Fisher’s least significant difference

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. 

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

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)... 

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. 

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).

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... 

Statistical Analysis. Data were analyzed using one- and two-way ANOVA (SAS Institute, Cary, NC). When ANOVA indicated significant differences, the treatment means were compared in pairs using Fisher s least significant difference procedure (36). Differences with P < 0.05 were considered significant. 

Statistical analyses were performed using Statgraphics Plus. The results were compared by analysis of variance and Fisher s least significance difference procedure. 

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). 

Table 2. Fisher s Least Standard Deviation (LSD) Test for Significance Difference Among Mean Intensities for Individual Aroxnasa...

Data were analyzed by analysis of variance (ANOVA) and Fisher s protected least significant difference (LSD) to compare differences between means of cell mass, of total lipids, and of conversion rates. Means differences were considered significant at the p <. 05 level. 

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. 

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