Tukey’s test

A 2 X 2 contingency table was used to evaluate the frequency of anomalies and resorptions within the fetal population and between litters. Body weight and body measurements were statistically analyzed by an Analysis of Variance and Tukey s test (13). In all cases, the level of significance was P < 0.05. 

Significantly different from control by an Analysis of Variance and Tukey s test (measurements) or the 2X2 contingency table (resorptions), P <0.05. 

Fig. 1.9. Effects of sesquiterpene lactones on European corn borer, (a) Glutathione levels (b) lipid peroxidation synergistic effects of-terthienyl (c) with sesquiterpene lactones from the Asteraceae on larval mortality. Means followed by the same letter are not significantly different in Tukey s test (P < 0.05).

Fig. 3. Comparison of METH-induced CPP in single histamine receptor gene knockout mice. Mice were injected 1 mg/kg of METH or saline every other day, and confined for 30 min to a compartment designed to condition the place preference. The CPP score were calculated using the staying time of mouse in each compartment for 15 min before and after the conditioning. Each value represents the mean S.E.M. of 6-18 mice. Statistical analysis was performed by means of one-way ANOVA followed by Tukey s test ( p < 0.05, p < 0.01).

Fig. 9. Effects of l-PDMP on biosynthesis of cortical gangliosides in rats with cerebral ischemia. Normal rats (n = 6), vehicle group ( , i.p. injections of vehicle twice a day from 24 h after ischemia) day 3 (n = 5), day 5 (n — 6), day 7 (n — 4), L-PDMP group (o, i.p. injections of 40 mg/kg L-PDMP twice a day from 24 h after ischemia) day 3 (n = 4), day 5 (n = 6), day 7 (n = 4). P < 0.05 versus vehicle group, P < 0.05 versus normal rats (Tukey s test).

Tukey s test Here, all groups are compared with all other groups in every possible pairing. With our data set, we would have to compare the first treatment against four others, the next against three others, and so on, giving a total of 4 + 3 + 2+ 1 = 10 comparisons. 

Performing Tukey s test With our experiment, a case could be made for performing either a Dunnett s or a Tukey s test. The general rule, that choices of statistical methodology should be made in advance of seeing the data, includes the selection of a follow-up test. Let us assume that a decision had been made that we would use Tukey s test. 

In most statistical packages, the implementation of the analysis of variance includes an option to select a Tukey s test. The format of the output varies enormously, but (as in Table 13.4) should include a list of confidence intervals for the difference between each possible pair of catalysts. Each line of output shows the difference calculated as the yield with the first metal minus that with the second. The results are shown ordered according to yield [palladium (highest) to platinum (lowest)]. 

Table 13.4 Generic output from Tukey s test, showing confidence limits for the differences between pairs of catalysts (percentage points)...

Tukey s test Confidence Intervals 99.28% Lower limit for difference Upper limit for difference Significant ... 

The ANOVA only tested statistical significance. However, Tukey s test reports confidence intervals for the sizes of the various differences, so we can also assess whether any increase in yield that might be achieved by a change of catalyst would be big enough to be of practical significance. 

Performing Dunnett s test In the real world, it would be naughty to start doing a Dunnett s test at this stage, since we have already seen the data and had previously committed ourselves to Tukey s test. However, just so you can see the procedure, we will perform Dunnett s test with platinum as control. 

If your package indicates the level of confidence used, it should be 98.47 per cent. This means that the individual error rate for each comparison is 1.53 per cent. This is higher than the corresponding figure (0.72 per cent) for Tukey s test. The reason for this is that we are now performing only four comparisons instead of 10 and so individual comparisons do not need to be performed to quite such high standards. 

When planning experiments, it is worth remembering that, as the number of treatments increases, there is a very steep increase in the number of comparisons that Tukey s test would make and the individual comparisons will have to be carried out to correspondingly high standards of proof. 

The data from our catalyst experiment are balanced , i.e. there are exactly equal numbers of replicates for each catalyst. This is not a requirement for the one-way ANOVA and, if a small amount of data loss occurs, the analysis can still go ahead. For any given number of observations, the power of the ANOVA will be greatest with a balanced data set and this is also true for Tukey s test. The only circumstance where power will be greater with an imbalanced data set is where a Dunnett s test is planned. Here, the control group is of special importance because it is used in all the comparisons. For this test, it is worthwhile trying to generate some extra data for the control group. 

Follow-up tests will rectify both of these short-comings. Tukey s test will look at the difference for every possible pair of levels of the factor. Dunnett s test will treat one level as a reference and then compare all other levels against that. A confidence interval is calculated for the difference between each pair of treatments. If the interval excludes zero, that comparison is statistically significant The intervals are calculated to give each comparison less than a 5 per cent risk of producing a false positive. In this way, the entire series of comparisons will accumulate a total 5 per cent risk. 

To test whether the differences between the treatments are significant, you can use Tukey s test (Data Sheet 2.3)... 

To test for statistical significance, use a randomized ANOVA. Each student is a block. Follow this with Tukey s test. 

Table 4.3 Distribution of amine contents ( xg/L) in red and white wines. ( = significance at HSD Tukey s test for unequal samples, =...

CF = caries free, n = 6 CP = with past caries experience, n = 7 CA = with active caries, n = 9. p < 0.05, compared with CF, by Tukey s test for comparison made at a given time point. ... 

The quantity represented by the letter "q" is determined from a table of values used just for this test. Two characteristics are needed to determine the appropriate value of q each time that it is used. These characteristics are represented by the letters "a" and "v." The letter a represents the number of groups, which in this example is 3. The letter v represents the df, which in this test is the df associated with the within-samples mean square. In this case, the value of v is 12, as calculated for and shown in the ANOVA summary table in Table 11.4. From the table of q values for Tukey s test (provided in Appendix 5) the value of q associated with an... 

Having gone through the calculations necessary for Tukey s test, we can look at how these results would lead to decision-making, and also compare the interpretation and decision-making with those that followed from using Bonferroni s methodology on the same dataset. 

It should be noted that these are not the only acceptable methods applicable to multiple comparisons from an ANOVA. In each individual case, the choice among possible approaches is largely dependent on the study design. For example, Dunnett s test can be used when the only comparisons of interest are each test treatment versus a control (for example, in a placebo-controlled, dose-ranging study). Like Tukey s test, Dunnett s method is more powerful than Bonferroni s. In general, other methods gain power compared with Bonferroni s method by... 

Suppose also that Tukey s test provided evidence of the same pattern of statistical significance ... 

Why would Tukey s test be useful to evaluate the pairwise comparisons in (b) ... 

Fig. 7. Relationship between caspase activation and neurotoxicity of PrP106-126. (A) The activity of caspase-3 (CPP32) was determined after 5-day exposure of cortical neurons to 50 pM PrP106-126 or scrambled PrP106-126 (Control). The remarkable increase in CPP32 activity induced by PrP106-126 was abolished by cotreatment of cultures with a specific (DEVD-CHO) or a nonselective (z-VAD-fmk) caspase inhibitor. (B) Viability of cortical neurons under the conditions described in (A). The neurotoxic effect of PrP106-126 was partially reduced by cotreatment of cultures with z-VAD-fmk, whereas DEVD-CHO was ineffective. Data are the mean SE of 6 determinations P < 0.01 versus control group (Tukey s test).

FIGURE 40.6 Neurons Fos positive in the (a) motor cortex, (b) locus ceruleus, (c) nucleus raphe magnus, and (d) periaqueductal grey. Vehicle (control) or EO-pCD (6,12 and 24 mg/kg) were administered orally 1.5 h before perfusion. Values represent mean SEM (n = 6 per group). p < 0.05, p < 0.01 or p < 0.001 versus control (one-way ANOVA followed by Tukey s test). (From Siqueira-Lima, P.S. et al.. Bask Clin. Pharmacol. Toxicol., 114(2), 188, 2014.)... 

A factorial experimental design formulations x packaging materials x storage temperature x evaluation times, with two repetitions were used. The physical, chemical, physicochemical and sensorial alterations were evaluated and their means compared by Tukey s test at the 5% level of probability or by statistical models (Cochram Cox, 1992). 

Figure 6. EOG response to various concentrations of L-serine and sodefrin in sexually undeveloped and hormone-treated male and female newts. Test females (n=10) received daily injections of 1 lU PRL and 25 lU human chorionic gonadotropin (HCG) for seven days. The EOG response was recorded around the spot 7 in Fig. 5b. Each column and vertical bar represent the mean of 10 determinations and SEM, respectively. Values with the same superscript do not differ significantly from each other at the 5% level (Tukey s test).

Significant differences are indicated p = 0.05) via Tukey s test for unequal sample sizes. Culver is not included in the ANOVA... 

The results must be evaluated from the clinical viewpoint, with the involvement of pain development in the cases treated with different washing solutions as compared to controls, and finally from the point of view of immunological and proinflammatory cytokines [15, 18], Statistical analysis, using the program Systat 7.0 and Tukey s test, was used for post hoc comparison (p<0.05 was considered significant). The study had statistically significant results. 

Spatially Relative Tasks. For all three relative tasks, we also found significant main effects of navigation technique using a one-way ANOVA for Proximity between Objects, (F2,53=7.724, p<0.001) for Proximity from Reference, (F2,53=9.544, p<0.001) for Cluster, (F2,53=3.975, p=0.025). Post-hoc Tukey s tests show consistent significant differences between the fastest two techniques (Zoom and DragMag) and the slowest (Hop) (all p<0.05), but no differences between Zoom and DragMag. 

Relationships between soil nutrient regimes and several empirical variables (site n=149). Different superscripts within rows indicate significant differences among the soil nutrient regimes (p<0.05, Tukey s test) (from Carter and Klinka 1990)... 

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