# What does a positive t-statistic mean?

#### land144

##### New Member
I just worked out a t-statistic for a hypothesis and I got 2.5. When I did the same hypothesis test with random values I ended up with 0.94. Is that a significant difference, since it's only about 1.5 difference? I'm not sure what a 2.5 t-statistic actually means (in words) so I can't comment on how they compare to one another.... can anyone help?
Also, what would a negative t-statistic imply?

#### williaml

##### New Member
Hi land144,
The t-test uses something called the t-distribution to work out if sample differences are significant. (see http://www.statistics4u.com/fundstat_eng/cc_distri_student_t.html)

It is basically a probability density function. The higher the absolute value of the t-statistic, the lower the probability - that is the lower the probability that the difference is random, i.e more probable that the difference observed is due to a systematic influence (i.e. experimental intervention). The actual distribution depends on the degrees of freedom, or in this case the number of observations-1. Using the criteria of alpha=0.05, one can work out what the critical t-value should be for the degrees of freedom.

Different statistical tests use different probablity functions, e.g. ANOVA uses the F distribution.

Assuming infinite degrees of freedom: Using random data to get a t-value of 0.94 is expected, as it would not be signficant - after all, it was randomly selected. Getting a t-value of 2.5 would be signficant, as alpha would be <0.05. Have a look at this table http://www.socr.ucla.edu/Applets.dir/T-table.html and see what you get with the df in your case.

You can't have a negative t-statistic because you can't have a 'negative probability' or something happening or not happening.

Hope this helps
William

#### spinningfeather

##### New Member
Hi land144,
The t-test uses something called the t-distribution to work out if sample differences are significant. (see http://www.statistics4u.com/fundstat_eng/cc_distri_student_t.html)

It is basically a probability density function. The higher the absolute value of the t-statistic, the lower the probability - that is the lower the probability that the difference is random, i.e more probable that the difference observed is due to a systematic influence (i.e. experimental intervention). The actual distribution depends on the degrees of freedom, or in this case the number of observations-1. Using the criteria of alpha=0.05, one can work out what the critical t-value should be for the degrees of freedom.

Different statistical tests use different probablity functions, e.g. ANOVA uses the F distribution.

Assuming infinite degrees of freedom: Using random data to get a t-value of 0.94 is expected, as it would not be signficant - after all, it was randomly selected. Getting a t-value of 2.5 would be signficant, as alpha would be <0.05. Have a look at this table http://www.socr.ucla.edu/Applets.dir/T-table.html and see what you get with the df in your case.

You can't have a negative t-statistic because you can't have a 'negative probability' or something happening or not happening.

Hope this helps
William
Just some tedious corrections:

1) You do not get the probability of the difference being random. And you do not get the probability of a certain t-value (you may not mean these things but you seem to invite that interpretation). The p-value just tells you the probability of observing a difference as extreme as the observed one or more extreme (which you did not, but which might have happened, unobserved data) if we assume that the null is true. That´s just what it is, and alpha controls Type I error rates.

2) t can be negative (depending on which mean is subtracted from which), but p cannot of course.

That´s all