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On the efficacy of procedures to normalize Ex-Gaussian distributions.

Marmolejo-Ramos F, Cousineau D, Benites L, Maehara R - Front Psychol (2015)

Bottom Line: Hence, it is acknowledged by many that the normality assumption is not met.This paper presents different procedures to normalize data sampled from an Ex-Gaussian distribution in such a way that they are suitable for parametric tests based on the normality assumption.Specifically, transformation with parameter lambda -1 leads to the best results.

View Article: PubMed Central - PubMed

Affiliation: Gösta Ekman Laboratory, Department of Psychology, Stockholm University Stockholm, Sweden.

ABSTRACT
Reaction time (RT) is one of the most common types of measure used in experimental psychology. Its distribution is not normal (Gaussian) but resembles a convolution of normal and exponential distributions (Ex-Gaussian). One of the major assumptions in parametric tests (such as ANOVAs) is that variables are normally distributed. Hence, it is acknowledged by many that the normality assumption is not met. This paper presents different procedures to normalize data sampled from an Ex-Gaussian distribution in such a way that they are suitable for parametric tests based on the normality assumption. Using simulation studies, various outlier elimination and transformation procedures were tested against the level of normality they provide. The results suggest that the transformation methods are better than elimination methods in normalizing positively skewed data and the more skewed the distribution then the transformation methods are more effective in normalizing such data. Specifically, transformation with parameter lambda -1 leads to the best results.

No MeSH data available.


Related in: MedlinePlus

Mean PoR (and ±1 SD) of a combined set of six normality tests for three EGds when n = 10, 15, 20, 30, and 50. The associated mean p-values for each case, and their ±1 SDs (in parenthesis), are shown in italics and between brackets. p-values below 0.05 are bolded.
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Figure 2: Mean PoR (and ±1 SD) of a combined set of six normality tests for three EGds when n = 10, 15, 20, 30, and 50. The associated mean p-values for each case, and their ±1 SDs (in parenthesis), are shown in italics and between brackets. p-values below 0.05 are bolded.

Mentions: An alternative method in which the combined results of various normality tests are used is proposed herein. There are approximately 40 different types of normality tests (see Razali and Wah, 2010) that can be categorized as regression/correlations, empirical distribution functions, measure of moments, or a combination of these (see Romão et al., 2010; Marmolejo-Ramos and González-Burgos, 2013). New normality tests are still being proposed (e.g., Akbilgiç and Howe, 2011; Harri and Coble, 2011; He and Xu, 2013), which may lead to new categorizations. Thus, it is seems rather inadvisable to rely solely on one test, especially when considering that tests also differ based on the different characteristics of the normal distribution on which they focus (Romão et al., 2010). Therefore, a comprehensive assessment of normality would require the combination of results given by normality tests from different categories. That is, an average of the p-values given by normality tests belonging to the categories mentioned above should give an educated approximation of the normality of a given distribution. Figure 2 shows the results of applying a normality-tests-combination method to the three EGds mentioned above when sample sizes are 10, 15, 20, 30, and 50 via the Marmolejo-Ramos and González-Burgos’ simulation method described above. The normality tests used were the SW, Shapiro–Francia (SF; these are regression/correlation-based tests), KS, Anderson–Darling (AD; these are empirical distribution function-based tests), Doornik–Hansen (DH), and the robust Jarque-Bera (rJB; these are measure of moments-based tests; details in relation to these tests can be found in Romão et al., 2010)1 .


On the efficacy of procedures to normalize Ex-Gaussian distributions.

Marmolejo-Ramos F, Cousineau D, Benites L, Maehara R - Front Psychol (2015)

Mean PoR (and ±1 SD) of a combined set of six normality tests for three EGds when n = 10, 15, 20, 30, and 50. The associated mean p-values for each case, and their ±1 SDs (in parenthesis), are shown in italics and between brackets. p-values below 0.05 are bolded.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4285694&req=5

Figure 2: Mean PoR (and ±1 SD) of a combined set of six normality tests for three EGds when n = 10, 15, 20, 30, and 50. The associated mean p-values for each case, and their ±1 SDs (in parenthesis), are shown in italics and between brackets. p-values below 0.05 are bolded.
Mentions: An alternative method in which the combined results of various normality tests are used is proposed herein. There are approximately 40 different types of normality tests (see Razali and Wah, 2010) that can be categorized as regression/correlations, empirical distribution functions, measure of moments, or a combination of these (see Romão et al., 2010; Marmolejo-Ramos and González-Burgos, 2013). New normality tests are still being proposed (e.g., Akbilgiç and Howe, 2011; Harri and Coble, 2011; He and Xu, 2013), which may lead to new categorizations. Thus, it is seems rather inadvisable to rely solely on one test, especially when considering that tests also differ based on the different characteristics of the normal distribution on which they focus (Romão et al., 2010). Therefore, a comprehensive assessment of normality would require the combination of results given by normality tests from different categories. That is, an average of the p-values given by normality tests belonging to the categories mentioned above should give an educated approximation of the normality of a given distribution. Figure 2 shows the results of applying a normality-tests-combination method to the three EGds mentioned above when sample sizes are 10, 15, 20, 30, and 50 via the Marmolejo-Ramos and González-Burgos’ simulation method described above. The normality tests used were the SW, Shapiro–Francia (SF; these are regression/correlation-based tests), KS, Anderson–Darling (AD; these are empirical distribution function-based tests), Doornik–Hansen (DH), and the robust Jarque-Bera (rJB; these are measure of moments-based tests; details in relation to these tests can be found in Romão et al., 2010)1 .

Bottom Line: Hence, it is acknowledged by many that the normality assumption is not met.This paper presents different procedures to normalize data sampled from an Ex-Gaussian distribution in such a way that they are suitable for parametric tests based on the normality assumption.Specifically, transformation with parameter lambda -1 leads to the best results.

View Article: PubMed Central - PubMed

Affiliation: Gösta Ekman Laboratory, Department of Psychology, Stockholm University Stockholm, Sweden.

ABSTRACT
Reaction time (RT) is one of the most common types of measure used in experimental psychology. Its distribution is not normal (Gaussian) but resembles a convolution of normal and exponential distributions (Ex-Gaussian). One of the major assumptions in parametric tests (such as ANOVAs) is that variables are normally distributed. Hence, it is acknowledged by many that the normality assumption is not met. This paper presents different procedures to normalize data sampled from an Ex-Gaussian distribution in such a way that they are suitable for parametric tests based on the normality assumption. Using simulation studies, various outlier elimination and transformation procedures were tested against the level of normality they provide. The results suggest that the transformation methods are better than elimination methods in normalizing positively skewed data and the more skewed the distribution then the transformation methods are more effective in normalizing such data. Specifically, transformation with parameter lambda -1 leads to the best results.

No MeSH data available.


Related in: MedlinePlus