Atheistic Null Hypothesis: There is/are no God/Gods

Damien Marie AtHope’s Art

Damien Marie AtHope’s Art

Damien Marie AtHope’s Art

With religion, it is like your brain is in a noose, squeezing out any hope of critical thinking about the religious beliefs. Leaving the victim faith-drunk as if all the oxygen of their mental freedom is cut off and hope for self-mastery is but some far away fantasy out of reach.

[Antireligionist] My blogs that address Religion: Archaeology, Anthropology, Philosophy and History

In scientific terms, a “LACK OF EVIDENCE” is/can be proof of non-existence. As with all things as new evidence is discovered views can change. I can prove something does not exist by its lack of existence, the box is empty? Is a box empty?

I can prove god is not in the box, but some say I can never prove the box is empty. But is it right to say the god Box is never empty even if we remove its needed contents? It’s an exercise in rhetoric with what we do know to say the god Box is not empty of all evidence and reason thus all it can be is empty of validity. And still today people say empty god boxes are possibly not empty?

More on Null Hypothesis

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. 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-oh”, 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.

Statistical inference can be done without a null hypothesis, by specifying a statistical model corresponding to each candidate hypothesis and using model selection techniques to choose the most appropriate model. (The most common selection techniques are based on either Akaike information criterion or Bayes factor.)

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.

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.

The null hypothesis and the alternate hypothesis are types of conjectures 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’.” 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. Symbols include H₁and H_a.

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.”

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.

Simple hypothesis

Any hypothesis which specifies the population distribution completely. For such a hypothesis the sampling distribution of any statistic is a function of the sample size alone.

Composite hypothesis

Any hypothesis which does not specify the population distribution completely. Example: A hypothesis specifying a normal distribution with a specified mean and an unspecified variance.

The simple/composite distinction was made by Neyman and Pearson.

Exact hypothesis

Any hypothesis that specifies an exact parameter value. Example: μ = 100. Synonym: point hypothesis.

Inexact hypothesis

Those specifying a parameter range or interval. Examples: μ ≤ 100; 95 ≤ μ ≤ 105.

Fisher required an exact null hypothesis for testing (see the quotations below).

A one-tailed hypothesis (tested using a one-sided test) is an inexact hypothesis in which the value of a parameter is specified as being either:

• above or equal to a certain value, or
• below or equal to a certain value.

A one-tailed hypothesis is said to have directionality.

Fisher’s original (lady tasting tea) example was a one-tailed test. The null hypothesis was asymmetric. The probability of guessing all cups correctly was the same as guessing all cups incorrectly, but Fisher noted that only guessing correctly was compatible with the lady’s claim. (See the quotations below about his reasoning.)

Goals of null hypothesis tests

There are many types of significance tests for one, two or more samples, for means, variances and proportions, paired or unpaired data, for different distributions, for large and small samples; all have null hypotheses. There are also at least four goals of null hypotheses for significance tests:

• Technical null hypotheses are used to verify statistical assumptions. For example, the residuals between the data and a statistical model cannot be distinguished from random noise. If true, there is no justification for complicating the model.
• Scientific null assumptions are used to directly advance a theory. For example, the angular momentum of the universe is zero. If not true, the theory of the early universe may need revision.
• Null hypotheses of homogeneity are used to verify that multiple experiments are producing consistent results. For example, the effect of a medication on the elderly is consistent with that of the general adult population. If true, this strengthens the general effectiveness conclusion and simplifies recommendations for use.
• Null hypotheses that assert the equality of effect of two or more alternative treatments, for example, a drug and a placebo, are used to reduce scientific claims based on statistical noise. This is the most popular null hypothesis; It is so popular that many statements about significant testing assume such null hypotheses.

Rejection of the null hypothesis is not necessarily the real goal of a significance tester. An adequate statistical model may be associated with a failure to reject the null; the model is adjusted until the null is not rejected. The numerous uses of significance testing were well known to Fisher who discussed many in his book written a decade before defining the null hypothesis.

A statistical significance test shares much mathematics with a confidence interval. They are mutually illuminating. A result is often significant when there is confidence in the sign of a relationship (the interval does not include 0). Whenever the sign of a relationship is important, statistical significance is a worthy goal. This also reveals weaknesses of significance testing: A result can be significant without a good estimate of the strength of a relationship; significance can be a modest goal. A weak relationship can also achieve significance with enough data. Reporting both significance and confidence intervals is commonly recommended.

The varied uses of significance tests reduce the number of generalizations that can be made about all applications.

The choice of the null hypothesis is associated with sparse and inconsistent advice. Fisher mentioned few constraints on the choice and stated that many null hypotheses should be considered and that many tests are possible for each. The variety of applications and the diversity of goals suggests that the choice can be complicated. In many applications the formulation of the test is traditional. A familiarity with the range of tests available may suggest a particular null hypothesis and test. Formulating the null hypothesis is not automated (though the calculations of significance testing usually are). Sir David Cox has said, “How [the] translation from subject-matter problem to statistical model is done is often the most critical part of an analysis”.

A statistical significance test is intended to test a hypothesis. If the hypothesis summarizes a set of data, there is no value in testing the hypothesis on that set of data. Example: If a study of last year’s weather reports indicates that rain in a region falls primarily on weekends, it is only valid to test that null hypothesis on weather reports from any other year. Testing hypotheses suggested by the data is circular reasoning that proves nothing; It is a special limitation on the choice of the null hypothesis.

A routine procedure is as follows: Start from the scientific hypothesis. Translate this to a statistical alternative hypothesis and proceed: “Because H_a expresses the effect that we wish to find evidence for, we often begin with H_a and then set up H₀ as the statement that the hoped-for effect is not present.” This advice is reversed for modeling applications where we hope not to find evidence against the null.

A complex case example is as follows: The gold standard in clinical research is the randomized placebo-controlled double-blind clinical trial. But testing a new drug against a (medically ineffective) placebo may be unethical for a serious illness. Testing a new drug against an older medically effective drug raises fundamental philosophical issues regarding the goal of the test and the motivation of the experimenters. The standard “no difference” null hypothesis may reward the pharmaceutical company for gathering inadequate data. “Difference” is a better null hypothesis in this case, but statistical significance is not an adequate criterion for reaching a nuanced conclusion which requires a good numeric estimate of the drug’s effectiveness. A “minor” or “simple” proposed change in the null hypothesis ((new vs old) rather than (new vs placebo)) can have a dramatic effect on the utility of a test for complex non-statistical reasons.

The choice of null hypothesis (H₀) and consideration of directionality (see “one-tailed test“) is critical.

Tailedness of the null-hypothesis test

Consider the question of whether a tossed coin is fair (i.e. that on average it lands heads up 50% of the time) and an experiment where you toss the coin 5 times. A possible result of the experiment that we consider here is 5 heads. Let outcomes be considered unlikely with respect to an assumed distribution if their probability is lower than a significance threshold of 0.05.

A potential null hypothesis implying a one-tail test is “this coin is not biased toward heads”. Beware that, in this context, the word “tail” takes two meanings: either as outcome of a single toss, or as region of extremal values in a probability distribution.

Indeed, with a fair coin the probability of this experiment outcome is 1/2⁵=0.031, which would be even lower if the coin were biased in favour of tails. Therefore, the observations are not likely enough for the null hypothesis to hold, and the test refutes it. Since the coin is ostensibly neither fair nor biased toward tails, the conclusion of the experiment is that the coin is biased towards heads.

Alternatively, a null hypothesis implying a two-tailed test is “this coin is fair”. This one null hypothesis could be examined by looking out for either too many tails or too many heads in the experiments. The outcomes that would tend to refuse this null hypothesis are those with a large number of heads or a large number of tails, and our experiment with 5 heads would seem to belong to this class.

However, the probability of 5 tosses of the same kind, irrespective of whether these are head or tails, is twice as much as that of the 5-head occurrence singly considered. Hence, under this two-tailed null hypothesis, the observation receives a probability value of 0.061. Hence again, with the same significance threshold used for the one-tailed test (0.05), the same outcome is not statistically significant. Therefore, the two-tailed null hypothesis will be preserved in this case, not supporting the conclusion that the coin is biased towards heads reached with the single-tailed null hypothesis.

This example illustrates that the conclusion reached from a statistical test may depend on the precise formulation of the null and alternative hypotheses.

Fisher said, “the null hypothesis must be exact, that is free of vagueness and ambiguity, because it must supply the basis of the ‘problem of distribution,’ of which the test of significance is the solution”, implying a more restrictive domain for H₀. According to this view, the null hypothesis must be numerically exact—it must state that a particular quantity or difference is equal to a particular number. In classical science, it is most typically the statement that there is no effect of a particular treatment; in observations, it is typically that there is no difference between the value of a particular measured variable and that of a prediction.

Most statisticians believe that it is valid to state direction as a part of null hypothesis, or as part of a null hypothesis/alternative hypothesis pair. However, the results are not a full description of all the results of an experiment, merely a single result tailored to one particular purpose. For example, consider an H₀ that claims the population mean for a new treatment is an improvement on a well-established treatment with population mean = 10 (known from long experience), with the one-tailed alternative being that the new treatment’s mean > 10. If the sample evidence obtained through x-bar equals −200 and the corresponding t-test statistic equals −50, the conclusion from the test would be that there is no evidence that the new treatmnent is better than the existing one: it would not report that it is markedly worse, but that is not what this particular test is looking for. To overcome any possible ambiguity in reporting the result of the test of a null hypothesis, it is best to indicate whether the test was two-sided and, if one-sided, to include the direction of the effect being tested.

The statistical theory required to deal with the simple cases of directionality dealt with here, and more complicated ones, makes use of the concept of an unbiased test.

The directionality of hypotheses is not always obvious. The explicit null hypothesis of Fisher’s Lady tasting tea example was that the Lady had no such ability, which led to a symmetric probability distribution. The one-tailed nature of the test resulted from the one-tailed alternate hypothesis (a term not used by Fisher). The null hypothesis became implicitly one-tailed. The logical negation of the Lady’s one-tailed claim was also one-tailed. (Claim: Ability > 0; Stated null: Ability = 0; Implicit null: Ability ≤ 0).

Pure arguments over the use of one-tailed tests are complicated by the variety of tests. Some tests (for instance the χ² goodness of fit test) are inherently one-tailed. Some probability distributions are asymmetric. The traditional tests of 3 or more groups are two-tailed.

Advice concerning the use of one-tailed hypotheses has been inconsistent and accepted practice varies among fields. The greatest objection to one-tailed hypotheses is their potential subjectivity. A non-significant result can sometimes be converted to a significant result by the use of a one-tailed hypothesis (as the fair coin test, at the whim of the analyst). The flip side of the argument: One-sided tests are less likely to ignore a real effect. One-tailed tests can suppress the publication of data that differs in sign from predictions. Objectivity was a goal of the developers of statistical tests.

It is a common practice to use a one-tailed hypotheses by default. However, “If you do not have a specific direction firmly in mind in advance, use a two-sided alternative. Moreover, some users of statistics argue that we should always work with the two-sided alternative.”

One alternative to this advice is to use three-outcome tests. It eliminates the issues surrounding directionality of hypotheses by testing twice, once in each direction and combining the results to produce three possible outcomes. Variations on this approach have a history, being suggested perhaps 10 times since 1950.

Disagreements over one-tailed tests flow from the philosophy of science. While Fisher was willing to ignore the unlikely case of the Lady guessing all cups of tea incorrectly (which may have been appropriate for the circumstances), medicine believes that a proposed treatment that kills patients is significant in every sense and should be reported and perhaps explained. Poor statistical reporting practices have contributed to disagreements over one-tailed tests. Statistical significance resulting from two-tailed tests is insensitive to the sign of the relationship; Reporting significance alone is inadequate. “The treatment has an effect” is the uninformative result of a two-tailed test. “The treatment has a beneficial effect” is the more informative result of a one-tailed test. “The treatment has an effect, reducing the average length of hospitalization by 1.5 days” is the most informative report, combining a two-tailed significance test result with a numeric estimate of the relationship between treatment and effect. Explicitly reporting a numeric result eliminates a philosophical advantage of a one-tailed test. An underlying issue is the appropriate form of an experimental science without numeric predictive theories: A model of numeric results is more informative than a model of effect signs (positive, negative or unknown) which is more informative than a model of simple significance (non-zero or unknown); in the absence of numeric theory signs may suffice.

History of statistical tests

Statistical hypothesis testing § Origins and early controversy

The history of the null and alternative hypotheses is embedded in the history of statistical tests.

• Before 1925: There are occasional transient traces of statistical tests for centuries in the past, which provide early examples of null hypotheses. In the late 19th century statistical significance was defined. In the early 20th century important probability distributions were defined. Gossett and Pearson worked on specific cases of significance testing.
• 1925: Fisher published the first edition of Statistical Methods for Research Workers which defined the statistical significance test and made it a mainstream method of analysis for much of experimental science. The text was devoid of proofs and weak on explanations, but it was filled with real examples. It placed statistical practice in the sciences well in advance of published statistical theory.
• 1933: In a series of papers (published over a decade starting in 1928) Neyman & Pearson defined the statistical hypothesis test as a proposed improvement on Fisher’s test. The papers provided much of the terminology for statistical tests including alternative hypothesis and H₀ as a hypothesis to be tested using observational data (with H₁, H₂… as alternatives). Neyman did not use the term null hypothesis in later writings about his method.
• 1935: Fisher published the first edition of the book “The Design of Experiments” which introduced the null hypothesis (by example rather than by definition) and carefully explained the rationale for significance tests in the context of the interpretation of experimental results; see The Design of Experiments#Quotations regarding the null hypothesis.
• Following: Fisher and Neyman quarreled over the relative merits of their competing formulations until Fisher’s death in 1962. Career changes and World War II ended the partnership of Neyman and Pearson. The formulations were merged by relatively anonymous textbook writers, experimenters (journal editors) and mathematical statisticians without input from the principals. The subject today combines much of the terminology and explanatory power of Neyman & Pearson with the scientific philosophy and calculations provided by Fisher. Whether statistical testing is properly one subject or two remains a source of disagreement. Sample of two: One text refers to the subject as hypothesis testing (with no mention of significance testing in the index) while another says significance testing (with a section on inference as a decision). Fisher developed significance testing as a flexible tool for researchers to weigh their evidence. Instead, testing has become institutionalized. Statistical significance has become a rigidly defined and enforced criterion for the publication of experimental results in many scientific journals. In some fields, significance testing has become the dominant and nearly exclusive form of statistical analysis. As a consequence, the limitations of the tests have been exhaustively studied. Books have been filled with the collected criticism of significance testing.

• Counternull
• Estimation statistics
• Likelihood-ratio test
• Presumption of innocence
• Statistical hypothesis testing

The Null Hypothesis (This post was originally posted at Disjointed Thinking.)

One of the most accurate ways to describe my religious beliefs (or lack thereof) is by way of a concept known as the “null hypothesis”. Like most atheists, I do not claim that I know God does not exist. I merely claim that there is not enough evidence to justify belief in God. And the best way to illustrate this claim is through the null hypothesis. This is a statistical concept that is used for hypothesis testing in science. Because statistics is not a strong point for many people, I will try to explain it using a minimum of stats jargon; however, some will be required, and I will try to explain what each term means the best that I can. I really feel that this is an important concept to understand when one is trying to assess evidence claims (which happens to us all the time). So hang on for the ride!

Basic Statistics

When I measure a certain phenomenon, such as people’s height, there will always be some variability in the results. And for many phenomena, this variability will result in a bell-shaped curve known as a “normal distribution”. There are some very interesting properties of the normal distribution, but what is important here is that the majority of the cases will be clustered around the mean (the statistical word for “average”), and then fewer cases will occur further away from the mean. So for instance, the mean height for a Canadian adult is about 5’8″ for men and 5’3″ for women.¹ So if I randomly selected a Canadian man, he would be most likely to have a height somewhere around 5’8″. Or if I wanted to be more precise, I could say that he is likely to fall between about 4’11” and 6’5″. I’d be very surprised if this randomly selected person turned out to be 8 feet tall. There are very few people who are that tall, so it would be very unusual to have chosen them. So the normal distribution tells us that the most frequent cases occur around the mean, and that cases occurring further away are less frequent.

Hypothesis Testing

So what would I do if someone told me of a town in rural Alberta where all the adult townspeople were over 7 feet tall? I would likely be very skeptical. Such a thing is very unlikely, isn’t it? It’s unusual to find even one person over 7 feet tall, let alone an entire town of both men and women over 7 feet tall! But to be a good scientist, I should hold onto my skepticism but remain open to the possibility that such a strange case is indeed true. I would want to head over to this town and start measuring. But let’s say I don’t have the resources to measure every single individual in the town. I might measure 40 or 50 of them. And perhaps the person who told me this story was exaggerating a little bit, and some were below 7 feet. But I might still ask, “Are the people in this town significantly taller than the general population?” And that is a great question with which to use hypothesis testing.

When scientists want to test a hypothesis, they must come up with two different hypotheses to compare. One of these (known as the alternate hypothesis) is the one they would ideally like to be confirmed; in my case, it is this: “The people in this rural town are statistically taller than the general population.” The other hypothesis is known as the null hypothesis, and in my case it would be the following: “There is no difference in the average height of the people in this rural town and the general population.” But why do we need to compare these two things? Why not just see if the alternate hypothesis is confirmed? The reason is because, like I mentioned earlier, phenomena always have some variability. If I measured the townspeople and found out that they averaged 6’8″, that doesn’t mean that every single person was 6’8″ tall. Some were taller, and some were shorter. So how would I know whether I was finding someactual difference between the townspeople and the general population, or if I just happened to select the 50 tallest people in the town? Hypothesis testing helps us to determine whether we just have a bad sample, or if the normal distribution for the town is actually different from the normal distribution for the general population. Or to put it another way, it helps us distinguish between real differences and random fluctuation. The null hypothesis says, “This is just random fluctuation,” and the alternate hypothesis says, “No, this is a real difference.” Scientists support the alternate hypothesis indirectly by disconfirming the null hypothesis. If the data that scientists collect don’t fit with the null hypothesis, then they have better evidence to support the idea that the alternate hypothesis is true. On the other hand, if the data do fit with the null hypothesis, this doesn’t necessarily mean that the null hypothesis is true; it just means that the data do not contradict it.

The Role of Evidence

Another way to look at the concept of the null hypothesis is to use the analogy of a court case. In the modern justice system, the defendant is considered innocent until proven guilty. The prosecution must provide sufficient evidence to prove his or her guilt. In some ways, this works similar to the null hypothesis. The null hypothesis is assumed to be true until sufficient evidence is provided to demonstrate otherwise. The evidence in favour of the alternate hypothesis must outweigh the evidence in favour of the null hypothesis.² If I want to prove the statement that the Albertan townspeople are significantly taller than the general population, I have to have sufficient evidence that my measurements are not just a reflection of random variability and then add more evidence suggesting that they are actually due to some real difference in height (whatever the cause of this unusually tall town might be).

The null hypothesis works very similarly when it comes to other types of claims. The statement, “God exists”, is a positive claim about the existence of an entity. So in this case, the null hypothesis would be, “God does not exist.” This works the same as any other positive claim: “Unicorns exist” vs. “Unicorns do not exist”, “It rained yesterday” vs. “It did not rain yesterday”, “Black swans exist” vs. “Black swans do not exist”, and so on. If one wants to prove the truth of these statements, they must provide evidence which is sufficiently inconsistent with the null hypothesis. If I try to prove that it rained yesterday by saying that I held my hand out the window and felt splashes of water, this might be good evidence, unless someone points out that I have a leaky eaves-trough directly above my window. In other words, if my evidence can be shown to be perfectly consistent with the idea that it did not, in fact, rain yesterday, then it should not be used to support the idea that it did rain yesterday. I should provide other evidence to support my claim. Or if I mention that I saw a black swan, but upon further examination it turns out to be a black duck, this is no longer evidence that black swans exist. The fact that the evidence must be thrown out does not prove that black swans don’t exist, but it no longer proves that they do. And if there were absolutely no good evidence to prove that black swans exist, why would anyone believe in them?

The claim that God exists is exactly the same as all these other claims. The burden of proof is always on the person making the positive claim. That person must provide good evidence to demonstrate that the claim is true. And if the evidence they provide is entirely consistent with the null hypothesis (that God does not exist), then the evidence is no good. Again, this does not prove that God does not exist, but if there is absolutely no good evidence to prove that God exists, why would anyone believe in him? This is why the null hypothesis is a crucial concept to grasp. Saying “The evidence does not prove that God exists” is entirely different than saying “The evidence proves that God does not exist”. The null hypothesis is a safe bet that requires other hypotheses to prove themselves to be true before one believes in them. If I went to a random rural town in Alberta, my first assumption would be that their average height is about the same as the average height of the general population. This doesn’t mean that it actually is the case that their average heights are the same, but I have no prior reason to think so until I have evidence to prove otherwise. It would be silly to point to an entirely random town for which one has no prior knowledge and say, “That town is filled with giants.” And it would be even sillier to take measurements of the townspeople, see that they have an average height similar to the general population, and still say, “That town is filled with giants.” As far as I am concerned, however, that is what most believers in God do.

Conclusion

I don’t intend to get into an examination of the evidence for and against the existence of God. I have written an entire ten-part series about just that. The intent of this article was to develop a process for assessing whether God exists. The general process is to assume that God does not exist until one finds sufficient evidence to support the claim that he does. To do otherwise is to choose a position that one likes before even taking a look at the evidence. (It’s like assuming the town is full of giants before even seeing a townsperson.) In many cases where this happens, people do this for emotional reasons. They have some desire to believe a certain thing, and so they make up their mind before they even take a look at the evidence. Such a process is irrational, especially since humans have “tendencies”. We often see patterns that are not there (like people who develop superstitions, for example); we seek out evidence to support the beliefs that we already hold and ignore disconfirming evidence, instead of trying to objectively assess all the evidence; and we often reach conclusions that we like and then make up justifications for them afterwards. The only way to avoid these tendencies is to acknowledge that we suffer from them and then try to minimize them through the use of rigorous processes such as hypothesis testing.

So when I say that I am a “null hypothesis atheist”, I mean that the evidence for God’s existence is either a) faulty, b) illusory, or c) consistent with the null hypothesis that God does not exist. I do not make the statement, “Therefore, God does not exist.” Instead, I simply say, “There is no good evidence to believe that God exists, and I don’t believe in things with no good evidence.” Sure, God might be out there, hiding behind some distant spiral galaxy or outside of space and time altogether. But I will take the conservative path that tries to minimize irrationality, because such a path is the best process we’ve developed to distinguish fact from fiction.

Notes:

1. I should note that human height is not technically normally distributed, but rather negatively skewed. I’m using this example for illustrative purposes.
2. Any statisticians reading this are probably cringing at this point. I understand that this is a distortion of how hypothesis testing actually works. But as an admittedly imperfect analogy, I still think it works well enough for providing non-statisticians with an understanding of the basic reasoning behind the null/alternate hypotheses.

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People don’t commonly teach religious history, even that of their own claimed religion. No, rather they teach a limited “pro their religion” history of their religion from a religious perspective favorable to the religion of choice. 

Damien Marie AtHope’s Art

Do you truly think “Religious Belief” is only a matter of some personal choice?

Do you not see how coercive one’s world of choice is limited to the obvious hereditary belief, in most religious choices available to the child of religious parents or caregivers? Religion is more commonly like a family, culture, society, etc. available belief that limits the belief choices of the child and that is when “Religious Belief” is not only a matter of some personal choice and when it becomes hereditary faith, not because of the quality of its alleged facts or proposed truths but because everyone else important to the child believes similarly so they do as well simply mimicking authority beliefs handed to them. Because children are raised in religion rather than being presented all possible choices but rather one limited dogmatic brand of “Religious Belief” where children only have a choice of following the belief as instructed, and then personally claim the faith hereditary belief seen in the confirming to the belief they have held themselves all their lives. This is obvious in statements asked and answered by children claiming a faith they barely understand but they do understand that their family believes “this or that” faith, so they feel obligated to believe it too. While I do agree that “Religious Belief” should only be a matter of some personal choice, it rarely is… End Hereditary Religion!

Opposition to Imposed Hereditary Religion

Damien Marie AtHope’s Art

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Animism: Respecting the Living World by Graham Harvey 

“How have human cultures engaged with and thought about animals, plants, rocks, clouds, and other elements in their natural surroundings? Do animals and other natural objects have a spirit or soul? What is their relationship to humans? In this new study, Graham Harvey explores current and past animistic beliefs and practices of Native Americans, Maori, Aboriginal Australians, and eco-pagans. He considers the varieties of animism found in these cultures as well as their shared desire to live respectfully within larger natural communities. Drawing on his extensive casework, Harvey also considers the linguistic, performative, ecological, and activist implications of these different animisms.” ref

Damien Marie AtHope’s Art

We are like believing machines we vacuum up ideas, like Velcro sticks to almost everything. We accumulate beliefs that we allow to negatively influence our lives, often without realizing it. Our willingness must be to alter skewed beliefs that impend our balance or reason, which allows us to achieve new positive thinking and accurate outcomes.

Damien Marie AtHope’s Art

Damien Marie AtHope’s Art

Damien Marie AtHope’s Art

Damien Marie AtHope’s Art

Damien Marie AtHope’s Art

Damien Marie AtHope’s Art

Damien Marie AtHope’s Art

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Damien Marie AtHope’s Art

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Damien Marie AtHope’s Art

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Low Gods “Earth” or Tutelary deity and High Gods “Sky” or Supreme deity

“An Earth goddess is a deification of the Earth. Earth goddesses are often associated with the “chthonic” deities of the underworld. Ki and Ninhursag are Mesopotamian earth goddesses. In Greek mythology, the Earth is personified as Gaia, corresponding to Roman Terra, Indic Prithvi/Bhūmi, etc. traced to an “Earth Mother” complementary to the “Sky Father” in Proto-Indo-European religion. Egyptian mythology exceptionally has a sky goddess and an Earth god.” ref

“A mother goddess is a goddess who represents or is a personification of nature, motherhood, fertility, creation, destruction or who embodies the bounty of the Earth. When equated with the Earth or the natural world, such goddesses are sometimes referred to as Mother Earth or as the Earth Mother. In some religious traditions or movements, Heavenly Mother (also referred to as Mother in Heaven or Sky Mother) is the wife or feminine counterpart of the Sky father or God the Father.” ref

“Any masculine sky god is often also king of the gods, taking the position of patriarch within a pantheon. Such king gods are collectively categorized as “sky father” deities, with a polarity between sky and earth often being expressed by pairing a “sky father” god with an “earth mother” goddess (pairings of a sky mother with an earth father are less frequent). A main sky goddess is often the queen of the gods and may be an air/sky goddess in her own right, though she usually has other functions as well with “sky” not being her main. In antiquity, several sky goddesses in ancient Egypt, Mesopotamia, and the Near East were called Queen of Heaven. Neopagans often apply it with impunity to sky goddesses from other regions who were never associated with the term historically. The sky often has important religious significance. Many religions, both polytheistic and monotheistic, have deities associated with the sky.” ref

“In comparative mythology, sky father is a term for a recurring concept in polytheistic religions of a sky god who is addressed as a “father”, often the father of a pantheon and is often either a reigning or former King of the Gods. The concept of “sky father” may also be taken to include Sun gods with similar characteristics, such as Ra. The concept is complementary to an “earth mother“. “Sky Father” is a direct translation of the Vedic Dyaus Pita, etymologically descended from the same Proto-Indo-European deity name as the Greek Zeûs Pater and Roman Jupiter and Germanic Týr, Tir or Tiwaz, all of which are reflexes of the same Proto-Indo-European deity’s name, *Dyēus Ph₂tḗr. While there are numerous parallels adduced from outside of Indo-European mythology, there are exceptions (e.g. In Egyptian mythology, Nut is the sky mother and Geb is the earth father).” ref

Tutelary deity

“A tutelary (also tutelar) is a deity or spirit who is a guardian, patron, or protector of a particular place, geographic feature, person, lineage, nation, culture, or occupation. The etymology of “tutelary” expresses the concept of safety and thus of guardianship. In late Greek and Roman religion, one type of tutelary deity, the genius, functions as the personal deity or daimon of an individual from birth to death. Another form of personal tutelary spirit is the familiar spirit of European folklore.” ref

“A tutelary (also tutelar) in Korean shamanism, jangseung and sotdae were placed at the edge of villages to frighten off demons. They were also worshiped as deities. Seonangshin is the patron deity of the village in Korean tradition and was believed to embody the Seonangdang. In Philippine animism, Diwata or Lambana are deities or spirits that inhabit sacred places like mountains and mounds and serve as guardians. Such as: Maria Makiling is the deity who guards Mt. Makiling and Maria Cacao and Maria Sinukuan. In Shinto, the spirits, or kami, which give life to human bodies come from nature and return to it after death. Ancestors are therefore themselves tutelaries to be worshiped. And similarly, Native American beliefs such as Tonás, tutelary animal spirit among the Zapotec and Totems, familial or clan spirits among the Ojibwe, can be animals.” ref

“A tutelary (also tutelar) in Austronesian beliefs such as: Atua (gods and spirits of the Polynesian peoples such as the Māori or the Hawaiians), Hanitu (Bunun of Taiwan‘s term for spirit), Hyang (Kawi, Sundanese, Javanese, and Balinese Supreme Being, in ancient Java and Bali mythology and this spiritual entity, can be either divine or ancestral), Kaitiaki (New Zealand Māori term used for the concept of guardianship, for the sky, the sea, and the land), Kawas (mythology) (divided into 6 groups: gods, ancestors, souls of the living, spirits of living things, spirits of lifeless objects, and ghosts), Tiki (Māori mythology, Tiki is the first man created by either Tūmatauenga or Tāne and represents deified ancestors found in most Polynesian cultures). ” ref, ref, ref, ref, ref, ref, ref

Mesopotamian Tutelary Deities can be seen as ones related to City-States 

“Historical city-states included Sumerian cities such as Uruk and Ur; Ancient Egyptian city-states, such as Thebes and Memphis; the Phoenician cities (such as Tyre and Sidon); the five Philistine city-states; the Berber city-states of the Garamantes; the city-states of ancient Greece (the poleis such as Athens, Sparta, Thebes, and Corinth); the Roman Republic (which grew from a city-state into a vast empire); the Italian city-states from the Middle Ages to the early modern period, such as Florence, Siena, Ferrara, Milan (which as they grew in power began to dominate neighboring cities) and Genoa and Venice, which became powerful thalassocracies; the Mayan and other cultures of pre-Columbian Mesoamerica (including cities such as Chichen Itza, Tikal, Copán and Monte Albán); the central Asian cities along the Silk Road; the city-states of the Swahili coast; Ragusa; states of the medieval Russian lands such as Novgorod and Pskov; and many others.” ref

“The Uruk period (ca. 4000 to 3100 BCE; also known as Protoliterate period) of Mesopotamia, named after the Sumerian city of Uruk, this period saw the emergence of urban life in Mesopotamia and the Sumerian civilization. City-States like Uruk and others had a patron tutelary City Deity along with a Priest-King.” ref

“Chinese folk religion, both past, and present, includes myriad tutelary deities. Exceptional individuals, highly cultivated sages, and prominent ancestors can be deified and honored after death. Lord Guan is the patron of military personnel and police, while Mazu is the patron of fishermen and sailors. Such as Tu Di Gong (Earth Deity) is the tutelary deity of a locality, and each individual locality has its own Earth Deity and Cheng Huang Gong (City God) is the guardian deity of an individual city, worshipped by local officials and locals since imperial times.” ref

“A tutelary (also tutelar) in Hinduism, personal tutelary deities are known as ishta-devata, while family tutelary deities are known as Kuladevata. Gramadevata are guardian deities of villages. Devas can also be seen as tutelary. Shiva is the patron of yogis and renunciants. City goddesses include: Mumbadevi (Mumbai), Sachchika (Osian); Kuladevis include: Ambika (Porwad), and Mahalakshmi. In NorthEast India Meitei mythology and religion (Sanamahism) of Manipur, there are various types of tutelary deities, among which Lam Lais are the most predominant ones. Tibetan Buddhism has Yidam as a tutelary deity. Dakini is the patron of those who seek knowledge.” ref

“A tutelary (also tutelar) The Greeks also thought deities guarded specific places: for instance, Athena was the patron goddess of the city of Athens. Socrates spoke of hearing the voice of his personal spirit or daimonion:

You have often heard me speak of an oracle or sign which comes to me … . This sign I have had ever since I was a child. The sign is a voice which comes to me and always forbids me to do something which I am going to do, but never commands me to do anything, and this is what stands in the way of my being a politician.” ref

“Tutelary deities who guard and preserve a place or a person are fundamental to ancient Roman religion. The tutelary deity of a man was his Genius, that of a woman her Juno. In the Imperial era, the Genius of the Emperor was a focus of Imperial cult. An emperor might also adopt a major deity as his personal patron or tutelary, as Augustus did Apollo. Precedents for claiming the personal protection of a deity were established in the Republican era, when for instance the Roman dictator Sulla advertised the goddess Victory as his tutelary by holding public games (ludi) in her honor.” ref

“Each town or city had one or more tutelary deities, whose protection was considered particularly vital in time of war and siege. Rome itself was protected by a goddess whose name was to be kept ritually secret on pain of death (for a supposed case, see Quintus Valerius Soranus). The Capitoline Triad of Juno, Jupiter, and Minerva were also tutelaries of Rome. The Italic towns had their own tutelary deities. Juno often had this function, as at the Latin town of Lanuvium and the Etruscan city of Veii, and was often housed in an especially grand temple on the arx (citadel) or other prominent or central location. The tutelary deity of Praeneste was Fortuna, whose oracle was renowned.” ref

“The Roman ritual of evocatio was premised on the belief that a town could be made vulnerable to military defeat if the power of its tutelary deity were diverted outside the city, perhaps by the offer of superior cult at Rome. The depiction of some goddesses such as the Magna Mater (Great Mother, or Cybele) as “tower-crowned” represents their capacity to preserve the city. A town in the provinces might adopt a deity from within the Roman religious sphere to serve as its guardian, or syncretize its own tutelary with such; for instance, a community within the civitas of the Remi in Gaul adopted Apollo as its tutelary, and at the capital of the Remi (present-day Rheims), the tutelary was Mars Camulus.” ref 

Household deity (a kind of or related to a Tutelary deity)

“A household deity is a deity or spirit that protects the home, looking after the entire household or certain key members. It has been a common belief in paganism as well as in folklore across many parts of the world. Household deities fit into two types; firstly, a specific deity – typically a goddess – often referred to as a hearth goddess or domestic goddess who is associated with the home and hearth, such as the ancient Greek Hestia.” ref

“The second type of household deities are those that are not one singular deity, but a type, or species of animistic deity, who usually have lesser powers than major deities. This type was common in the religions of antiquity, such as the Lares of ancient Roman religion, the Gashin of Korean shamanism, and Cofgodas of Anglo-Saxon paganism. These survived Christianisation as fairy-like creatures existing in folklore, such as the Anglo-Scottish Brownie and Slavic Domovoy.” ref

“Household deities were usually worshipped not in temples but in the home, where they would be represented by small idols (such as the teraphim of the Bible, often translated as “household gods” in Genesis 31:19 for example), amulets, paintings, or reliefs. They could also be found on domestic objects, such as cosmetic articles in the case of Tawaret. The more prosperous houses might have a small shrine to the household god(s); the lararium served this purpose in the case of the Romans. The gods would be treated as members of the family and invited to join in meals, or be given offerings of food and drink.” ref

“In many religions, both ancient and modern, a god would preside over the home. Certain species, or types, of household deities, existed. An example of this was the Roman Lares. Many European cultures retained house spirits into the modern period. Some examples of these include:

• Brownie (Scotland and England) or Hob (England) / Kobold (Germany) / Goblin / Hobgoblin
• Domovoy (Slavic)
• Nisse (Norwegian or Danish) / Tomte (Swedish) / Tonttu (Finnish)
• Húsvættir (Norse)” ref

“Although the cosmic status of household deities was not as lofty as that of the Twelve Olympians or the Aesir, they were also jealous of their dignity and also had to be appeased with shrines and offerings, however humble. Because of their immediacy they had arguably more influence on the day-to-day affairs of men than the remote gods did. Vestiges of their worship persisted long after Christianity and other major religions extirpated nearly every trace of the major pagan pantheons. Elements of the practice can be seen even today, with Christian accretions, where statues to various saints (such as St. Francis) protect gardens and grottos. Even the gargoyles found on older churches, could be viewed as guardians partitioning a sacred space.” ref

“For centuries, Christianity fought a mop-up war against these lingering minor pagan deities, but they proved tenacious. For example, Martin Luther‘s Tischreden have numerous – quite serious – references to dealing with kobolds. Eventually, rationalism and the Industrial Revolution threatened to erase most of these minor deities, until the advent of romantic nationalism rehabilitated them and embellished them into objects of literary curiosity in the 19th century. Since the 20th century this literature has been mined for characters for role-playing games, video games, and other fantasy personae, not infrequently invested with invented traits and hierarchies somewhat different from their mythological and folkloric roots.” ref

“In contradistinction to both Herbert Spencer and Edward Burnett Tylor, who defended theories of animistic origins of ancestor worship, Émile Durkheim saw its origin in totemism. In reality, this distinction is somewhat academic, since totemism may be regarded as a particularized manifestation of animism, and something of a synthesis of the two positions was attempted by Sigmund Freud. In Freud’s Totem and Taboo, both totem and taboo are outward expressions or manifestations of the same psychological tendency, a concept which is complementary to, or which rather reconciles, the apparent conflict. Freud preferred to emphasize the psychoanalytic implications of the reification of metaphysical forces, but with particular emphasis on its familial nature. This emphasis underscores, rather than weakens, the ancestral component.” ref

“William Edward Hearn, a noted classicist, and jurist, traced the origin of domestic deities from the earliest stages as an expression of animism, a belief system thought to have existed also in the neolithic, and the forerunner of Indo-European religion. In his analysis of the Indo-European household, in Chapter II “The House Spirit”, Section 1, he states:

The belief which guided the conduct of our forefathers was … the spirit rule of dead ancestors.” ref

“In Section 2 he proceeds to elaborate:

It is thus certain that the worship of deceased ancestors is a vera causa, and not a mere hypothesis. …

In the other European nations, the Slavs, the Teutons, and the Kelts, the House Spirit appears with no less distinctness. … [T]he existence of that worship does not admit of doubt. … The House Spirits had a multitude of other names which it is needless here to enumerate, but all of which are more or less expressive of their friendly relations with man. … In [England] … [h]e is the Brownie. … In Scotland this same Brownie is well known. He is usually described as attached to particular families, with whom he has been known to reside for centuries, threshing the corn, cleaning the house, and performing similar household tasks. His favorite gratification was milk and honey.” ref

Damien Marie AtHope’s Art

Expressions of Atheistic Thinking:

• Around 2,600 years ago, Ajita Kesakambali, ancient Indian philosopher, who is the first known proponent of Indian materialism. ref
• Around 2,535 to 2,475 years ago, Heraclitus, Greek pre-Socratic philosopher, a native of the Greek city Ephesus, Ionia, on the coast of Anatolia, also known as Asia Minor or modern Turkey. ref
• Around 2,500 to 2,400 years ago, according to The Story of Civilization book series certain African pygmy tribes have no identifiable gods, spirits, or religious beliefs or rituals, and even what burials accrue are without ceremony. ref
• Around 2,490 to 2,430 years ago, Empedocles, Greek pre-Socratic philosopher and a citizen of Agrigentum, a Greek city in Sicily. ref
• Around 2,460 to 2,370 years ago, Democritus, Greek pre-Socratic philosopher considered to be the “father of modern science” possibly had some disbelief amounting to atheism. ref
• Around 2,399 years ago or so, Socrates, a famous Greek philosopher was tried for sinfulness by teaching doubt of state gods. ref
• Around 2,341 to 2,270 years ago, Epicurus, a Greek philosopher known for composing atheistic critics and famously stated, “Is God willing to prevent evil, but not able? Then he is not omnipotent. Is he able, but not willing? Then he is malevolent. Is he both able and willing? Then whence cometh evil? Is he neither able nor willing? Then why call him god?” ref

This last expression by Epicurus, seems to be an expression of Axiological Atheism. To understand and utilize value or actually possess “Value Conscious/Consciousness” to both give a strong moral “axiological” argument (the problem of evil) as well as use it to fortify humanism and positive ethical persuasion of human helping and care responsibilities. Because value-blindness gives rise to sociopathic/psychopathic evil.

Damien Marie AtHope’s Art

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Damien Marie AtHope’s Art

Damien Marie AtHope’s Art

Damien Marie AtHope’s Art

Damien Marie AtHope (Said as “At” “Hope”)/(Autodidact Polymath but not good at math):

Axiological Atheist, Anti-theist, Anti-religionist, Secular Humanist, Rationalist, Writer, Artist, Jeweler, Poet, “autodidact” Philosopher, schooled in Psychology, and “autodidact” Armchair Archaeology/Anthropology/Pre-Historian (Knowledgeable in the range of: 1 million to 5,000/4,000 years ago). I am an anarchist socialist politically. Reasons for or Types of Atheism

My Website, My Blog, & Short-writing or Quotes, My YouTube, Twitter: @AthopeMarie, and My Email: damien.marie.athope@gmail.com