Least Significant Difference test

Individual comparisons using Fisher s least significant difference test are based on the following null hypothesis and one-tailed alternative hypothesis... 

Figure 9. Concentrations of nitrogen, sulfur and phosphorus in white oak litter during 19-month litterbag study along a tri-state atmospheric deposition gradient from Illinois to Ohio. Values are mean s diXSE (n=20 for 6 and 13 months n=4 for 19 months). Different lowercase letters indicate a significance difference between study sites (p <0.05 Fisher s least significant difference test) (Kuperman, 1999).

Means and standard deviations (SD) were calculated with SPSS (Version 11.5.1, SPSS Inc., Chicago, IL, USA) statistical software. SPSS was used to verify significant differences between treatments by one-way analysis of variance (ANOVA) followed by least significant difference test (LSD) at p < 0.05 to identify differences among groups. 

Analysis of variance (ANOVA) was carried out on the quantitative data for each compound identified in the GCMS analyses. For those compounds exhibiting significant difference in the ANOVA, Fisher s least significant difference test was applied to determine which sample means differed significantly p < 0.05). 

Once a significant difference has been demonstrated by an analysis of variance, a modified version of the f-test, known as Fisher s least significant difference, can be used to determine which analyst or analysts are responsible for the difference. The test statistic for comparing the mean values Xj and X2 is the f-test described in Chapter 4, except that Spool is replaced by the square root of the within-sample variance obtained from an analysis of variance. 

Fisher s least significant difference a modified form of the f-test for comparing several sets of data. (p. 696) flame ionization detector a nearly universal GC detector in which the solutes are combusted in an H2/air flame, producing a measurable current, (p. 570)... 

Statistical Analysis. Statistical analyses (two-way ANOVA) were performed by using the Statistical Analysis System (SAS, 1990). Means were compared by the least significant difference (LSD) test at a = 0.05. 

Significantly different (p < 0.05) by one-way analysis of variance (ANOVA) with the Least Significant Difference post hoc test using JMP program from SAS, Cary, NC on a Macintosh. Reproduced with permission from (Ischiropoulos et al., 1992a). 

NS = not significant LSDto.ooi = least significant difference (standard error of difference x Student s test value) at the 0.001 level = significant at the 0.001 level... 

This analysis allows us to split the variability observed for B into contributions due to different factors. The probability (p-value) provides a measure of the statistical significance (at a confidence level of 95%) of each factor. Overall at least one of the factors has had a significant effect (p = 0.0001) on the measured level of B. This is in a good agreement with previous observations. Multiple range tests (Fisher s least significant difference (LSD)) was performed to determine which of the treatment means were significantly different from each other, and the results are summarized in Table 4.5.5. 

T LSD — least significant difference values calculated when the F-test was significant at P < 0.05. 

Each treatment was conducted in triplicate and all experiments were repeated at least twice. The statistical significance of the evaluated data was analyzed by one-way analysis of variance. Differences among the mean values were tested using the least significant difference multiple range test. Values were considered significant when p<0.05, except when otherwise indicated. 

Fisher s least significant difference (LSD) test Linear regression to test for dose-effect trends Pairwise comparison Pearson s correlation coefficient Student s t-test Williams s t-test... 

Figure 2. Median and 95% confidence interval for radiocesium concentration in soil derived from the Chernobyl accident (squares, left v-axes) and weapons test (circles, right y-axes). Groups followed by the same characters are not significant different ( /-test, P > 0.05). Hollows (1) are defined where at least three from definite measured four points within a 3 m radius have a significantly higher altitude (> 10 cm) than the sampling plot, collines (3) are defined where at least three points have a significant lower altitude (> 10 cm) than the sampling plot. Plots which are not defined in that way (more or less on the same level) are grouped in class 2. N = 30 for each class, 10 points are excluded due to missing measurements within a 3 m radius.

Statistical Analysis. Data are presented as means SEM. Statistical comparisons between groups were performed using ANOVA. Fisher s Protected Least Significant Difference (PLSD) test was used to analyze the difference in lipid levels and the Mann-Whitney U-test was used for differences in atherosclerotic levels between dietary groups. 

An analysis of variance (ANOVA) was carried out to evaluate the significance of different adhesive formulations on shear strength. The results were further analyzed using the Least Significant Difference (LSD) test at p 0.05, to further evaluate the effects of adhesive formulations on the physical properties, shear strength and... 

There was a consistent decline in substrate TFR and air TFR the first three days [p <. 05, Least Significant Difference (LSD) test], after which the level of these behaviors -became rather uniform (Table 1). Locomotion declined also, but more slowly a significant (p <. 05) decline did not occur until Day 4, although locomotion continued to decline afterwards. 

Analysis of variance was performed using the software package Statgraphics Plus (Centurion) to detect significant differences (p< 0.05) between measurements on different days. The two-fector ANOVA test was performed on the results of the MRI measuiemraits corresponding to each measurement day (tissue type and tomato sample) and the F-ratio was calculated to measure how diffo ent the means at 95% Least Significant Difference (LSD) confidence level were in relation to the variations within each sample. 

The least significant difference method described above is not entirely rigorous it can be shown that it leads to rather too many significant differences. However, it is a simple follow-up test when ANOVA has indicated that there is a significant difference between the means. Descriptions of other more rigorous tests are given in the references at the end of this chapter. 

The color changes in the samples were monitored by measuring the Hunter L, a, b values of the pressurized and control fish samples using a Minolta Chromameter II reflectance equipment. The differences between the mean values were analyzed using the least significant difference (LSD) multiple comparison test of Steel and Torrie, (1960). The general linear model (GLM) procedure of the Statistical Analysis System (SAS) on McGill University mainframe was used. 

Data were analysed using the Statgraphics software (STCC Inc., Rockville, Maryland). Multifactor analysis of variance, and multiple range analysis (Least significant difference, LSD) were done to determine the sources of variation in the data and the effects of antioxidant types, processing treatments and storage on the oxidation of the fish products. Tests of significance were done at the 99% confidence level (p < 0.01). 

Comparison of test/control/reference Least significant difference significance p <0.05... 

Testing for differences at a regional level using least significant difference criteria showed a significant elevation of PS-product in the frontal cortical region in lead-treated animals for lysine, histidine and thiamine. With thiamine, and to a lesser extent lysine, smaller increases were also apparent in other regions (Table 2). 

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