Intro 
In science, chance and randomness play very important roles in the acceptance or rejection of a hypotheses of observed causeeffect relationships. Sample and effect size also play significant roles. 
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Ideas to Explore 

Chance & Randomness 
Chance is considered a random cause with known properties. In science, an alternative (null) hypothesisthat the observed result happened by chanceis tested and either accepted or rejected. Science has standards for error rates in rejecting a null hypothesis, the minimum being p<.05. This means that, minimally, the probability (p) of making a mistake by rejecting the null hypothesis (that the cause was just pure chance) when it should have been accepted, is 5 or less in 100, or 1 in 20. 

Sample & Effect Size 
The size of a cause's effect determines the number of measurements or observations (sample size) required to reach a probability (p) level. If the effect size is large, then fewer observations are needed. And more observations are required to reach higher probability levels, e.g., p<.01, p<.001. For example, in experiments on the effects of consciousness or intention on random number generators (RNGs), the effect size is very small, so thousands and thousands of observations are required to reach even the lowest (p<.05) probability level. On the other hand, heavily loaded dice may only require a few hundred rolls to conclude at p<.05 that the dice may be loaded. 

Alternative Hypotheses 
Often, the actual cause might not be pure chance at all but some hidden, unknown, unnoticed, unconsidered or uncontrolled causes. In such cases, the null hypothesis might rejected, but the alternative research hypothesis might not state the true causal relationship. The real science of science is crafting welldesigned and controlled experiments in which all possible causes other than the hypothesized ones are controlled or eliminated, and formulating and evaluating all plausible alternative hypotheses when the null hypothesis is ejected. 

Worth Noting 

Randomness, the 'Devine Force' 
