Gender - Universitetet i oslofolk.uio.no/trondr/yt_survey_full.pdf · Reincarnation 2 (

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Gender

Female Male

Abrahamic 16 29Reli gious Agnostic 9 20 ident ity Atheist 32 194

Other 18 40

H0: Pr(row i and column j)=Pr(row i)*Pr(column j)

H1: Anything goes as long as the probabilities sum to one

Example of zero-hypothesis:

Pr(female and atheist)=Pr(female)Pr(atheist)

Pr(data | H1)Bayes factor: B= --------------------- Pr(data | H0)

(Where the parameters in H0 and H1 have been summed (integrated) over, using theirprior distribution.)

Bayes formula:

1Pr(H0 | D)= --------------------------- 1 + Pr(H1)/Pr(H0) B 1= ------ if Pr(H0)=Pr(H1)=50% 1+B

Me:

Gunel & Dickey (1974) – Bayes factors for independence in contingency tables, Biometrika, Vol 61, No 3, pp 545-557

B x∗∗∣all marginsH1 vs H0=B IJ a∗∗∑'g x∗∗ '∣x.. , a∗∗/{B IJ x∗∗a∗∗ x..x∗ . x..x.∗}

where * is the set of possible indexes,a∗∗ is the prior Dirichlet-parameters, with ai , j=1 being a flat prior,

BK y∗≡∏k=1

K yk

∑k=1

Kyk

and

g x∗∗∣x.. , a= x..x∗∗B IJ x∗∗a∗∗/B IJ a∗∗

is the Dirichlet-multinomial distribution function

B x∗∗∣all margins H1 vs H0=1 / x..x∗∗ ∫pij≥0,∑ pij=1

∏ j=1

Jp ., jx . , j∏i=1

Ipi , .x i, .∏i , j

dpi , j

where x..x∗∗= x..∏i , j x i , j

and a '.' stand for sum over the index .

Frequentist test: calculate the maximal probability forgetting something as extreme as you did, given that H0 is true. H1 defines what extreme means.

Reject when this goes below a given significance level. The lower the level, the more seldom do you want to reject a correct zero-hypothesis. Usual; 5%, 1% or 0.1%.

If H0 is rejected with a significance level of 5%, it is rejected with a confidence of 95%.

Frequentist test: calculate the maximal probability forgetting something as extreme as you did, given that H0 is true. H1 defines what extreme means.

Reject when this goes below a given significance level. The lower the level, the more seldom do you want to reject a correct zero-hypothesis. Usual; 5%, 1% or 0.1%.

If H0 is rejected with a significance level of 5%, it is rejected with a confidence of 95%.

Bonferroni: If a significance level of p % is wanted for a string of k tests, we put the individual significance level to p/k %.

Two frequentist tests:

1) Fisher's exact method. Distribution under H0 of data conditioned on the row and column sums, is hyper-geometric.Use that to calculate the p-value, identifying extremes throughthe alternative (dependency) hypothesis.

2) Pearson's Chi-square method. Use central limit theorem to justify that the sum over cells of (observed-estimate)2/estimateis approximately chi-square distributed with (I-1)(J-1)-1 degrees of freedom. Calculate the probability to get a result higher than you did, using that assumption. Only gives reliable results whenthe expected count is larger than 5 (and preferably larger than 10, too).

Joining of groups in order to make the calculationsmanageable:


Countries divided into USA and the rest



Religious identity divided into: Abrahamic, agnostic, atheistand 'other'. Same for religious upbringing.




Belief in creationism, evolution, big bang etc. divided intoyes/no for each separate belief.




Belief in creationism, evolution, big bang etc. divided intoyes/no for each separate belief.

Should also join groups in the feminism issue, but unsurehow to precede. (Alternatives: yes, no, male supporter of equal rights, non-answer)

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Gender

Female Male

Abrahamic 16 29Reli gious Agnostic 9 20 ident ity Atheist 32 194

Other 18 40

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Gender

Female Male

Abrahamic 16 (9,4) 29 (35.5)Reli [2.14] [-1.10]gious Agnostic 9 ( 6.07) 20 (22.9)ident [1.18] [-0.62]ity Atheist 32 (47.3) 194 (178.5) [-2.23] [1.14]

Other 18 (12.1) 40 (45.8) [1.68] [-0.86]

Chi-square, pval=0.05% Fisher, pval=0.05%

Bayesian: B=26.35 Pr(H0|D)=3.65%

Religious identity #gro Chi-square Fisher's Bayes- Pr(H0|D) Conclusionversus ups p-value p-value factor (Pr(H0)=0.5)

Feminism 4 (18%) 20% ≈0.0083 ≈99.2% No dependency detected

Country 2 64.2% 64.6% 0.012 98.8% No dependency detected. Bayesian evidence for independence.

Age group 5 (58%) ------- ≈4*10-5 ≈100% No dependency detected. Too many groups.

Sexual 4 (0.096%) 0.2% ≈ ≈ % 2 33 Indications of dependency * ,orientation but in the end

.inconclusive

Switch religion? 3 6*10-6 4.3*10-6 ≈2330 ≈0.004% Strong indications of *** *** dependency. More abrahamic followers answering 'never' than expected. Agnostics switching more than exp.

Religious 4 (5.3%) 3.7% 0.018 98.2% Inconclusive. Bayesian testupbringing * unstable suggests evidence for independence, but it's very unrealistic to say Pr(H0)=0.5 before data, here.


Parents know? 2 (0.90%) 0.13% 10.72 8.5% Dependency probably detected. Less abrahamic answering 'no' than exp. Speak with 5 (52%) --------- ≈5.6*10-5 ≈100% Too many groups!Parents? But no dependency seen.

Friends gender 5 (35%) -------- ≈0.00038 ≈99.96% Too many groups! But no dependency seen.

Friends religion 5 (34%) ---------- ≈9*10-5 99.999% No indication of dependency. Too many groups?

Supernatural 2 3.6*10-10 2.8*10-10 39933527 2.5*10-8 Clear case of dependencyexperiences? *** *** More 'other' and less atheists answering 'yes' than exp.

Tell about 2 (12%) 7.2% 1.03 49% No clear evidence ofsupernatural dependency. People experience? answering 'no' to the previous removed.

Own videos? 3 15.4% 13.4% 0.016 96.6% Evidence for independence.


Videos with 3 (2.2%) 2.1% ≈0.64 61% Faint indications of religious topic? * dependence but nowhere near conclusive.

Discuss religion? 5 (34%) -------- ≈0.0055 ≈99.4% Too many groups! No dependency found.

Judge concerns? 2 0.05% 0.06% 27.9 3.46% Probably dependency. More ** ** abrahamic answering 'yes' than expected.

Fear judgement? 4 (3.6%) -------- ≈0.016 ≈98.4% Too many groups, but indicates independence

Running (against 2 76.7% 75.7% 0.010 99.0% Indicates independenceclock or people)

Contest attitude 2 (79.5%) 71.0% 0.138 98.6% Indicates independence


Creationism 2 (<2.2*10-16) <2.2*10-16 4.6*1025 2.17*10-27 Clear case of dependence. (yes/no) *** More abrahamic answering yes than exp.

Evolution 2 (<2.2*10-16) 8.5*10-15 2.2*1012 4.5*10-13 Clear case of dependence.(yes/no) *** More abrahamic answering no than exp.

Big bang 2 (2.6*10-13) 2.0*10-12 6.0*109 1.7*10-10 Clear case of dependence. *** More abrahamic answering no than exp.

Abiogenesis 2 4.5*10-15 <2.2*10-16 2.8*1014 3.6*10-15 Clear case of dependence. *** *** Less abrahamic answering yes than exp.

Life after death 2 <2.2*10-16 <2.2*10-16 2.3*1035 4.3*10-36 Clear case of dependence. *** *** More abrahamic answering yes than exp. (Curiously enough: 8 'no's)


Reincarnation 2 (<2.2*10-16)<2.2*10-16 1.4*1014 7.1*10-15 Clear case of dependence. *** More 'other' answering yes than exp.

Age of Earth 5 (<2.2*10-16) 5.3*10-14 high Low? Clear case of dependence. *** but More abrahamic answering unstable '25000-10mill' and '5000- 10000' than expected.

Attitude towards 3 (<2.2*10-16) 1.4*10-14 ≈1.46*1012 ≈6.84*1013 Clear case of dependence. stemcell *** More abrahamic opposedresearch than expected.

Education 9 (8.7%) -------- --------- ------------ Way too many groups, but chi-square does not indicate dependency.

Education of parents Same results


Stance towards 5 (<2.2*10-16) ---------- High but Low? Way too many groups. mastrubation unstable Approximate method suggests dependency. Exact methods used only on atheists vs abrahamic followers clearly indicates dependency.

Kids? 4 (10%) --------- ≈0.0032 ≈99.7% Too many groups. No suggestion of dependency.

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Religious upbringing

Abrahamic Agnostic Atheist Other

Abrahamic 38 (33.1) 1 (2.7) 0 (2.1) 6 (7.0)Reli [0.85] [-1.06] [-1.46] [-0.39]gious Agnostic 28 (21.3) 1 (1.8) 0 (1.4) 0 (4.5)ident [1.45] [-0.58] [-1.17] [-2.13]ity Atheist 158 (166) 17(13.8) 12(10.7) 39 (35.4) [-0.62] [0.83] [0.39] [0.61]

Other 39 (42.6) 3 (3.6) 5 (2.8) 11 (9.1) [-0.55] [-0.30] [1.35] [0.64]


Bayesian: B≈0.018 Pr(H0|D)≈81.6%

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Evolution

No Yes

Abrahamic 20 (4,0) 25 (41.0)Reli [7.96] [-2.50]gious Agnostic 1 ( 2.6) 28 (26.4)ident [-0.99] [0.31]ity Atheist 3 (20.2) 223 (205.8) [-3.83] [1.20]

Other 8 (5.2) 50 (52.8) [1.24] [-0.38]

Chi-square, pval<2.2*10-16 Fisher, pval=8.5*10-15

Bayesian: B=2.2*1012 Pr(H0|D)=4.55*10-13

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Feminism

Male supporter No Yes

Abrahamic 25 (27.4) 6 (2.4) 11 (12.2) Reli [-0.45] [2.32] [-0.35] gious Agnostic 16 (18.2) 2 (1.6) 10 (8.2) ident [-0.52] [0.31] [0.64] ity Atheist 153 (146) 9 (12.8) 62 (65.3) [0.59] [-1.06] [-0.41]

Other 34 (36.5) 3 (3.2) 19 (16.3) [-0.41] [-0.11] [0.66]


Bayesian: B≈0.083 Pr(H0|D)≈99.2%

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Country

not USA USA

Abrahamic 15 (18.7) 30 (26.3) Reli [-0.85] [0.72] gious Agnostic 12 (12.0) 17 (17.0) ident [-0.01] [0.01] ity Atheist 98 (93.4) 127 (131.6) [0.47] [-0.40]

Other 22 (22.8) 33 (32.2) [-0.18] [-0.15]



Switch religion?

Multiple times Never Once

Abrahamic 2 (10.1) 31 (17.5) 12 (17.5) Reli [-2.54] [3.24] [-1.31] gious Agnostic 13 (6.5) 4 (11.3) 12 (11.3) ident [2.56] [-2.16] [0.22] ity Atheist 47 (50.5) 88(87.7) 91 (87.7) [-0.49] [0.02] [0.34]

Other 18 (13.0) 16 (22.5) 24 (22.5) [1.40] [-1.37] [0.31]


Bayesian: B≈2330 Pr(H0|D)≈0.043%

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Concerns for judgement

No Yes

Abrahamic 17 (27.1) 28 (17.8)Reli [-1.95] [2.40]gious Agnostic 12 (17.5) 17 (11.5)ident [-1.31] [1.62]ity Atheist 147 (135) 77 (88.8) [1.02] [-1.26]

Other 37 (33.2) 18 (21.8) [0.66] [-0.82]



Concerns for judgement

No Yes

Fun for others 6 (4.9) 2 (3.14)Stan not for me [0.52] [-0.65] ce Indifferent 40 (37.6) 22 (24.4)to [0.39] [-0.48]wards Bad behaviour 6 (11.5) 13 (7.5)mast [-1.63] [2.03]urbation Fun & healthy 151 (150.5) 97 (97.5) [0.04] [-0.05] It's immature 4 (2.43) 0 (1.57) [1.01] [-1.25]


Bayesian: B=0.82 Pr(H0|D)=55%

Gender - Universitetet i oslofolk.uio.no/trondr/yt_survey_full.pdf · Reincarnation 2 (

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