Welcome to Really Simple Statistics (RSS). There are lots of places online where you can ponder over the minute details of complicated equations but very few places that make statistics understandable to everyone. I won’t explain exceptions to the rule or special cases here. Let’s just get comfortable with the fundamentals.
What is a p value?
P value is a short form for probability value and another way of saying significance value. It refers to the chance that you are willing to take in being wrong. (I know, once in your life is too many times to be wrong.)
No matter how careful you are, random chance plays a part in everything. If you try to guess whether you’ll get heads or tails when you flip a coin, your chance of guessing correctly is only 50%. Half the time, you’ll flip tails even if you wanted to flip heads.
In research, we don’t like 50/50 odds. We instead only want to risk that 5% or 1% of our predictions are wrong. And, if you just picked 1% or 5%, you’ve just picked a peck of picked peppers. Whoops, I mean you’ve just picked a p value.
P values are almost always expressed out of 1. For example, a p value of 0.05 means you are willing to let 5% of your predictions be wrong. A p value of 0.1 means you are willing to let 10% of them be wrong. Don’t let that pesky decimal place fool you. A p value of 0.01 means 1% and a p value of 0.1 means 10%.
When you do a statistical test in software like SPSS or Systat, it will tell you the exact p value associated with your specific set data. For instance, it might indicate that the p value of your result is 0.035, or “Men are significantly taller than women, p=0.035.” That means there is a 3.5% chance that men are NOT actually taller than women and this result happened only because of random chance.
Really Simple Statistics!
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hi is there a link between correlation coefficient and p-value?
Hi there. Correlations and p-values are two different things that go together. A correlation is a test of relationships between variables. (Other tests of relationships would be t-tests, chi-squares, anovas, etc.) A p-value tells you if the relationship is strong enough to pay attention to. Does that help? Good luck my dear stats friend
You are just fab!!!
“That means there is a 3.5% chance that men are NOT actually taller than women and this result happened only because of random chance.”
No. There’s always a great need to be careful when you discuss the meaning of p-values. The p-value is not the probability that the hypothesis is true!
The p-value is the probability to obtain a result as extreme (in the direction of the alternative) as the observed outcome if the null hypothesis is true. “If men are not taller than women then we would only see a difference that is at least this large 3.5 % of the times we repeated this experiment with the same number of men and women.” That’s unfortunately far more difficult to interpret than what you wrote above, but it is the correct interpretation.
I really appreciate what you are doing here and the RSS posts are a great idea. Just trying to make sure that you don’t go from “simple statistics” to “wrong”. Keep up the good work!
Understood. As you say, far more difficult to explain. Your comment will serve as part 2 for those who wish to get into the nitty gritty, exactly what is going on.
You say: ‘For instance, it might indicate that the p value of your result is 0.035, or “Men are significantly taller than women, p=0.035.” That means there is a 3.5% chance that men are NOT actually taller than women[...]‘
It doesn’t mean this at all! You’ve got the conditioning the wrong way round. See (for instance) http://www.plosmedicine.org/article/info:doi/10.1371/journal.pmed.0020124
If the p value in your example is 0.035, then the chance that met are NOT taller than women will typically be a lot different from 3.5% (and in particular it can be very much bigger than 3.5%).
For those who want to get into the nitty gritty, this comment is for you.