JonBenet Ramsey inside job, intruder theory and the null hypothesis

tricia griffith wrote:
Anti-K, this whole forum has example after example after example that an intruder did not commit this crime.

No one can show one scintilla of evidence of an intruder.

As owner, I do my best to stay out of actual discussions about a crime.

The JBR case is the one expection.

Websleuths is a leader in true crime information as well as discussion. People come here to get information. It is imperative we deal with the facts. Not fantasy.

All I ask for are facts and a logical connecting of the dots. Logic and facts.

When I get time I will be going through the forum to make sure the JonBenet Ramsey forum is being held up to the high standards just like all our other forums on Websleuths.

The days of allowing anyone to post anything because it's part of their "theory" are gone. Facts and logic. Very simple.

Host Tricia Griffith is a veteran radio disc jockey and owner of Websleuths.com and owner of Forums for Justice.org.

tricia griffith wrote:
Anti-K, this whole forum has example after example after example that an intruder did not commit this crime.

No one can show one scintilla of evidence of an intruder.

Host Tricia Griffith is a veteran radio disc jockey and owner of Websleuths.com and owner of Forums for Justice.org.

wiki wrote:
In inferential statistics, the term "null hypothesis" is a general statement or default position that there is no relationship between two measured phenomena, or no association among groups.[1] Rejecting or disproving the null hypothesis—and thus concluding that there are grounds for believing that there is a relationship between two phenomena (e.g. that a potential treatment has a measurable effect)—is a central task in the modern practice of science; the field of statistics gives precise criteria for rejecting a null hypothesis.
The null hypothesis is generally assumed to be true until evidence indicates otherwise. In statistics, it is often denoted H0 (read “H-nought”, "H-null", "H-O", or "H-zero").
The concept of a null hypothesis is used differently in two approaches to statistical inference. In the significance testing approach of Ronald Fisher, a null hypothesis is rejected if the observed data are significantly unlikely to have occurred if the null hypothesis were true. In this case the null hypothesis is rejected and an alternative hypothesis is accepted in its place. If the data are consistent with the null hypothesis, then the null hypothesis is not rejected. In neither case is the null hypothesis or its alternative proven; the null hypothesis is tested with data and a decision is made based on how likely or unlikely the data are. This is analogous to the legal principle of presumption of innocence, in which a suspect or defendant is assumed to be innocent (null is not rejected) until proven guilty (null is rejected) beyond a reasonable doubt (to a statistically significant degree).
In the hypothesis testing approach of Jerzy Neyman and Egon Pearson, a null hypothesis is contrasted with an alternative hypothesis and the two hypotheses are distinguished on the basis of data, with certain error rates.
Proponents of each approach criticize the other approach. Nowadays, though, a hybrid approach is widely practiced and presented in textbooks. The hybrid is in turn criticized as incorrect and incoherent—for details, see Statistical hypothesis testing.

wiki wrote:
Principle[edit]
Hypothesis testing requires constructing a statistical model of what the data would look like given that chance or random processes alone were responsible for the results. The hypothesis that chance alone is responsible for the results is called the null hypothesis. The model of the result of the random process is called the distribution under the null hypothesis. The obtained results are then compared with the distribution under the null hypothesis, and the likelihood of finding the obtained results is thereby determined.[3]
Hypothesis testing works by collecting data and measuring how likely the particular set of data is, assuming the null hypothesis is true, when the study is on a randomly selected representative sample. The null hypothesis assumes no relationship between variables in the population from which the sample is selected.
If the data-set of a randomly selected representative sample is very unlikely relative to the null hypothesis (defined as being part of a class of sets of data that only rarely will be observed), the experimenter rejects the null hypothesis concluding it (probably) is false. This class of data-sets is usually specified via a test statistic which is designed to measure the extent of apparent departure from the null hypothesis. The procedure works by assessing whether the observed departure measured by the test statistic is larger than a value defined so that the probability of occurrence of a more extreme value is small under the null hypothesis (usually in less than either 5% or 1% of similar data-sets in which the null hypothesis does hold).
If the data do not contradict the null hypothesis, then only a weak conclusion can be made: namely, that the observed data set provides no strong evidence against the null hypothesis. In this case, because the null hypothesis could be true or false, in some contexts this is interpreted as meaning that the data give insufficient evidence to make any conclusion; in other contexts it is interpreted as meaning that there is no evidence to support changing from a currently useful regime to a different one.
For instance, a certain drug may reduce the chance of having a heart attack. Possible null hypotheses are "this drug does not reduce the chances of having a heart attack" or "this drug has no effect on the chances of having a heart attack". The test of the hypothesis consists of administering the drug to half of the people in a study group as a controlled experiment. If the data show a statistically significant change in the people receiving the drug, the null hypothesis is rejected.
Basic definitions[edit]
The null hypothesis and the alternate hypothesis are terms used in statistical tests, which are formal methods of reaching conclusions or making decisions on the basis of data. The hypotheses are conjectures about a statistical model of the population, which are based on a sample of the population. The tests are core elements of statistical inference, heavily used in the interpretation of scientific experimental data, to separate scientific claims from statistical noise.
"The statement being tested in a test of [statistical] significance is called the null hypothesis. The test of significance is designed to assess the strength of the evidence against the null hypothesis. Usually, the null hypothesis is a statement of 'no effect' or 'no difference'."[4] It is often symbolized as H0.
The statement that is hoped or expected to be true instead of the null hypothesis is the alternative hypothesis.[4] Symbols include H1 and Ha.
Statistical significance test: "Very roughly, the procedure for deciding goes like this: Take a random sample from the population. If the sample data are consistent with the null hypothesis, then do not reject the null hypothesis; if the sample data are inconsistent with the null hypothesis, then reject the null hypothesis and conclude that the alternative hypothesis is true."[5]
The following sections add context and nuance to the basic definitions.
Example[edit]
Given the test scores of two random samples of men and women, does one group differ from the other? A possible null hypothesis is that the mean male score is the same as the mean female score:
H0: μ1 = μ2
where
H0 = the null hypothesis,
μ1 = the mean of population 1, and
μ2 = the mean of population 2.
A stronger null hypothesis is that the two samples are drawn from the same population, such that the variances and shapes of the distributions are also equal.

MurderMysteryReader wrote:Lou Smit had the experience Thomas and Kolar lacked and was a much better detective. If he had more time I have no doubt Lou Smit would have figured out who killed JonBenet Ramsey. Thomas and Kolar are RDI and never looked at this case with objectivity.

MurderMysteryReader wrote:I agree about Lou Smit not being to solve JonBenet Murder if Mr. Cruel killed her.  I doubt very highly anyone could solve it if Mr. Cruel was the killer.