It is a fact that the data of a study have a normal distribution when their values present a bell-shaped curve, symmetric around the mean, which is called a normal or Gaussian curve. The normal curve approaches the abscissa axis indefinitely without, however, reaching it. As the curve is symmetric around the mean, the probability of a value greater than the mean occurring is equal to the probability of a value less than the mean occurring, that is, both probabilities are equal to 50%. In the norm distribution, the mean, median and mode are at the same point on the curve, or very close.

There are basically 3 ways to check whether the distribution of quantitative data is normal or non-normal. The first one is to verify if the mean, mode and median have identical or very similar values. Very large differences in the values of the 3 main measures of central tendency indicate that the distribution cannot be considered normal. Another empirical way of testing the distribution pattern of the data is to construct a frequency histogram of the data on the normal distribution curve (Gauss curve). Several specific computer programs perform this type of comparison of sample data with the characteristic data of the normal curve. If the histogram is very skewed, the distribution is considered non-normal. The third way is to apply specific statistical tests to verify the hypothesis of normality. Examples are the Kolgomorov-Smirnov test (KS) and the Shapiro-Wilks test (W).

If the data distribution of a quantitative variable cannot be considered normal, we must use the nonparametric tests used for qualitative variables with an ordinal scale.

Assuming that the data distribution is normal or approximately normal, parametric tests are indicated for comparison between groups. These tests base their decision on the comparison of parameters (mean, standard deviation), this comparison will only make sense if the parameters are representative of the distributions being compared.

Normally distributed data