[R] Homework help: t test hypothesis testing with summarized data?

[Zembower, Kevin]

Peter and Moshe, thank you both for your suggestions and hints. I'm proud to say that it took me less than an hour to find my mistake:
> s_pooled <- (((n-1)*(s_x^2)) + ((m-1)*(s_y^2))) /  (n+m-2)
> s_pooled
[1] 1.939521
> t_obs <- (xbar - ybar) / (sqrt(s_pooled) * (sqrt(1/n + 1/m)))
> t_obs
[1] 2.15578
> qt(c(.025, .975), n+m-2)
[1] -1.987934  1.987934
> # Therefore, reject H0 at the 0.05 level of significance.

Just to be clear about the 'homework' aspect of my questions: my homework is to work the problems out 'longhand' with just a calculator and printed tables. (In fact, 10 weeks into a 14 week course, we haven't been asked yet to use a computer.) I do this before I ask any questions regarding homework on this forum. On my own, I'm trying to answer some of the questions and examples in my textbook using R. My 'Homework help:' subject may have been misleading. I may change it to 'Extra-credit help:' to acknowledge the academic aspect of my question but distinguish it from my homework. I used 'Homework help:' because I didn't want anyone to suspect from the nature of the questions that I was trying to sneak in a homework question without acknowledging it.

Thanks, again, for all your help for this statistics student.

-Kevin

-----Original Message-----
From: Peter Dalgaard [mailto:p.dalgaard at biostat.ku.dk] 
Sent: Wednesday, November 07, 2007 6:50 PM
To: Zembower, Kevin
Cc: r-help at stat.math.ethz.ch
Subject: Re: [R] Homework help: t test hypothesis testing with summarized data?

Zembower, Kevin wrote:
> Is this how a t hypothesis test is done when I don't have the actual
> data, but just the summarized statistics: 
>   
>> #Homework 9.2.6 [1]
>> n<-31
>> xbar<-3.10
>> s_x<-1.469
>> m<-57
>> ybar<-2.43
>> s_y<-1.35
>> s_pooled<- (((n-1)*s_x^2) + ((m-1)*s_y^2)) / (n + m - 2)
>> s_pooled
>>     
> [1] 1.939521
>   
>> t_obs <- (xbar -  ybar) / (s_pooled * (sqrt(1/n + 1/m)))
>> t_obs
>>     
> [1] 1.547951
>   
>> qt(c(.025, .975), n+m-2)
>>     
> [1] -1.987934  1.987934
>   
>> # Therefore, fail to reject H0 at the 0.05 level of significance
>>
>>     
>
> Or am I again overlooking a canned procedure or an easier calculation
> using the t distribution.
>   
I don't know if someone told you last time, but there's an Internet code 
of honor about helping with homework.... Don't expect more than hints.

You're on track but there's a mistake.

Here's a way of testing your result:

 > x <- scale(rnorm(31))*1.469+3.10
 > y <- scale(rnorm(57))*1.35+2.43
 > t.test(x,y, var.equal=TRUE)




> Thank you for your continued advice and help.
>
> -Kevin
>
> [1] An Introduction to Mathematical Statistics and its Applications,
> fourth ed., Larsen and Marx.
>
> Kevin Zembower
> Internet Services Group manager
> Center for Communication Programs
> Bloomberg School of Public Health
> Johns Hopkins University
> 111 Market Place, Suite 310
> Baltimore, Maryland  21202
> 410-659-6139 
>
> ______________________________________________
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> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>   


-- 
   O__  ---- Peter Dalgaard             Øster Farimagsgade 5, Entr.B
  c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
 (*) \(*) -- University of Copenhagen   Denmark          Ph:  (+45) 35327918
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