Effect is statistically significant

To determine whether an effect is statistically significant or not, a statistical interpretation method is used. Different possibilities have been described. An overview of them is given below. 

The probability that this overall effect is statistically significant The statistical confidence limits on the overall effect... 

If the calculated value of the applied statistical test is above the associated tabular value for the threshold or level of significance a, i.e. the confidence is (1-a) x 100%, the difference or effect is statistically significant. The hypothesis is rejected and the conclusion is that such a difference may in the future be expected in (1-a) x 100% cases provided the experiment is done under identical conditions. Hence only in a x 100% cases can a different outcome be expected. 

For example, if an effect has to be of magnitude 15% to be of practical importance, and our data gives us as our estimate of it 5% 2%, it is clear that the effect is statistically significant but not of practical importance. Alternatively if our result was 5% 10%, then it is not statistically significant on our present data but may still be of practical importance. 

Compare the P-value to an acceptable significance value a (sometimes called an alpha value). If p a, then the observed effect is statistically significant, the null hypothesis is ruled out, and the alternative hypothesis is valid. 

Table 6-6. Estimated decreases in percent of fatalities for teen drivers (15-17 years old) in states with different levels of GDL ( indicates that the effect is statistically significant at p<.05) (data from Morrisey et aL, 2006).

Here treatment results in a somewhat earlier onset of a condition which occurs eventually in all animals. Failure to age-adjust will result in a comparison of 29/50 with 21/50, which is not statistically significant. Age adjustment will essentially ignore the early and late deaths, which contribute no comparative statistical information, and be based on the comparison of 9/10 with 1/10, which is statistically significant. Here age adjustment sharpens the contrast, rather than avoiding bias, by avoiding diluting data capable of detecting treatment effects with data that are of little or no value for this purpose. 

A chemical for which there is statistically significant evidence based on at least one study conducted in accordance with established scientific principles that acute or chronic health effects may occur in exposed employees. 

A statistical significant effect is not always relevant from the practical point of view. Therefore, a worst-case level combination experiment with regard to the studied response (e.g., resolution) is determined and performed with replicates. In this experiment, only the method parameters with major effects (both statistically significant and almost significant) are considered. As can be seen in Figure 15, the major effect, temperature and pH, are easily detected. The worst-case combinations... 

So the statistician does this type of analysis for each treatment group versus the control. When this is done the toxicologist can determine whether any of the observed effects are statistically significant -whether and to what degree of confidence the observed effect can be said to have been caused by the chemical treatment. 

Interest in the effects of ozone on alveolar macrophages has been spurred by the observation that relatively low concentrations of ozone potentiate respiratory infections in animals and perhaps man. Coffin et al ob-ser a decrease in the number of bacteria phagocytized by alveolar macrophages obtained from rabbits exposed to various concentrations of ozone as low as 0.3 ppm. Some suggestion of a lack of threshold is present, but it is not clear whether the difference from the controls at lower ozone concentrations is statistically significant. 

P-value the probability of an observation-based statistic being larger than the computed value the block effect is highly significant... 

If the confidence interval of the effect of a factor contains zero, then the effect is not significantly different from zero. When zero is outside the confidence interval, then the factor has a statistically significant influence. 

Reports often state that an effect was significant at the 95% probability level or use an asterisk to denote significance at 95% and double asterisks for significance at 99%. Significance at the 95% level means that the null hypothesis (Hg = the effect is not significant) has been rejected because the probability that the test statistic, which has been calculated from the data, could have come from a population for which Hg is true has fallen below 5%. Most statistical tests have the same sequence of events ... 

It is clear from the table of analysis of variance that the factor effect is statistically highly significant. The effect of blocks is also important, which justifies the division of experimental conditions into blocks. 

If the confidence limit excludes the possibilities proposed by the null hypothesis, the outcome is statistically significant. With a properly conducted one-sided test, the risk of an accidental false positive when investigating a treatment that has no real effect is held at the usual 5 per cent. 

For each individual we calculate the difference in the measured value, under the two circumstances. These individual changes are then used to calculate a 95 per cent Cl for the mean effect. If the interval excludes zero, the result is statistically significant. 

By convention, the critical probability for rejecting the NH is 5% (i.e. P = 0.05). This means we reject the NH if the observed result would have come up less than 1 time in 20 by chance. If the modulus of the test statistic is less than the tabulated critical value for P = 0.05, then we accept the NH and the result is said to be not significant (NS for short). If the modulus of the test statistic is greater than the tabulated value for P = 0.05, then we reject the NH in favour of the alternative hypothesis that the treatments had different effects and the result is statistically significant . 

The are a number of ways of doing this. If the experiments have been replicated, ANOVA will reveal which effects are statistically significant. Otherwise, we rely on the fact that most of the effects are probably small and distributed randomly about zero. Thus, we look for the effects with the largest absolute values that stand out from the others. Making a normal probability plot of the distribution of their values is a widely used method. 

However, if one compares the values of the lattice parameter obtained when a different kind of a systematic error was assumed and accounted for in the data, the difference between the two is statistically significant (4.1583 vs. 4.1574 A for sample displacement and zero shift effects, respectively). This is expected given the different contribution from different errors as seen in Figure 5.19. Usually, both effects are present in experimental data. The refinement of two contributions simultaneously is, however, not feasible due to strong correlations between sample displacement and zero shift parameters as shown in Figure 5.21. 

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