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Paul Shashkov
Paul Shashkov

Normality Download] [portable]

Hello William,I am doing well. I hope that you are doing well too.1. What sort of error are you getting? The usual problem relates to trust. You can address this issue as described in the Troubleshooting section of key is that Solver needs to load before the Real Statistics add-in. Many months ago, I changed the name of the Real Statistics add-in to XRealstats.xlam to ensure that this would happen.Charles

Normality Download] [portable]

Hello,some 35 years ago I started working with Statistica. It was a fine program. Since I was retired 12 years ago I have been trying to make my own programs for time series analysis, mainly in VBA for Excel but the development of the statistical know how is going much faster then my abillity to make my (working!) programs so I am happy to find the Real Statistic Resource Software Pack and I am going to download it. At least my recent hobby helps me to understand what it is all about. I should have got this knowledge 45 years ago!Matija

Hello Teresa,See the following webpage a description of all the data analysis tools, see

Hello, thank you very much for sharing this resource. I downloaded it without problems, but unfortunately the KAPPA DE FLEISS does not appear as a formula. Why will it be?Greetings from ChileChristina

To cope with the real-world variability of testing conditions, specific testing and data evaluation procedures must be implemented. Testing may occur under a wide range of altitude, temperature, and driving conditions. However, requirements concerning (i) trip composition (e.g., roughly equal shares of urban, rural, and motorway driving) and (ii) driving dynamics (e.g., the permissible range of accelerations) aim to ensure that vehicles are tested in a fair, representative, and reliable manner. Still, due to a number of factors (e.g., traffic, driver, and wind), any on-road test remains, to some extent, random and non-reproducible. Thus, the main challenge was the development of a data evaluation method that assesses ex post the normality of test conditions to enable a reliable assessment of vehicle emissions. To this end, two methods were adopted within the RDE: the moving averaging windows (MAW) and the power binning method. The MAW method divides the test into sub-sections (windows) and uses the distance-specific average carbon dioxide (CO2) emissions of each window to assess the normality of operating conditions. The power binning method categorizes the instantaneous on-road emissions into power bins based on the corresponding power at the wheels. The normality of the resulting power distribution is established through a comparison with a standardized wheel-power frequency distribution. Both methods include criteria to ensure that a realized test covers the range of driving dynamicity permitted by the RDE test procedure9-10. The two methods typically give results within 10%; however, differences on the order of 50% have been reported11,12. An in-depth assessment of the two data evaluation methods is still missing. The European Commission acknowledges this shortcoming in Recital 14 of the RDE Regulation13,14 and foresees a review of these two methods in the near future with the objective of retaining them or developing a unified method for the evaluation of gaseous pollutants and particle number emissions.

The normality of driving was conducted with the MAW evaluation method, excluding cold start and idling and weighing the NOx emissions with CO2 emission deviations greater than 25% of the type approval cycle according to the MAW method (see Appendix 5)8. The free EMROAD software was used.

A source of uncertainty originates from the determination of road loads for the measurement of CO2 emissions with the WLTC; these measurements are used to evaluate the normality of driving conditions with the RDE data evaluation. Ideally, the chosen road loads resemble those of the unloaded vehicle tested with the PEMS on the road. The flexibilities granted in by the WLTP (e.g., to determine the road load based on conservative generic parameters or the vehicle with the highest test mass within a family) may cause substantial deviations in the CO2 emissions determined by the WLTC and measured later on the road. In consequence, the methods may yield a biased evaluation of the actual driving severity. The WLTP provisions for setting the road load may potentially need to be specified for RDE purposes.

Linear models, including ANOVA and linear regression models, are applicable for statistical analysis of data from a wide range of experimental studies (Littell et al., 2002). However, appropriate use of linear models for statistical inference involves certain assumptions about the data, including normality, constant variance, and independence of the errors (residuals) (Neter et al., 1996). When these assumptions are reasonably satisfied, inferences can be drawn with respect to populations based on the sample data using common statistical techniques including t tests, F tests, tests on regression parameters, and calculation of confidence intervals and prediction intervals (D'Agostino and Stephens, 1986; Neter et al., 1996). Although some departure from normality does not tend to create a serious problem, the possibility of a serious departure from the assumption of normality should be examined to avoid making invalid inferences from the data (Neter et al., 1996).

Researchers sometimes proceed directly to the use of linear models, ANOVA, or linear regression procedures with statistical analysis software without making an assessment or having prior knowledge of whether the assumption of normality, or at least near-normality, is valid. Such knowledge is not only of value to the researcher in selecting appropriate statistical methods and models, but may also be of value to other researchers working in the same subject area (Shojo and Iwaisaki, 1999; Tang et al., 1999). In the case of linear regression analysis, researchers may limit their analysis to calculating least-squares estimates of linear regression equations, which do not require an assumption about the distribution of the error terms; however, such an assumption is needed to calculate confidence intervals for the regression parameters or to develop confidence bands for the regression lines (Neter et al., 1996).

When a significant departure from normality is identified, the linear model may need to be modified or, in other cases, remedial measures, such as transformation of the response variable (generally investigated when both the normality and constant variance assumptions are violated), may be used to satisfy assumptions (Neter et al., 1996). Generalized linear models may be used in cases when the response variable can be assumed to follow certain other statistical distributions, such as the binomial, negative binomial, Poisson, or exponential distribution (Littell et al., 2002). When assumptions cannot be made about the underlying distribution of the data, nonparametric methods can be used (Hollander and Wolfe, 1999).

A wide variety of goodness-of-fit tests are available to assess the normality of sample data from a single population or, in the cases of linear regression analysis and analysis of variance, from a set of residuals (D'Agostino, 1986b). Because the mean and variance of the population from which the sample is drawn are usually unknown, they are typically estimated by the sample mean and sample variance. Goodness-of-fit tests examine the probability of the null hypothesis (H0: the sample values or residuals are drawn from a normal population) being true given the sample data. If the probability is determined to be small, the null hypothesis is rejected and the alternative hypothesis (H1: H0 is not true) is accepted. Despite the many tests that have been developed for assessing normality or departures from normality, there is no single test that is optimal for all possible deviations from normality.

Graphical techniques, which represent some of the simplest goodness-of-fit tests, can help to identify major departures from the assumed statistical distribution, as well as to reveal interesting features of the data (D'Agostino, 1986a). However, graphical techniques should not be used alone to assess normality, because they may lead to spurious conclusions. Rather, these tools should be used in conjunction with formal hypothesis tests.

Formal hypothesis tests for normality can generally be classified into five groups: chi-square tests, empirical distribution function tests, moment tests, regression tests, and other miscellaneous tests (D'Agostino, 1986b).

There are certain difficulties involved in assessing normality using sample data (Neter et al., 1996). First, random variation in a sample can make determination of a probability distribution difficult unless the sample size is large. Second, in the case of regression analysis, the errors (residuals) may not appear to be normally distributed if an inappropriate regression function is used or if the variance of the errors is not constant.

The objectives of the present study were 1) to test the normality of extract pH and EC data obtained using the pour-through method from a container substrate (without plants) using large samples, 2) to test the normality of selected transformations of the pH and EC variables for comparative purposes, 3) to illustrate the use of some graphical and statistical tools for assessing normality, and 4) to examine possible correlations among substrate temperature and extract pH and EC over the 12-week study period. Large samples were collected from containers of a single, uniformly blended and irrigated substrate without plants to preclude the difficulties noted earlier, with repeat samples collected over time to allow a more thorough assessment.


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