Mastering Normality Assessment: Graphical And Numerical Techniques For Detecting Normal Distributions In Data

Determine whether a distribution of data is approximately Normal from graphical and numerical evidence.

Looking at a z-score normal probability chart. If the graph is not linear and data is not evenly spread out (such as an exponential slope) it is not a normal distribution. Check if data fits within three standard deviations (use min. and max.). Check if empirical rule applies.

There are several ways to determine whether a distribution of data is approximately normal. Below are some graphical and numerical methods to evaluate a given dataset:

Graphical Evidence:

1. Histogram: A histogram is a graphical representation of the distribution of a dataset. If the histogram is bell-shaped and symmetrical around the mean, it is an indication that the distribution might be normal.

2. Q-Q Plot: A Q-Q plot (quantile-quantile plot) is a graphical representation of the relationship between the data and a normal distribution. If the points are close to a straight line, it indicates that the data is approximately normal.

3. Box-plot: A box-plot is a graphical representation of the five-number summary of a dataset. If the box-plot is symmetrical, it indicates that the data is approximately normal.

Numerical Evidence:

1. Skewness and Kurtosis: Skewness measures the symmetry of a distribution, and kurtosis measures the peakedness of a distribution. If the skewness and kurtosis values are close to 0, it indicates that the distribution is approximately normal.

2. Shapiro-Wilk Test: The Shapiro-Wilk test is a statistical test that tests the normality of a dataset. If the p-value from the test is greater than 0.05, it indicates that the dataset is approximately normal.

Overall, it is important to use both graphical and numerical methods to determine whether a dataset is approximately normal. A distribution that appears normal on a histogram may not necessarily be normal, and a normal distribution may not necessarily appear normal on a histogram. Therefore, it is important to evaluate the dataset using various methods before concluding whether the distribution is normal.

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