How does a normal probability plot determine if a distribution is normal?

General
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how does a normal probability plot determine if a distribution is normal?

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How does a normal probability plot determine if a distribution is normal?

Cevap:
A normal probability plot, also known as a normal quantile plot or a QQ plot, is a graphical tool used to assess the normality of a distribution. It compares the observed data to the expected values if the data were to follow a normal distribution.

To interpret a normal probability plot, you look at how closely the data points align with the straight line on the plot. Here are the steps to determine if a distribution is normal using a normal probability plot:

  1. Plot the data: The first step is to plot the observed data points in a scatterplot format, with the x-axis representing the quantiles of a theoretical normal distribution and the y-axis representing the observed values.

  2. Check the linearity: If the data points closely follow a straight line pattern, it suggests that the distribution is approximately normal. The closer the points align to the straight line, the better the fit to a normal distribution. Any deviations from the straight line indicate departures from normality.

  3. Assess the tails: Look for any patterns or deviations in the tails of the plot. If the data points diverge from the straight line at the tails, it suggests heavy-tailedness or skewness in the distribution. Outliers may also appear as points far away from the straight line.

  4. Interpret the plot: If the data points closely follow a straight line, and there are no significant deviations or patterns in the tails, it indicates that the distribution is approximately normal. However, if the points deviate significantly from the straight line or show distinct patterns in the tails, it suggests a departure from normality.

It’s important to note that the normal probability plot is a visual tool and should be used in conjunction with other statistical tests and techniques to determine the normality of a distribution. It provides a graphical representation of the data’s departure from normality and helps in making informed decisions about the distribution’s characteristics.