| Re: Statistics : T-test, P-value [message #58025] |
Mon, 14 January 2008 06:25  |
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Mike[2]
Messages: 99
Registered: December 2005
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Member |
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>>>> On Jan 14, 7:18 am, Spon <christoph.b...@gmail.com> wrote:
>> On Jan 14, 7:20 am, Nick <jungbin...@hotmail.com> wrote:
>> There are two kinds of data - A group and B group which I
>> have to analyze.
>> I came to know these correlation by using 'CORRELATE'
>> function. However, I want to know whether these
>> correlation is reasonable or not. So I want to calculate
>> p-value by T-test. Is there any idea calculate p-value
>> through t-test through IDL?
> Try the TM_TEST function. The second value it returns
> should be your p value. You'll have to figure out which
> keyword (if any) you need for your particular dataset.
There are many test statistics that are distributed according to
the t-distribution, but you must be careful in how you calculate
them.
IDL's TM_TEST calculates t and the p-value for the Student's
t-test, which is useful for testing the hypothesis that two data
sets have the same mean.
CORRELATE calculates Pearson's correlation coefficient, which
follows the t-distribution, but the test statistic is not the
same as Student's t.
My stats book says that, for Pearson's correlation coefficient,
r, the test statistic is r if the number of data points, N, small
(N<=150). If N>150, use t = r sqrt((N-2)/(1-r**2)). This
follows the t-distribution with N-2 degrees of freedom. You
could use IDL's T_PDF function to calculate p-values for that.
Nick - Would you post some sample data?
Mike
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| Re: Statistics : T-test, P-value [message #58113 is a reply to message #58025] |
Tue, 15 January 2008 03:21  |
JMB
Messages: 13
Registered: January 2008
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Junior Member |
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>> I came to know these correlation by using 'CORRELATE'
>> function. However, I want to know whether these
>> correlation is reasonable or not. So I want to calculate
>> p-value by T-test. Is there any idea calculate p-value
>> through t-test through IDL?
Hi Nick,
I don't know if you can find something useful for you in the following
small program:
After calculation of the Pearson correlation coefficient with the IDL
correlate function,
you can test your coefficient in 2 ways:
- by computing its CONFIDENCE INTERVAL based on the number of data
points.
0 should not be included in this confidence interval to claim that
your correlation is significant.
- by using a t-test of a null hypothesis on the correlation
coefficient
;----------------------------------------------------------- -----------------
; Significance Tests on Pearson's Correlation
; Based on http://davidmlane.com/hyperstat/B62223.html
PRO CORR_TTEST,corr=corr,N=N,sl=sl, ro=ro
; corr: Pearson's correlation coefficient to be tested
; N: Number of samples
; sl: Significance level accepted (ex:0.05,0.001,)
; ro: Correlation value predicted by theory (Null Hypothesis)
; Assumptions
; 1. The N pairs of scores are sampled randomly and independently.
; 2. The distribution of the two variables is bivariate normal.
; NULL hypothesis is ro=ro
IF N_Elements(ro) EQ 0 THEN ro=0
IF corr EQ 1.0 THEN corr=0.9999999d ; avoid Floating divide by 0
IF ro EQ 1.0 THEN ro=0.9999999d ; avoid Floating divide by 0
IF corr EQ -1.0 THEN corr=-0.9999999d ; avoid Floating divide by 0
IF ro EQ -1.0 THEN ro=-0.9999999d ; avoid Floating divide by 0
;----------------------------------------------------------- -----------------
; COMPUTE CONFIDENCE INTERVAL OF CORRELATION COEFFICIENT
;----------------------------------------------------------- -----------------
; Conversion of Pearson's correlation to the normally distributed
variable zp
; Fisher's transformation
zp=0.5*alog((1+corr)/(1-corr))
;Compute zp standard error
sig_zp=1/sqrt(N-3)
; Compute z value from significance level sl
; 99% confidence interval example corresponds sl=0.01 and gives to
z=2.58
z=gauss_cvf((sl)/2.)
low_zp=zp-z*sig_zp
high_zp=zp+z*sig_zp
r_high=(exp(2*high_zp)-1)/(exp(2*high_zp)+1)
r_low=(exp(2*low_zp)-1)/(exp(2*low_zp)+1)
print,''
print, "High End Case for r: ",r_high," Low End Case for r:
",r_low
; Preliminary result of significance based on Pearson correlation
interval
; If the 0 is included in the range between r_low and r_high,
; You can't claim your result is Statistically significant at
significance level (sl)
; (or confidence level (1-sl)
IF r_low LT 0 AND r_high GT 0 THEN $
print,"This is NOT a statistically significant relationship!" ELSE $
print,"This is a statistically significant relationship!"
;----------------------------------------------------------- -----------------
;----------------------------------------------------------- -----------------
; T test significance
;----------------------------------------------------------- -----------------
print,''
print,'---T TEST result
; if Null hypothesis is ro=0
IF ro EQ 0 THEN BEGIN
Df=N-2
t=corr*sqrt(Df)/sqrt(1-corr^2)
pt=2*(1-T_PDF(t, Df))
IF pt LT sl THEN $
print,"The correlation is significant repect to significance level
",string(sl,format='(F7.5)') ELSE $
print,"The correlation is NOT significant repect to significance level
",string(sl,format='(F7.5)')
ENDIF ELSE BEGIN
; if Null hypothesis is ro<>0
zpro=0.5*alog((1+ro)/(1-ro))
zt=(zp-zpro)/sig_zp
pzt=2*(1-GAUSS_PDF(zt))
IF pzt LT sl THEN $
print,"The null hypothesis that the population correlation is
",string(ro,format='(F7.4)')," can be rejected." ELSE $
print,"The null hypothesis that the population correlation is
",string(ro,format='(F7.4)')," CAN'T be rejected."
ENDELSE
END
;----------------------------------------------------------- -----------------
Regards,
Let us know,
Jérôme
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