NORMAL DISTRIBUTION: Does This Approximate It?

Question

Sample size (n)= 81
Mean= 141.89
SD=2.23
Skew= -0.04
Kurtosis= -0.34

1. When I look at my data in a histogram, it doesn't look like a normal distribution, but aren't these skew and kurtosis results fairly good since they both approximate 0?

2. What I'm trying to do here is pick an appropriate sample size that will support the Central Limit Theorem where the outer prediction interval bands (i.e., two-tailed 95%) on each side of the Mean are likely to contain my outliers (residuals) and where reversion to the Mean is most likely. Is the best way to do this to find a sample size that has both a skew and kurtosis that are close to 0? Are there other test statistics that you would use given my objectives?

Answer 1

First, There are tests for normality you can use to determine whether your data is "normal" enough. One such test is the Kolmogorov-Smirnov test or the Anderson-Darling test. You can find these online or they are found in many stat packages like Minitab.

Second, if your data cannot have negative values, sometimes a log-normal distribution is more appropriate.