Least significant difference ANOVA

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). 

For data satisfying the ANOVA requirements, the least significant difference (LSD) is useful for making planned comparisons among several means. Any two means that differ by more than the LSD will be significantly different. The LSD is useful for showing on graphs. 

If significant differences are indicated in ANOVA, we are often interested in the cause. Is one mean different from the others Are all the means different Are there two distinct groups that the means fall into There are several methods to determine which means are significantly different. One of the simplest is the least significant difference (LSD) method. In this method, a difference is calculated that is judged to be the smallest difference that is significant. The difference between each pair of means is then compared with the least significant difference to determine which means are different. 

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. 

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. Differences In the amounts of IfeP (ng/cm ) between the control and laundered swatches were expressed In percentages of Insecticide residue remaining. Statistical differences were tested with Factorial Experimental ANOVA, Least Significant Means, and Duncan s Mhiltlple Range 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 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... 

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. 

A sub-set of four samples from each treatment was used for each analysis. Statistical analysis of data was carried out using one way analysis of variance (ANOVA). Differences among mean values were established using the least significant difference (LSD) multiple range test (Steel and Torrie, 1980). Values were considered significant when p<0.05. 

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). 

ANOVA means that at least one group shows a significantly different result fi-om the others. 

FIGURE 3.11 Differences in the sensorial characteristics of the Vin Santo obtained after 6 and 18 months of aging. The values (conditions as indicated) represent the means of two complete replicates, based on nine point scales (indicates a sensory attribute with at least one of the population means significantly different at the 0.1 a level with respect to the others, on the basis of ANOVA see Fig. 3.9 legend, (from Domizio et ai, 2007)... 

Again, even this information does not provide the most comprehensive answer possible in this situation. In this context of more than two treatment groups, the ANOVA is called an omnibus test. It is an overall test of statistical significance. The statistically significant result says that, somewhere, there is at least one statistically significant difference between pairs of the dose treatment groups. There are three pairs of dose treatment groups to consider ... 

Determination of cellular lactate production. Lactate concentration changes were evaluated on culture medium by H nuclear magnetic resonance analysis (NMR Gemini 300 spectrometer, Varian, Palo Alto, CA). Experiments were performed as already reported.6 Statistical analysis. All results were expressed as means standard error of the mean (SEM) taking into consideration at least three different experiments performed in duplicate. The means were compared by analysis of variance (ANOVA), p<0.05 was considered significant. 

Figure 9.19 ANOVA results for all 14( LI... 17, R1... R7) spot stress values telling us that with the p value being essentially zero, at least one sample mean is significantly different from the other sample means.

Analysis of variance (ANOVA) tests whether one group of subjects (e.g., batch, method, laboratory, etc.) differs from the population of subjects investigated (several batches of one product different methods for the same parameter several laboratories participating in a round-robin test to validate a method, for examples see Refs. 5, 9, 21, 30. Multiple measurements are necessary to establish a benchmark variability ( within-group ) typical for the type of subject. Whenever a difference significantly exceeds this benchmark, at least two populations of subjects are involved. A graphical analogue is the Youden plot (see Fig. 2.1). An additive model is assumed for ANOVA. 

The one-way analysis of variance is used where there is a single factor that will be set to three or more levels. It is not appropriate to analyse such data by repeated /-tests as this will raise the risk of false positives above the acceptable level of 5 per cent. If the ANOVA produces a significant result, this only tells us that at least one level produces a different result from one of the others. It does not tell us which level differs from... 

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