# Is mean significant and not abnormal?

#### Mistermishka

##### New Member
Hi everyone!
I am having some troubles with interpreting the significance of mean.
Mean= 0.19609
St. Dev=0.12341
n=141
I get t-statistic of 18.86763( ratio mean/ st. error)
I thought that for the mean to be significant and expected (not abnormal) t-stat has to be within the interval -1.645<t<1.645 with 95% level of confidence.. or am I wrong?
How do I explain enormous t-statistic, does it make any sense at all?
Thank you

#### ledzep

##### Point Mass at Zero
I am assuming you are trying to test if the mean is significantly different from zero?

The large t statistic mean that there is an enormous evidence that your sample mean is significantly different from zero, at the level of significance you've chosen.

If the t-stats fall within the critical values from distribution (namely, -1.645, and 1.645 in your case), then it will mean you cannot reject your null hypothesis of mean equal to zero.

If the test statistic fall within the critical region (i.e. between the values from distribution), then you can't reject null. If the stat falls in the rejection region (i.e. outside the critical values), then you can reject the null hypothesis.

#### Mistermishka

##### New Member
Thank you!
Another quick question if you don't mind.. What does it mean if I get similar large t-stats for skewness and kurtosis? Does it mean that they are significantly different from zero too and therefore my data is far from normal?

#### ledzep

##### Point Mass at Zero
Thank you!
Another quick question if you don't mind.. What does it mean if I get similar large t-stats for skewness and kurtosis? Does it mean that they are significantly different from zero too and therefore my data is far from normal?
First of all, I've never tested and never seen hypothesis tests being carried out to test if kurtosis or skewness are equal to zero. (May be I missed out all the fun)

By the same token we've used for mean, if the test statistics for Kurtosis and Skewness is greater than the critical value, then it would mean that skewness and Kurtosis are signficantly different from zero. Now, would it mean the data is far from normal? I think so. Because, if the skweness is non-zero, then distribution would be asymetric, and if the kurtosis is non zero, then the distribution of data would be more (or less, if negative) peaked than the bell-shaped curve.