolving with the research community, and are considered reliable. SPSS is also widely available, although less favoured by the professionals. All these packages have comprehensive websites and manuals associated with them ... associated with

3o From the Functional Imaging Laboratory, University College London: www.fil.ion.ucl.ac.uk

Figure 2.16 (Plate 1). Examples of voxel-based group mapping. (a) Child development shown by white matter correlations with age. (b) Aging shown by grey matter correlations with age (the bar shows the T score). (c) Gender difference in perfusion measured by arterial spin labelling. (a) Reprinted with permission from Paus, T., et al., in Science 283 (5409), 1908-1911, Copyright 1999 American Association for the Advancement & Science. (b) Reprinted from Good, C. D., et al. 2001, in Neuroimage. 14, 21-36, Copyright 2001 with permission from Elsevier Science Ltd. (c) Reprinted with permission from Parkes, L. M., Rashid, W., Chard, D. and Tofts, P. S. 2003. (submitted)

Figure 2.16 (Plate 1). Examples of voxel-based group mapping. (a) Child development shown by white matter correlations with age. (b) Aging shown by grey matter correlations with age (the bar shows the T score). (c) Gender difference in perfusion measured by arterial spin labelling. (a) Reprinted with permission from Paus, T., et al., in Science 283 (5409), 1908-1911, Copyright 1999 American Association for the Advancement & Science. (b) Reprinted from Good, C. D., et al. 2001, in Neuroimage. 14, 21-36, Copyright 2001 with permission from Elsevier Science Ltd. (c) Reprinted with permission from Parkes, L. M., Rashid, W., Chard, D. and Tofts, P. S. 2003. (submitted)

them, and the software is often available through academic sources. The concepts discussed here come from three principle traditions - pure statistics, the physical sciences and psychology, - and this can be seen in the origins of the books in the Table 2.2.

2.2.2.1 Group Comparisons: t-Tests and their Nonparametric Equivalents

An investigation of new MR parameters in a disease may result in many data. To test their usefulness, it is tempting to carry out multiple t-tests, for example to see if any of the parameters differ between clinical groups. Correlation with clinical scores may also be carried out (see below). If 20 tests are carried out at the p = 0.05 significance level, and in truth there were no associations, then on average one test will come out positive by chance (this is known as a type I error). Thus the results of multiple comparisons must be treated with caution. The Bonferroni correction for multiple comparisons (Bland and Altman, 1995) allows for this by suggesting that the appropriate p-value

Table 2.2. Statistics books, from backgrounds of medical statistics, physical sciences and psychology

Title

Authors

Date published

Number of pages

Description

Statistical Methods in

Peter

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