[R] S: appropriate significance tests

soeren.vogel at eawag.ch soeren.vogel at eawag.ch
Wed Oct 20 21:17:31 CEST 2010

```Thanks Greg for the additional remarks. Basically I have two questions, let me try to specify them as follows:

(1) Height and intelligence may correlate at, say, X, but speed and finger length may correlate at Y. Despite any sense of such a statement, is X significantly larger than Y? How can I perform this significance test (of two correlation coefficients) if I don't have the original data, but only the correlation coefficients, the degrees of freedom and the standard errors?

(2) Let's assume I've studied whether height (as independent) has an influence on (a, regression 1) intelligence and (b, regression 2) speed. Suppose I found out that my linear regression between intelligence and height, (1), reveals a standardised estimate of .6 for height, while for the regression between speed and height, (2), reveals an estimate of .65 for height. Is the estimate for height in regression 1 significantly higher than that for height in regression 2?

> I have asked a couple of persons how much they like music by Robbie Williams or Nora Jones. Additionally I recorded their hair colour and their attitude towards pop music (ATP). After my analysis, I'd like to state that for RW and NJ neither hair colour nor ATP is of *different* importance, whereas the hair colour is much more important for liking RW. I thus thought that I should compare two regression estimates for significant differences since saying that the one is lower/higher than the other doesn't satisfy my editor.
>
> On 20.10.2010, at 20:48, Greg Snow wrote:
>
> It is not completely clear what question you are trying to answer or what you are trying to accomplish.  But here are some additional questions that may help:
>
> What tests would you use if you could use the original data?
> What assumptions are you willing to make about the data and/or statistics?
> What are you trying to accomplish?
>
> --
> Gregory (Greg) L. Snow Ph.D.
> Statistical Data Center
> Intermountain Healthcare
> greg.snow at imail.org
> 801.408.8111
>
>
>> -----Original Message-----
>> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-
>> project.org] On Behalf Of soeren.vogel at eawag.ch
>> Sent: Wednesday, October 20, 2010 7:33 AM
>> To: r-help at r-project.org
>> Subject: [R] S: appropriate significance tests
>>
>> Hello
>>
>> (1) How can I compare two Pearson correlation coefficients for
>> significant differences without the use of the raw data?
>>
>> (2) How can I compare two linear regression coefficients for
>> significant differences without the use of the raw data?
>>
>> (3) How can I compare two multiple correlation coefficients (as
>> produced in a linear regression) for significant differences, again, if
>> the raw data should not be used?
>>
>> <src type="perhaps useful">
>> da <- data.frame(
>>  "y1"=sample(1:5, 40, repl=T),
>>  "y2"=sample(1:5, 40, repl=T),
>>  "x1"=sample(1:5, 40, repl=T),
>>  "x2"=sample(1:5, 40, repl=T)
>> )
>> cro1 <- cor(da\$y1, da\$x1)
>> cro2 <- cor(da\$y2, da\$x1)
>> lmo1 <- lm(y1 ~ x1 + x2, data=da)
>> lmo2 <- lm(y2 ~ x1 + x2, data=da)
>> </src>
>>
>> Thanks, Sören
>>
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