Alternative hypotheses equivalence

In this case, the alternative hypothesis states that the two treatments are clinically equivalent the null hypothesis is saying that the two treatments are not equivalent. Note that the alternative encapsulates the objective we are trying to disprove the null in order to establish equivalence. 

Operationally, this is equivalent to the method of using two simultaneous one-sided tests to test the (composite) null hypothesis that the treatment difference is outside the equivalence margins versus the (composite) alternative hypothesis that the treatment difference is within the margins. ... 

With the p-value methodology we are rejecting the null hypothesis Hg in favour of the alternative hypothesis Hj, providing the two (one-sided) p-values are < 2.5 per cent. We have then established equivalence and we can talk in terms of the treatments being significantly equivalent. The terminology sounds almost contradictory, but is a correct statement. If either of the two p-values is above 2.5 per cent then the treatments are not significantly equivalent. 

Alternate hypothesis The average effect of the investigational drug on SBP is not equivalent to the average effect of the placebo on SBP. 

Alternate hypothesis The investigational drug does show equivalent efficacy to the comparator drug (the reference drug). 

Following the logic of our memory lip, you will see that the alternate hypothesis in this case, just like in the case of a superiority trial, expresses what we are hoping to find, while the null hypothesis states what we are hoping not to find. The actual natures of the null and alternate hypotheses in an equivalence trial are... 

Fig. 140. Computer drawing of the reconstruction of the Zebrin Purkinje cells bands in the unfolded adult C57/B6 mouse cerebellum. The drawing was from immunostained 40 fim thick coronal frozen sections. The continuity of the bands has been determined as best as possible. On the left and bottom are the scales in millimeters. The two axes have different magnifications. On the right are marked the approximate boundaries of the vermal lobules. The flocculus and paraflocculus are not illustrated. One place where the data are ambiguous is within lobule V-VI, where a large number of short bands more caudally are dramatically reduced to just three at the rostral limit. It is not clear whether the P2 + or P3 + bands extend through the anterior lobe vermis (see also Fig. 139). The reconstruction data from coronal sections were not suitable to resolve the issue, so the cerebellum has also been reconstructed from horizontal sections. The upper inset panel shows the data from such a reconstruction, equivalent to the region indicated by a rectangle on the main drawing (scale in millimeters). The preferred interpretation is that the P2+ compartment does not extend far into the anterior lobe vermis, and that the first lateral Zebrin + band in lobules I-IV is continuous with P3+ (as indicated by continuous lines in the upper inset panel and as shown in the main drawing). The alternative hypothesis, that the first lateral Zebrin + band in lobules I-IV is continuous with P2+, is shown schematically in the lower inset panel. Eisenman and Hawkes (1993).

Option 1. If both variances are assumed to be equal or they have been shown to be equivalent by an F-test, the separate estimates are pooled (see Section 3.3) to give a value for S (p). The null hypothesis and alternative hypothesis are... 

Rejecting the null hypothesis is equivalent to accepting the alternative hypothesis—that the two populations are unequal. Accepting the null hypothesis is equivalent to accepting the statement accepting that the mean world temperature was not the same in 1950 and in 2010. 

The first limitation is that NHST lacks a certain degree of direct applicability. The basic concept underlying the safety of an ingredient added to infant formulas is the reasonable certainty of no harm concept without a requirement for the demonstration of benefit. NHST, however, is generally formulated to demonstrate the superiority of one condition versus another. The fundamental idea in the formulation of reasonable certainty of no harm is one of equivalence, not of difference. While one can manipulate the null and alternative hypothesis in this circumstance (e.g., to make the no difference condition the alternative hypothesis), the resulting formulation is awkward and shifts the probabilistic control of the important error rate to that of power rather than to the more direct alpha level of the resulting test. Due to its highly unusual nature, it is likely that this test s results will not be properly understood and interpreted. 

This is a single-sided test since we mily care about degradation in process quality. Should Option B increase product quality, then it is another reason to implement it. Note that it is very important to carefully state all the definitions at this point as there are multiple equivalent approaches that one can take. In this particular example, it has been assumed that the difference is defined as - //g, which impUes that if this difference is greater than 0.1, then it can be assumed that the new drying option is not good. If the difference had been defined as Hb then the alternative hypothesis would have been defined as Hi. A < A, with A = —0.1. 

Lodish and Porter (1980) have suggested an alternative hypothesis that inhibition of host cell protein synthesis by VSV is due to the successful competition by large amounts of VSV transcripts for a limited number of ribosomes. They concluded from in vivo studies that viral and cellular mRNA are about equivalent in their efficiencies of translational initiation but viral transcripts are simply in large excess and, for this reason, can successfully out-compete the cellular transcripts for available ribosomes. In a follow-up publication, Lodish and Porter (1981) described a correlation between the concentration of intracellular VSV mRNA and the extent to which cellular protein synthesis is inhibited by VSV wild-type and various mutants. Although this mechanism can successfully explain the switch from host to viral protein synthesis, it does not explain the overall reduction in total protein synthesis. In addition, a recent study by Rosen et al. 

Thus we have an alternative route to the experimentally observable property A it is the statistical average of the results of measurement on very many identical systems. The ergodic hypothesis tells us that this interpretation and the time-dependent interpretation are equivalent. 

In conclusion, under the hypothesis that the reaction has no barrier in excess of its endoergicity, Att/°j(0) = 0, the enthalpy of reaction 3.10 is given by the Arrhenius activation energy for the forward reaction minus a heat capacity term. This term can be estimated by using statistical mechanics, provided that a structure for the activated complex is available. It is often found that T A Cjj > is fairly small, ca. — 1 kJmol-1 at 298.15 K [60], and therefore, the alternative assumption of a,i Ar//" is commonly accepted if T is not too high. Finally, note that either 3,1 Ar//." or Atf/°j(0) = 0 are not equivalent (see equation 3.22) to another current (but probably less reliable) postulate, Ea- = 0. 

Within the framework of hypothesis testing, the null and alternative hypotheses of interest for equivalence when dealing with means are as follows ... 

Having calculated the level of significance can be obtained from appropriate tables. The Wilcoxon signed rank test is the non-parametric equivalent of the paired t-test. The Kruskal-Wallis test is another rank sums test that is used to test the null hypothesis that k independent samples come from identical populations against the alternative that the means of the populations are unequal. It provides a non-parametric alternative to the one-way analysis of variance. 

Since the dimensionless time for a first-order reaction is the product of the reaction time t and a first-order rate constant k, there is no reason why k(x)t should not be interpreted as k(x)t(x), that is, the reaction time may be distributed over the index space as well as the rate constant. Alternatively, with two indices k might be distributed over one and t over the other as k x)t(y). We can thus consider a continuum of reactions in a reactor with specified residence time distribution and this is entirely equivalent to the single reaction with the apparent kinetics of the continuum under the segregation hypothesis of residence time distribution theory, a topic that is in the elementary texts. Three indices would be required to distribute the reaction time with a doubly-distributed continuous mixture. 

Proposed Mechanism Responsible for Calcium Efflux. Calcium-ion efflux from brain tissue does not appear to be a function of carrier frequency, since equivalent results are obtained at carrier frequencies of 50, 147, and 450 MHz provided the internal electric field intensity is the same in each brain. However, an important question remains why should there be alternate ranges, or windows, of internal electric field intensity which cause efflux enhancement An hypothesis that is consistent with and helps explain this finding is ... 

The probability of committing a type I error is the probability of rejecting the null hypothesis when it is true (for example, claiming that the new treatment is superior to placebo when they are equivalent in terms of the outcome). The probability of committing a type I error is called a, which is sometimes referred to as the size of the test. The probability of committing a type II error is the probability of failing to reject the null hypothesis when it is false. This probability is also called beta (P). The quantity (1 - P) is referred to as the power of the statistical test. It is the probability of rejecting the null hypothesis (in favor of the alternate) when the alternate is true. As stated earlier it is desirable to have low error probabilities associated with a test. As we would like a and p to be as low as possible the quanti-... 

Given that the research questions in these trials are different from those used in superiority trials, the formats of the null and alternate hypotheses are also different. The research question associated with an equivalence trial is Does the test drug demonstrate equivalent efficacy compared with the comparator drug The null hypothesis,... 

Sakurai, Ikeda and Okabe reported values of equivalent to 30-50 layers of FeS [12], which makes the modeling of the reaction step via an absorption equilibrium somewhat strained. As an alternative, semi-empirical approach we can adopt the parabolic rate hypothesis used in the oxidation of metals [15] and apply it to the formation of reaction product on the surface,... 

As described above, L-CPT I contains two hydrophobic transmembrane s ments. The first import mechanism hypothesis which can be formulated is that either of the transmembrane segments could function as a signal anchor sequence. Whether HI and H2 play an equivalent role or only one of them acts as a specific signal anchor sequence still remains to be elucidated. Alternatively, HI or H2 could function as a stop-transfer sequence in cooperation with a matrix-signd sequence which could be ensured by either al, o2 or a3. Thus, further studies will be required to determine whether OMM insertion of L-CPT I follows the signal anchor sequence or stop-transfer model. 

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