[R] prop.test correct true and false gives same answer

[(Ted Harding)]

On 27-Mar-2013 21:04:51 David Arnold wrote:
> All,
> How come both of these are the same.  Both say "1-sample proportions
> test without continuity correction." I would suspect one would say
> "without" and one would say "with."
> 
> 
>> prop.test(118,236,.5,correct=FALSE,conf.level=0.95)
> 
>       1-sample proportions test without continuity correction
> 
> data:  118 out of 236, null probability 0.5 
> X-squared = 0, df = 1, p-value = 1
> alternative hypothesis: true p is not equal to 0.5 
> 95 percent confidence interval:
>  0.4367215 0.5632785 
> sample estimates:
>   p 
> 0.5 
> 
>> prop.test(118,236,.5,correct=TRUE,conf.level=0.95)
> 
>       1-sample proportions test without continuity correction
> 
> data:  118 out of 236, null probability 0.5 
> X-squared = 0, df = 1, p-value = 1
> alternative hypothesis: true p is not equal to 0.5 
> 95 percent confidence interval:
>  0.4367215 0.5632785 
> sample estimates:
>   p 
> 0.5

Note what is said (admittedly somewhat deeply tucked away)
under "Details" in ?prop.test:

 "Continuity correction is used only if it does not exceed
  the difference between sample and null proportions
  in absolute value."

In your example, the sample proportion exactly matches the
null-hypothesis proportion (0.5).

Confirmation:
[A] Your same example:
  prop.test(118,236,.5,correct=TRUE,conf.level=0.95)
  #         1-sample proportions test without continuity correction
  # data:  118 out of 236, null probability 0.5 
  # X-squared = 0, df = 1, p-value = 1
  # alternative hypothesis: true p is not equal to 0.5 
  # 95 percent confidence interval:
  #  0.4367215 0.5632785 
  # sample estimates:
  #   p 
  # 0.5 

[B1] Slightly change x, but keep "correct=TRUE":
  prop.test(117,236,.5,correct=TRUE,conf.level=0.95)
  #         1-sample proportions test with continuity correction
  # data:  117 out of 236, null probability 0.5 
  # X-squared = 0.0042, df = 1, p-value = 0.9481
  # alternative hypothesis: true p is not equal to 0.5 
  # 95 percent confidence interval:
  #  0.4304724 0.5611932 
  # sample estimates:
  #         p 
  # 0.4957627 

[B2] Slightly change x, but now "correct=FALSE":
  prop.test(117,236,.5,correct=FALSE,conf.level=0.95)
  #         1-sample proportions test without continuity correction
  # data:  117 out of 236, null probability 0.5 
  # X-squared = 0.0169, df = 1, p-value = 0.8964
  # alternative hypothesis: true p is not equal to 0.5 
  # 95 percent confidence interval:
  #  0.4325543 0.5591068 
  # sample estimates:
  #         p 
  # 0.4957627 

So it doesn't do the requested continuity correction in [A] because
there is no need to. But in [B1] it makes a difference (compare
with [B2]), so it does it.

Hoping this helps,
Ted.

-------------------------------------------------
E-Mail: (Ted Harding) <Ted.Harding at wlandres.net>
Date: 27-Mar-2013  Time: 21:21:39
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