T-Test

Username

Hi,

what type of significance test is done by the T-Test operator (left-sided, right-sided or both-sided)? I couldn't find any info in the documentation.

Thanks

steffen

Hello,

the description says:

Determines if the null hypothesis (all actual mean values are the same) holds for the input performance vectors.

so I say it is a both-sided test with H0: mu1=mu2, H1: mu1!=mu2

greetings

Steffen

Username

steffen wrote:
Hello, the description says: so I say it is a both-sided test with H0: mu1=mu2, H1: mu1!=mu2 greetings Steffen

I looked at the source code and it does look like a left sided test, doesn't it?

steffen

Nope

As far as I see the following method TTestSignificanceTestOperator#getProbability(PerformanceCriterion pc1, PerformanceCriterion pc2) calculates the p-value of the test. The test itself is ''performed'' here:
TTestSignificanceTestOperator#TTestSignificanceTestResult#toString() , i.e. here:

result.append("Values smaller than alpha=" + Tools.formatNumber(alpha) + " indicate a probably significant difference between the mean values!" + Tools.getLineSeparator());

the comparison of pvalue < alpha is no clear indication for a left-sided test...

this is the used formula:
http://en.wikipedia.org/wiki/Student';s_t-test#Unequal_sample_sizes.2C_equal_variance => two-sided-test

BUT looking at this formula raises another questions:
First: I have read somewhere that the assumption of equal variances is not a problem if the sizes of the test samples are equal. On the other hand, if this is not valid, no one can guarantee anything for the true alpha error. What do you think about it?

Second:
I thought in case of  a two-sided test the alpha parameter must be divided by 2. Or is this already implied by the test statistics ?

greetings

Steffen

PS:

Username wrote:
I looked at the source code and it does look like a left sided test, doesn't it?

I prefer such argumentations with class names and line numbers
   

Username

steffen wrote:
Second: I thought in case of  a two-sided test the alpha parameter must be divided by 2. Or is this already implied by the test statistics ?

That's why I guessd it's a one sided test. 

steffen

Hello again

steffen wrote:
Second: I thought in case of  a two-sided test the alpha parameter must be divided by 2. Or is this already implied by the test statistics ?

Username wrote:
That's why I guessd it's a one sided test.

I checked it and found that it is ok that alpha is not divided. You can see the t-test as a special case of ANOVA with two groups. In this case t=sqrt(F) (regarding the teststatistics). The F-teststatistics is tested again the 1-alpha-quantile for the same hypothesis, so ...

I guess everything is clear now

greetings

Steffen