Normal Probability Plot

Normal probability plot (Chambers 1983) is a graphical technique for assessing whether a data set is approximately normally distributed. The data are plotted against a theoretical normal distribution such that the points should form an approximate straight line. Deviations from this straight line indicate departures from normality.
 Normal probability plot is a special case of the probability plot. We closed the normal probability plot separately because of its importance in many applications.
 The points on this plot form a nearly linear pattern, which indicates that the normal distribution is a good model for the data set.
This plot was produced by doing the following.
1. Data compiled from the smallest to the largest.
2. Percentile of each data value is determined.
3. Of percentiles, normal calculation is done to determine the corresponding z-score.
4. Each z-score plotted against the corresponding data values.
 If the distribution is close to normal, planning points will be close to the line. systematic deviation from the line indicates a non-normal distribution ..
 Normal probability plot is formed by:
• Vertical axis: the value of the response requests
• Horizontal axis: Normal order statistic median
 Observations are plotted as a function of the normal median statistics in the order defined as:
 N (i) = G (U (i))
 where U (i) is the median of the uniform order statistics (defined below) and G is the percent point function of the normal distribution. Percent point function is the inverse of the cumulative distribution function (the probability that x is less than or equal to a certain value). That is, given the probabilities, we want to fit the cumulative distribution function of x.
 Uniform order statistic median is defined as:
 U (i) = 1 - U (n)
For i = 1
 U (i) = (i - 0.3175) / (n + 0.365)
for i, = 2 3, ..., n-1
 U (i) = 0.5 (1 / n)
for i = n
 In addition, a straight line can be fit to the points and added as a reference line. The further points vary from this line, the greater the indication of deviation from normality.
 Probability plot for distributions other than normal is calculated in exactly the same way. Normal percent point function (G) simply replaced by the percent point function of the desired distribution. That is, the probability plot can easily be generated for any distribution that you have a percent point function.
 One benefit of a computational method that estimates the probability plot intercept and slope of the fitted line in the facts and estimates for the parameters of location-scale distribution. Although this is not very important for the normal distribution because of the location and the scale predicted by the mean and standard deviation, respectively, can be useful for other distributions.
 The correlation coefficient of the points on the normal probability plot can be compared with the critical value table to provide a formal test the hypothesis that the data came from a normal distribution.

Normal probability plot, sometimes called qq plot, is a graphical way of assessing whether a set of data that looks like it may have come from a standard bell-shaped curve (normal distribution). To calculate normal probability plot, first sort your data, then count equally percentile of a distribution is normal. Optionally, you can choose to have a normal distribution of mean and standard deviation are the same as your data, or you can save time by using evenly within percentile of the standard normal distribution. Finally, plot distance versus percentile evenly sorted data. A fairly straight line showed that close to a normal distribution. A curved line clearly shows the distribution deviates from normality.