Chi-squared analysis

The training of most pathologists in statistics remains limited to a single introductory course which concentrates on some theoretical basics. As a result, the armertarium of statistical techniques of most toxicologists is limited and the tools that are usually present (t-tests, chi-square, analysis of variance, and linear regression) are neither fully developed nor well understood. It is hoped that this chapter will help change this situation. 

In Tables 10 and 11, meta-analyses based on 576 cases gleaned by Goodman from a number of reports, there are only moderate variations in mortality among cases grouped by route of administration or by age. Using chi-square analysis, Goodman found no statistically significant age-related differences in susceptibility to the lethal effects of atropine. 

Table 16.2 Generic output from a contingency chi-square analysis of rates of expulsion of two designs of IUD...

The issue of goodness-of-fif with nonlinear regression is not straightforward. Numerous methods can be used to explore the goodness-of-fif of the model to the data (e.g., residual analysis, variance analysis, and Chi-squared analysis). It is always a good idea to inspect the plot of the predicted [y(x,)] versus observed y, values to watch for systematic deviations. Additionally, some analytical measure for goodness-of-fit should also be employed. 

In a third method of evaluating the data, a chi-square analysis was used to asses near-IR spectral variability. For... 

The check box attributes were analyzed using a Chi-square analysis (Figure 5), but none of the attributes were significantly different by tea type (at ofO.OS). 

Table 1 Summary of results from chi-square analysis of student responses to selected questions from module rating survey distributed in semester 2, 2007...

In QSAR and QSPR studies, the standard ways of removing redundancy from large numbers of topological and topographical indices include principal component analysis, chi-squared analysis, and multiple regression analysis (MRA). Most QSAR and QSPR applications deal with very small datasets, and so the dimensionality does not cause a problem for PCA or chi-squared analysis. MRA does not impose any restrictions on the type and number of descriptors. The selection process is based on two principles, namely, to cover as much of parametric space as possible (principle of variance) while choosing independent descriptors (principle of orthogonality). 

Data from ref. 34 Data from ref. 35 Data from tef.36 Probability values (p) of the occuirence of abnormal litters or fetuses by comparison of treatment with alkaloid vs. earner controls obtained by chi-square analysis using two-tailed Fisher exact results One-tailed p-values, students t vs. controls. 

In a third method of evaluating the data, a chi-square analysis was used to assess NIR spectral variability. For each time point, the pooled variance of the NIR absorbance values at individual wavelengths is calculated as the weighted average of the variances. A chi-square statistic is then calculated and compared to a tabulated value for significance at the 5% level, with significant values indicating that the variances are not equal. 

Nine chemicals were considered to have increased the tumor incidence relative to controls, but the level of significance was stated only as being less than 0.02 (i.e., P>0.02) (C3). Apparently, the same pesticide, a-(2,4-dichlo-rophenoxy)propionic acid [also called 2-(2,4-DP)], was tested twice and evaluated twice by the Technical Panel. Hence, the actual number of carcinogens listed as C3 by the Technical Panel is eight. The significance of seven of these eight chemicals has been recalculated by chi-square analysis using... 

Table 1 Chi square analysis of the perceived relative speed of a following vehicle...

A Pearson chi square analysis [42] was performed to evaluate the answers. The postulated null hypothesis was The perceived approaching speed is not influenced by adding additional motion cues . The answers were classified in three categories. The perceived relative speed of the following vehicle was underestimated, correctly estimated, or overestimated. The statistic test for significance (see Table 1) is performed by comparing the sum over all residues = with the value for a... 

You should be able to use Chi Square analysis to determine differences between your class data and data sets from other human populations. 

As an example, let s say that Chi-square analysis of your data gives a p-value of 0.17. This means that there is a 17% probability that the difference between the observed and the expected values is due to chance. It also means that there is an 83% (100% -17% = 83%) probability that the difference is not due to chance the difference is real. 

In this part of the exercise, you will use chi-square analysis to determine whether or not there is any differecKe in the genotype distribution between your class and another population group. If the p-value that is calculated tor this (xxnparison is less than 0.05, then the different between your class and the other population group is probably real. If the p-value is greater than 0.05, then there is probably no difference between your class and the other population group. 

For assays in which putative repellent treatments were presented in the T-maze olfactometer with or without citrus and versus clean air, the number of Diaphorina citri remaining at the release point and not entering the olfactometer was compared between treatments using one-way analysis of variance, followed by Tukey s honest significant difference test (p <. 05). For psyllids leaving the release arm, the number of psyllids choosing the control arm versus the treatment arm was compared with chi-square (/ ) analysis at p <. 05. The data from all four replicates were combined for the analysis. 

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