P <0.05, and where does it (sometimes) come from

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Philadelphia Eagles 10 , , 150 .

10 ! , 1/(2^10) =  1/1024 = 0.0009. . , , Eagles , . , , . ( , ).

p<0.05

, p- 0.05 — 5%, , , , . : , , , p≈0.05.

. , , , . xkcd: (p>0.05), , , (p>0.05). , , , , — p<0.05.

( ) , , p<0.05. , , . . , -, 50%, British Journal of General Practice. .

, : 49% 51% . 60 55%. , , 13 , , . , 10 . 50%, 77%, p- 0.046. ( — , -, ).

, , 10 13 — . : , .

, 13, 90, 61? , p- 0.0005 , 90 — . , .

P- - . “ , , , 1 20” , 5%- p- 30% . — . , , . p- 0 1.

p- ( , ). — :

: P- α α/N N .

: α/N N , α . , , : h1,…,hN — N p- N , 0 1. , α/N = P(min(h1,…,hN) < α/N) = 1 – (1 – α/N)^N ≈ 1 – e^-α ≈ 1 – (1-α) = α. e^x ≈1+x, x.

. , . , , (.. ), ( ). , ( Github).

(, ), . 2*3*4=24 , — 12 000. 50% , 12 000/2=6 000 . p=0.05, 50.75% (90 ) p=0.0005, 51.5%.

: . p-.

P- . , , . , p-.

. 1 000 : , 50%; , 50.75%; , 51.5% (, “”). , p-:

13 hispanic 1    0.122530416511473
14 female hispanic 2    0.180797304026783
15 young hispanic 2    0.25172233581543
16 young female hispanic 3    0.171875
17 white 1    0.0462304905364621
18 female white 2    0.572232224047184
19 young white 2    0.25172233581543
20 young female white 3   0.9453125
21 adult 1    0.368777154492162
22 female adult 2    0.785204746078306
23 asian 1    0.953769509463538
24 female asian 2    0.819202695973217
      
      

        
        
        
      

    
        
        
        
      
      

        
        
        
      

    
    

— ( — 0, “” — 1, “ ” — 3). 60 : 1 , 9 1, 26 — 2, 24 —- 3. p- 0.05/60=0.00083

1000 . , 0.05 0.00083. — p-, — ( 1000) .

p<0.05 5% ( ), — 50% , — 95. , 23% 72% . , - , .

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3. : p- , (, , p-). , .

   
   
   
   
   

4. : , . p- .

   
   
   
   
   

-, p=0.00000000012 . , , , ( , ) . , , p- .

, , . , p- 1/1000 p- 1e-3. p- , . 

, Eagles. -, 10 , 11- ( 11- , 10) , 11 . -, 10 — , . , . .

. Eagles - , “ , ” (. .: , Seattle Seahawks), “ , ”, . , :

1. : , , , , , — 20 .

   
   
   
   
   

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3. : / , , , , — 10 .

   
   
   
   
   

1 , 4000 . Eagles? , , 1/1024, 4000 , 4 . , ; , . . Eagles 15:26.

, - . - ( 6- ) “, ”. , , , . №1 , , ; №1 , .