# 2-way ANOVA p-value output

#### student.XY

##### New Member
Hi everyone, I'm new here!

Confused with my p-value output in a 2-way ANOVA test. Probably a stupid question but currently re-learning statistics. What do the p-values below tell me?
< 2e-16
1.16e-09
8.19e-08

Appreciate anyone who can explain this please
Thanks

#### Miner

##### TS Contributor
Other than the fact that they are extremely small (p<<<<<<<< 0.05), you have taken them out of context, so we cannot explain more than that. Note: e-16 is scientific notation indicating that the decimal has been shifted 16 spaces to the right (e.g., 1e-5 = 0.00001).

#### joeb33050

##### Member
They tell me that there's (very) probably a relationship between the sets of number pairs.
Teeny p suggests strong relationship.
I'm trying to imagine the numbers to get such a small p.

#### Karabiner

##### TS Contributor
They tell me that there's (very) probably a relationship between the sets of number pairs.
Sorry, this is not correct. It is the probability of the sample data, given H0.
Not the probabilty of H1, given the sample data.
Teeny p suggests strong relationship.
Absolutely not! The p-value is never an effect size measure.
The statistical test of significance is about "may i decide that there is a non-zero effect in the population?"
It is NOT about how large any effect might be.
I'm trying to imagine the numbers to get such a small p.
Very, very large sample size. Or trivial effects which are so large that one knew before for sure.

With kind regards

Karabiner

#### Miner

##### TS Contributor
I agree with Karabiner. Statistical significance only means that the effect is large RELATIVE TO the experimental error. It does NOT mean that it is of any practical importance. Small p-values can occur, as Karabiner said, from very large sample sizes, or where the experiment deliberately excluded or controlled for virtually all sources of experimental error. When this is done, the results will not typically generalize to a broader population.

#### joeb33050

##### Member
Ya got a p ~ 0, n is BIG, and I wrote some wrong. " What do the p-values below tell me?"
If Ho: mu1 = mu2, because variance 1 = variance 2, (F), then teeny p means the neither the variances nor the means are likely equal. "Likely" "suggests" "probably" are stats speak. We can't prove anything with stats. Youse guys haul out extraneous stuff; look at the question. I stand by my answer.,