Good Evaluating Normality Essay Example

In this paper we should decide if data is normally distributed using Skewness, Kurtosis, Shapiro-Wilk test, a histogram and QQ plot. I use Minitab 16 Software to perform calculations.
Before analysis we must say that the ID variable is not being used in our research as it just characterize the number of observation. TRT variable is dummy variable and it cannot be counted as normally distributed variable. Hence, we perform our calculations only for 7 remaining variables.

Histograms

We know that if the data is normally distributed, it must be look like bell-shaped curve as on the graphs above. The following variables are seemed to be normally distributed:

Age

TotalCW6
Q-Q Plots
Age:
Stage:
Weighin:
TotalCIN:
TotalCW2:
TotalCW6:
TotalCW4:
We know that if data is located close to the straight line this is an evidence of the normal distribution. According to the QQ plots above we can conclude that the normal distribution is for variables:
Age
TotalCW6

Shapiro-Wilk’s Test

The following table represents the results of Shapiro-Wilk’s Test of normality:
As we know, if the significance of the statistic is higher than 0.05 then we are 95% confident that there is no significant difference between normal distribution and distribution of the tested variable. Hence according to Shapiro-Wilk’s test, the following variables seem to be normally distributed:
Age

Weighin

TotalCW4
TotalCW6

Skewness and Kurtosis

The following table represents skewness and kurtosis for all variables:
Descriptive Statistics: AGE; WEIGHIN; STAGE; TOTALCIN; TOTALCW2; TOTALCW4;
Variable Skewness Kurtosis
AGE -0,35 0,58
WEIGHIN 0,83 0,70
STAGE 0,82 -0,61
TOTALCIN 2,04 6,35
TOTALCW2 1,15 2,13
TOTALCW4 0,55 -0,74
TOTALCW6 0,88 1,39
Skewness is a measure of symmetry. If the value of skewness is large than 1 or less than -1 then the distribution is significantly different from symmetric distribution. Hence, we can conclude that only these variables have symmetric distribution:
Age

Weightin

Stage
TotalCW4
TotalCW6

Kurtosis is a measure of shape. The following variables are close to the shape of Gaussian distribution:

Age

Weightin

Stage
TotalCW4

References

Quine, M.P. (1993) "On three characterisations of the normal distribution", Probability and Mathematical Statistics, 14 (2), 257-263