# What is level of significance?

I do understand the Type $\text {I}$ error and Type $\text {II}$ error. I also do understand that

$\text{level of significance} = \text {P(Type I error)}$. However, how do I explain it to a person (having no statistics background) in very simple language. E.g. I need to make someone understand the meaning of following result:

"At the 5% level of significance, the Anderson - Darling test suggests that the loss data follows a Normal distribution"

I am bit confused as to how to make someone understand this without making things too confusing for the client.

Also, if possible, will like to know about degrees of freedom too.

• The quoted sentence is not something you can conclude from an Anderson-Darling test --- failure to reject normality does not imply the data follows a normal distribution. So making people understand an incorrect conclusion might be counterproductive. – Glen_b -Reinstate Monica May 12 '14 at 10:38
• Your final sentence is not part of the preceding question but is an unrelated question. Don't ask about unrelated things in a single question. If you search on degrees of freedom there are some good discussions. – Glen_b -Reinstate Monica May 12 '14 at 10:40
• Dear Mr Glen, Thanks a lot for your comments. I have noted your suggestions. – Katherine Gobin May 12 '14 at 11:54
• @KatherineGobin you can edit your question (bottom left "edit" link) to incorporate those suggestions and improve your answer. – Alexis May 12 '14 at 13:33

If you can't explain something, do you really understand it?

The statement

"At the 5% level of significance, the Anderson - Darling test suggests that the loss data follows a Normal distribution"


is not exactly correct. It should be "we cannot reject the hypothesis that the data are normal".

I have found that (at least with American clients) the best way to explain p values is with an analogy to a trial: Mr. Null (the distribution is normal!) is accused of being wrong. The prosecution introduces evidence to prove this (the Anderson Darling test) but the evidence is not enough to convict Mr. Null, so we find him not guilty.

Note that we do not find him "innocent". We just say that we don't have enough evidence to convict. In a criminal trial the prosecution needs "beyond a reasonable doubt" and the significance level is an attempt to make that numeric.

• Dear Sir, Thanks a lot for enlightenment. I have a very basic understanding of Statistics, so at times I myself find it bit difficult to understand. But at times, being part of my job, need to make my clients few concepts like VaR etc. But thanks Sir, I will try to rephrase my wordings as you have suggested that "we cannot reject the hypothesis that the data are normal" . Regards Katherine – Katherine Gobin May 12 '14 at 11:48