Statistics paired test

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. 

Paired r-tcst A statistical significance test for comparing two sets of data where there are no repeat measurements of a single test material but there are single measurements of a number of different test samples. To perform this test you use t = ( v(i, /h/yi) where x,, , v( are the mean and standard deviation of n differences. (Section 3.9)... 

In some cases we do not have the luxury of repeated measurements of a single test material, but do have one-off measurements of a number of different test materials performed by two methods. The two methods can be compared by considering the results of each pair of one-off measurements. This is possible as for a particular test material measured by each method the difference in the result should be zero if the two methods give equivalent results. For a number of analyses of different materials any pair of materials is the same and so the mean of the differences can be tested against zero. If the two methods give equivalent results within measurement uncertainty the difference between results on the same material by each method should be zero. In a paired /-test, therefore, the mean xd and standard deviation sd of the differences are calculated and a /-statistic determined from equation 3.5 with /x = 0 ... 

Parametric statistics (t-test, ANOVA) are by far the most commonly used in studies of sensory-motor/psychomotor performance due, in large part, to their availability and ability to draw out interactions between dependent variables. However, there is also a strong case for the use of non-parametric statistics. For example, the Wilcoxon matched-pairs statistic maybe preferable for both between-group and within-subject comparisons due to its greater robustness over its parametric paired f-test equivalent, with only minimal loss of power. This is important due to many sensory-motor measures having very non-Gaussian skewed distributions as well as considerably different variances between normal and patient groups. 

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. 

We kept track of breeding activity of experimental pairs by counting the litters and pups present throughout the year. All data were analyzed by Wilcoxon matched pairs test using CSS/PC Complete Statistical System - 2.1 (StatsSoft Inc., 1988). 

A final and useful application of the /-statistic is in the paired /-test. This is applicable when, e.g., several different materials containing different levels of analyte are studied using two different methods. Any differences between the results of the two methods might be masked by differences between the analyte levels in the samples if a conventional /-test were used. So it is necessary to determine for each material the difference between the results of the two methods, which would average zero if the null hypothesis, i.e., that the methods give indistinguishable results, is correct. The value of / is then obtained from... 

As the results were not distributed normally, median values were used for the descriptive statistics, while parameter-free test procedures were used for the analytical statistics (Wilcoxon test for paired differences by Wilcoxon/Mann and Whitney) (ClauC and Ebner 1992). 

We found that the Statistical MCDC test method was the most effective for achieving high I-O pair and output coverage, while uniform random input testing was the least effective. The Statistical MCDC method also appears to be a fair test profile as there is fairly balanced coverage of output values. 

After irradiation was performed, non- irradiated and irradiated samples of the blood parameter, Hematocrit, and the beam parameter,Flux peak, were compared. The paired test was used to determine the differences between the controlled samples and irradiated samples. A two- factor analysis were further conducted to examine the differences in the samples according to the age, gender of patients. The SPSS software version 12 was utilized to perform statistical calculations and analyses of the data. 

The statistical paired t-test was used in order to make a comparison in gait parameters between left and right forelimbs, and the left and right hind limbs. The Mann-Whistney... 

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

The results of such multiple paired comparison tests are usually analyzed with Friedman s rank sum test [4] or with more sophisticated methods, e.g. the one using the Bradley-Terry model [5]. A good introduction to the theory and applications of paired comparison tests is David [6]. Since Friedman s rank sum test is based on less restrictive, ordering assumptions it is a robust alternative to two-way analysis of variance which rests upon the normality assumption. For each panellist (and presentation) the three products are scored, i.e. a product gets a score 1,2 or 3, when it is preferred twice, once or not at all, respectively. The rank scores are summed for each product i. One then tests the hypothesis that this result could be obtained under the null hypothesis that there is no difference between the three products and that the ranks were assigned randomly. Friedman s test statistic for this reads... 

The data were statistically analyzed using the SOLO Statistical System (BMDP Statistical Software, Inc., Los Angeles, CA) on a personal computer. Differences between groups were tested by the Mann-Whitney test or a paired t-test in cases where paired data sets were tested. Possible relationships were studied with (multiple) linear regression using least-square estimates. 

Paired-data performance, involving comparison of predicted and observed values for exact locations in time and space. This may be a more rigorous test than needed for many purposes timing differences can have severe impacts on the statistical comparison. 

Statistical measures for the paired-data, and integrated paired-data performance tests noted above are essentially identical. 

Frequency domain performance has been analyzed with goodness-of-fit tests such as the Chi-square, Kolmogorov-Smirnov, and Wilcoxon Rank Sum tests. The studies by Young and Alward (14) and Hartigan et. al. (J 3) demonstrate the use of these tests for pesticide runoff and large-scale river basin modeling efforts, respectively, in conjunction with the paired-data tests. James and Burges ( 1 6 ) discuss the use of the above statistics and some additional tests in both the calibration and verification phases of model validation. They also discuss methods of data analysis for detection of errors this last topic needs additional research in order to consider uncertainties in the data which provide both the model input and the output to which model predictions are compared. 

The following description and corresponding MathCad Worksheet allows the user to test if two correlation coefficients are significantly different based on the number of sample pairs (N) used to compute each correlation. For the Worksheet, the user enters the confidence level for the test (e.g., 0.95), two comparative correlation coefficients, r, and r2, and the respective number of paired (X, Y) samples as N and N2. The desired confidence level is entered and the corresponding z statistic and hypothesis test is performed. A Test result of 0 indicates a significant difference between the correlation coefficients a Test result of 1 indicates no significant difference in the correlation coefficients at the selected confidence level. 

The wheat bran used in these studies was milled for us from a single lot of Waldron hard red spring wheat. Other foods and diet ingredients were purchased from local food suppliers. Data from HS-I was analyzed statistically by Student s paired t test, each subject acting as his own control. A three-way analysis of variance (ANOVA) was performed to test for significant differences betwen diet treatments, periods and individuals in HS-II and HS-III. 

---