Statistical test paired

Statistical test for comparing paired data to determine if their difference is too large to be explained by indeterminate error. 

Dependencies may be detected using statistical tests and graphical analysis. Scatter plots may be particularly helpful. Some software for statistical graphics will plot scatter plots for all pairs of variables in a data set in the form of a scatter-plot matrix. For tests of independence, nonparametric tests such as Kendall s x are available, as well as tests based on the normal distribution. However, with limited data, there will be low power for tests of independence, so an assumption of independence should be scientifically plausible. 

The organizing laboratory performs statistical tests on the results from participating laboratories, and how outliers are treated depends on the nature of the trial. Grubbs s tests for single and paired outliers are recommended (see chapter 2). In interlaboratory studies outliers are usually identified at the 1% level (rejecting H0 at a = 0.01), and values between 0.01 < a < 0.05 are flagged as stragglers. As with the use of any statistics, all data from interlaboratory studies should be scrutinized before an outlier is declared. 

We know from Chapter 6 that data variability is a spoiler for t-tests and the large SDs for the weights in the first two columns of Table 12.1 are a prime contributor to the non-significant outcome of the two-sample /-test. It would be attractive to be able to base a statistical test solely on the column ofweight changes, as these are considerably less variable. This is exactly what the paired /-test does. 

Mean values for aggregation in dosage groups are compared to the vehicle control groups (for rabbits control values before drug administration). Statistical significance is evaluated by means of the Student s t-test (paired for rabbits unpaired for others). 

Tabulate the number of cells in the Scenedesmus colonies for the initial sample, the control (no Daphnia culture water) algal culture, and your experimental culture(s). All of the data from one lab section can also be combined to give replicates. Calculate the mean and standard deviation of colony size for the initial, control, and all treatments. Plot histograms of the size distribution of colonies (1-16 cells) of the different treatments and do simple statistical tests to compare the mean sizes (e.g., paired t tests) or the distributions. 

FCC catalysts obtained from different refineries were analysed by ICP and XRF techniques for the elements Al, Ni, V, Ti Fe and the results were compared statistically by Paired t-test. Regression analysis and F-test. It was observed that both the techniques are equivalent and there is no significant difference between the results for the analysis of Al, Ni, V, Ti Fe in FCC catalysts. However, statistical analysis indicates that XRF is more precise compared to ICP. Therefore, XRF technique can be used routinely for the analysis of Al, Ni, V, Ti and Fe in FCC catalysts in place of ICP with advantage. 

Nonparametrical statistical test (Wilcoxon matched pairs test) were applied for two-choice experiments because data were characterized by a high level of variability. The sexual activation experiment was analyzed by Student s test. 

For experiments 1—3, in which individual males were simultaneously presented with two models in a choice test, paired, within-subjects chi-square tests were used to compare the frequency of males that clasped female-scented vs. unscented models (Exp. s 1,2) or female-scented vs. male-scented models (Exp. 3 see Snedecor Cochran, 1989). Wil-coxon signed-ranks tests were used to compare the number of clasps per male of scented vs. unscented models. In experiments 4 and 5, chi-square tests were used to compare the frequency of males that clasped models in the different treatment groups. Mann-Whitney U-tests were used to compare the number of clasps per male in the different groups. An alpha level of p <. 05, one-tailed was required for statistical significance. 

In the previous example, the measurements came from independent samples. If we have pairs of tissue types with each pair coming from the same animal, we cannot consider the samples from the two tissue types independent and we have to use statistical tests that account for the correlations within each pair, such as the paired t-test or the nonparametric Wilcoxon signed-rank test. A typical situation in which these tests are recommended is for testing the change in bioimpedance before versus after a treatment. 

A statistical test provides a mechanism for making quantitative decisions about a set of data. Any statistical test for the evaluation of quantitative data involves a mathematical model for the theoretical distribution of the experimental measurements (reflecting the precision of the measurements), a pair of competing hypotheses and a user-selected criterion (e.g., the confidence level) for making a decision concerning the validity of any specific hypothesis. All hypothesis tests address uneertainty in the results by attempting to refute a specific claim made about the results based on the data set itself. 

We have already seen (Sections 3.4 and 6.3) that when paired results are compared, special statistical tests can be used. These tests use the principle that, when two experimental methods that do not differ significantly are applied to the same chemical samples, the differences between the matched pairs of results should be close to zero. This principle can be extended to three or more matched sets of results by using a non-parametric test devised in 1937 by Friedman. In analytical chemistry, the main application of Friedman s test is in the comparison of three (or more) experimental methods applied to the same chemical samples. The test again uses the statistic, in this case to assess the differences that occur between the total rank values for the different methods. The following example illustrates the simplicity of the approach. 

If a pair of counts are rejected by this criterion then, recount the rest of the filters in the submitted set. Apply the test and reject any other pairs failing the test. Rejection shall include a memo to the industrial hygienist stating that the sample failed a statistical test for homogeneity and the true air concentration may be significantly different than the reported value. 

The slope and the intercept of a regression line are not independent but related variables. This causes them not to possess independent confidence intervals. Instead, they originate a confidence region, with the form of an ellipse, that encompasses simultaneously [significance level of (1 - a)100%] the values the slope and the intercept of the regression line can take. Therefore a simple statistical test to compare the 24 regression lines is to verify whether their (intercept, slope) data pairs are situated within the confidence ellipse of the unmodified regression line. If they are, the null hypothesis cannot be rejected [the data pairs... 

The amplitude and peak latency of the a- and b-waves and the OPs were expressed as the percentage of the control ERG values during the initial perfusion of the control solution. Statistical analysis of the ERG changes was done with the Student s t -test (paired), with p<0.05 indicating a significant difference. 

The 61 cases and 71 controls who comprised the follow-up samples, included 57 of the original matched pairs, 4 cases whose matched control could not be retested and 14 controls whose matched case could not be retested. Rather than reduce the sample size further by excluding unmatched cases or controls who had already been retested, it was decided to analyse the follow-up data using statistical tests for unmatched pairs. 

The difference in the correct rates between the two tasks was examined by applying statistical analyses (paired t-test) on the data of the ten participants for each moving velocity. The results revealed that the correct rates for the direction discrimination task were significantly higher than those for the pattern discrimination task at the velocity of 14.4 deg/s (t(18) = 2.21, p < 0.05), 28.8 deg/s (t(18) = 3.62, p < 0.01) and 43.2 deg/s (t(18) = 3.66, p < 0.01). These results suggested that the direction discrimination task was much easier than the pattern discrimination task. 

Most researchers who have worked with discrete event simulation are familiar with classical statistical analysis. By classical, we mean those tests that deal with assessing differences in means or that perform correlation analysis. Included in these tests are statistic procedmes such as t-tests (paired and unpaired), analysis of variance (univariate and multivariate), factor analysis, linear regression (in its various forms ordinary least squares, LOGIT, PROBIT, and robust regression) and non-parametric tests. 

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