One-way ANOVA

FIGURE 12.3 One-way ANOVA. One-way analysis of variance of basal rates of metabolism in melanophores (as measured by spontaneous dispersion of pigment due to Gs-protein activation) for four experiments. Cells were transiently transfected with cDNA for human calcitonin receptor (8 pg/mL) on four separate occasions to induce constitutive receptor activity. The means of the four basal readings for the cells for each experiment (see Table 12.4) are shown in the histogram (with standard errors). The one-way analysis of variance is used to determine whether there is a significant effect of test occasion (any one of the four experiments is different with respect to level of constitutive activity). 

Independent measures /-test One-way ANOVA Multi-way ANOVA Repeated measures /-test Repeated measures ANOVA Repeated measures ANOVA One-way ANOVA Multi-way ANOVA One-way ANOVA Multi-way ANOVA ... 

Table 3 Moisture content statistics ANOVA one-way-test (soy) and independent T— test (freezing, fresh microwaving and stored microwaving). F, S, FM and SM rrfer respectively to fresh, frozen, fresh microwaved and frozen microwaved. Numbers refer to the formulations described in table 1. Different letters refer to statistically different samples...

A variety of statistical methods may be used to compare three or more sets of data. The most commonly used method is an analysis of variance (ANOVA). In its simplest form, a one-way ANOVA allows the importance of a single variable, such as the identity of the analyst, to be determined. The importance of this variable is evaluated by comparing its variance with the variance explained by indeterminate sources of error inherent to the analytical method. 

Let s use a simple example to develop the rationale behind a one-way ANOVA calculation. The data in Table 14.7 show the results obtained by several analysts in determining the purity of a single pharmaceutical preparation of sulfanilamide. Each column in this table lists the results obtained by an individual analyst. For convenience, entries in the table are represented by the symbol where i identifies the analyst and j indicates the replicate number thus 3 5 is the fifth replicate for the third analyst (and is equal to 94.24%). The variability in the results shown in Table 14.7 arises from two sources indeterminate errors associated with the analytical procedure that are experienced equally by all analysts, and systematic or determinate errors introduced by the analysts. 

It should be noted that in this example the performance of only one variable, the three analysts, is investigated and thus this technique is called a one-way ANOVA. If two variables, e.g. the three analysts with four different titration methods, were to be studied, this would require the use of a two-way ANOVA. Details of suitable texts that provide a solution for this type of problem and methods for multivariate analysis are to be found in the Bibliography, page 156. 

A one-way (simple) ANOVA with six replicates can be conducted by either regarding each titration technique or each batch as a group, and looking for differences between groups. 

The superscript a,b,c,d,e,f,g,h indicates significance difference from 1,2,3,4,5,6,7,8 groups, respectively. The data is analyzed by one-way ANOVA(F-test) followed by Newmann Keul s Studentized range test... 

Estimation of the analytical variance by one-way ANOVA (2 portions x 10 laboratories). 

KEY ND=levels below the sensitivity of the assay. Data were analyzed by one-way ANOVA... 

PlB one-way analyiia of varianoe (ANOVA) thowed F value p<0.OS. p[Pg.314]

Observations and data analysis Each sample was taken in 5 replicates. The data are analyzed using t-test for dependent variables or when have large sample or more than two combinations one-way ANOVA. 

Statistical analysis Each sample was taken in at least 5 replicates. The statistical analysis of the photosynthetic efficiency (Fv/Fm) of the species that were examined was performed using a one way-ANOVA analysis. 

One-way analysis of variance (ANOVA) to test the significant effect of the degrading impact on each soil characteristic was performed using the computer software, SPSS 10.0.5J (SPSS Japan Inc., Tokyo). The Dunnett T3 test was chosen as the post-hoc test. 

Physico-chemical characteristics of the soils were summarized in Table 1. The values were comparable to that described in the previous reports about the SERS (Doi and Sakurai 2003 Doi et al. 2004 Sakurai et al. 1998). The one-way ANOVA indicated that most of the soil variables significantly reflected the land degradation with high values of bulk density, sand content and exchangeable acidity, and low values of moisture content, pH, OM, base (K, Ca, Mg) contents, EC, CEC, base saturation rate, TN and TC contents, available phosphorus and MPN on the glucose medium with no antibiotics. These results also told that the human activities induced several soil environmental gradients. 

The One Way ANOVA test was used to determine statistical significance. Input concentrations between summer and the fall winter season were not significant however, for dissolved As and Zn, total As and Zn differences were significant at p < 0.01. 

One-way-ANOVA tests were made to control the quality of the data. To achieve the proposed objectives, multiple comparison of means of the four groups was made by Tukey (p<0,05) test. The Dunnett (p<0,05) test was used to compare the means of three groups of mining sites with the control group (Seaman et al. 1991). Pearson correlation coefficients were also obtained to confirm the tests results. 

There are various other ways of examining the variate in question in this case. Let us first examine simple one-way ANOVA of the variate by sex as in Table 16.16. In neither of the two cases was there any indication of significant treatment differences at any reasonable level. Because the two sexes did not show any pretreatment differences based on the two-factor analysis of the covariate, let us combine the two sexes and analyze the data by one-way ANOVA as in Table 16.17. In this case, because of the increased sample sizes for combining the two sexes, there was indication of some treatment differences (p = 0.0454). Unfortunately, this analysis assumes that because there were no pretreatment differences between the two sexes, that pattern will hold during the posttreatment period. That often may not be the case because of biological reasons. 

Values with different superscripts in the same column are significantly different at P<0.05 (a,b), PC0.01 (a,c) and PC0.001 (a,d) determined by one-way ANOVA and Tukey test, nc = not calculated because the HPLC chromatogram revealed an undefined peak co-eluted with zeaxanthin that was also detectable in the canthaxanthin diet. 

Analysis of Variance (ANOVA). Keeping in mind that the total variance is the sum of squares of deviations from the grand mean, this mathematical operation allows one to partition variance. ANOVA is therefore a statistical procedure that helps one to learn whether sample means of various factors vary significantly from one another and whether they interact significantly with each other. One-way analysis of variance is used to test the null hypothesis that multiple population means are aU equal. 

One uses ANOVA when comparing differences between three or more means. For two samples, the one-way ANOVA is the equivalent of the two-sample (unpaired) t test. The basic assumptions are (a) within each sample, the values are independent and identically normally distributed (i. e., they have the same mean and variance) (b) samples are independent of each other (c) the different samples are all assumed to come from populations having the same variance, thereby allowing for a pooled estimate of the variance and (d) for a multiple comparisons test of the sample means to be meaningful, the populations are viewed as fixed, meaning that the populations in the experiment include all those of interest. 

In this setting there is a technique, termed one-way analysis of variance (one-way ANOVA), which gives an overall p-value for the simultaneous comparison of all of the treatments. Suppose, for example, we have four treatment groups with means Pi, p2> P 3 P4. This procedure gives a p-value for the null hypothesis ... 

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