What is a Normal Probability Plot?

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  • What is a Normal Probability Plot?

A normal probability plot is a graphical representation of a data set used to assess whether the data follows a normal (bell-shaped) distribution. It is similar to a quantile-quantile plot (Q-Q Plot), which plots the quantiles of the data set against the quantiles of a normal distribution with the same mean and standard deviation as the data set.

How to Draw a Normal Probability Plot?

Even though you can use Microsoft Excel to draw it, it does not provide an easy way to draw it. The best and the most common way to draw this plot is to use software such as Minitab, Python or R.

In Minitab, you click on Graph and then select Probability Plot... to create this plot.

How to Interpret the Results of a Normal Probability Plot?

If the data follows a normal distribution, the points on the normal probability plot will fall approximately along a straight line. Suppose the data deviates significantly from the normal distribution. In that case, the points on the plot will not follow a straight line and may show nonlinear patterns or deviations from the theoretical normal distribution. This can indicate that the data is skewed, has shorter or longer tails than expected, or exhibits other departures from normality.

For example, in the above Normal Probability Plot, all points are in a straight line enclosed by an envelope with a 95% Confidence Interval. Based on the visual look of this graph, we can confirm with 95% confidence that the data follows Normal Distribution.

A more technical approach would be to look at the P-value. Since the P-Value is more than 0.05 (it is much higher), we can say with 95% confidence that the data comes from a Normal Distribution.

However, if you look at the above example, the data points do not fall in a straight line, and the P-Value is less than 0.05; we can confirm that this data comes from a Non-Normal Distribution.

Conclusion

In conclusion, a normal probability plot is a useful graphical technique for assessing whether a sample of data comes from a normally distributed population. If the data is normally distributed, the points on the plot should roughly form a straight line. Deviations from this line may indicate that the data is not normally distributed. Normal probability plots can be a helpful tool for identifying whether a sample of data meets the assumptions of specific statistical tests or models.


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