This study's hypothesis of obtaining multiple, stimuli-responsive optical signal changes using molecularly engineered inorganic NPs can further be expanded to drug delivery and other imaging applications.
Conditional on the number of PTV carriers at the gene, n, a P-value can then be obtained by asking for the probability, under the null hypothesis, of obtaining the same or a larger BF than the one actually calculated from the data.
The significance is the probability, according to the null hypothesis $h$, of obtaining data that leads us to falsely reject this hypothesis $h$: \[ \text{Significance}_{F} = \alpha = P_{h}(R_{r}) = \sum_{s \in S} F s) P_{h}(s) d s, \] The probability $\alpha$ is alternatively called the type-I error, and it is often denoted as the significance or the p-value.
The power is the probability, according to the alternative hypothesis $h'$, of obtaining data that leads us to correctly reject the null hypothesis $h$: \[ \text{Power}_{F} = 1 - \beta = P_{h'}(F_{1}) = \sum_{s \in S} F s) P_{h'}(s) d s. \] The probability $\beta$ is called the type-II error of falsely accepting the null hypothesis.
The P value is defined as the probability, under the assumption of no effect (the null hypothesis H0), of obtaining a result equal to or more extreme than what was actually observed.
It turns out that in almost every case (for almost any pair of hypotheses) the actual likelihood of obtaining such evidence (i.e., evidence that has a likelihood ratio value less than ε) will be much closer to 1 than this factor indicates.[21] Thus, the theorem provides an overly cautious lower bound on the likelihood of obtaining small likelihood ratios.
With a null hypothesis of equality, obtained means and variances of the two FC axes were tested with t-test and Levene's test, respectively.
This is more generally expressed as: The probability of a hypothesis (H) given an observation (O) is equal to the probability of obtaining the observation given the hypothesis is true, multiplied by the prior probability of the hypothesis, divided by the unconditional probability of obtaining the observation.
The strategy shepherds the robots to places where the probability of obtaining a unique hypothesis for a set of multiple robots is a maximum.
This example of the long lasting divergence of myosin functional hypotheses clearly indicates a general difficulty of obtaining clinching evidence for dynamic actions of proteins even with the use of well-disseminated single-molecule techniques.
The proposed design strategy is a multi-scale numerical optimisation procedure that does not make use of any simplifying hypothesis to obtain a true global optimum configuration of the system.
