1. Exploratory Data Analysis
1.3. EDA Techniques
1.3.6. Probability Distributions
1.3.6.7. Tables for Probability Distributions

Critical Values of the Normal PPCC Distribution

How to Use This Table This table contains the critical values of the normal probability plot correlation coefficient (PPCC) distribution that are appropriate for determining whether or not a data set came from a population with approximately a normal distribution. It is used in conjuction with a normal probability plot. The test statistic is the correlation coefficient of the points that make up a normal probability plot. This test statistic is compared with the critical value below. If the test statistic is less than the tabulated value, the null hypothesis that the data came from a population with a normal distribution is rejected.

For example, suppose a set of 50 data points had a correlation coefficient of 0.985 from the normal probability plot. At the 5% significance level, the critical value is 0.9761. Since 0.985 is greater than 0.9761, we cannot reject the null hypothesis that the data came from a population with a normal distribution.

Since perferct normality implies perfect correlation (i.e., a correlation value of 1), we are only interested in rejecting normality for correlation values that are too low. That is, this is a lower one-tailed test.

The values in this table were determined from simulation studies by Filliben and Devaney.

Critical values of the normal PPCC for testing if data come from a normal distribution
```
N          0.01          0.05

3        0.8687        0.8790
4        0.8234        0.8666
5        0.8240        0.8786
6        0.8351        0.8880
7        0.8474        0.8970
8        0.8590        0.9043
9        0.8689        0.9115
10        0.8765        0.9173
11        0.8838        0.9223
12        0.8918        0.9267
13        0.8974        0.9310
14        0.9029        0.9343
15        0.9080        0.9376
16        0.9121        0.9405
17        0.9160        0.9433
18        0.9196        0.9452
19        0.9230        0.9479
20        0.9256        0.9498
21        0.9285        0.9515
22        0.9308        0.9535
23        0.9334        0.9548
24        0.9356        0.9564
25        0.9370        0.9575
26        0.9393        0.9590
27        0.9413        0.9600
28        0.9428        0.9615
29        0.9441        0.9622
30        0.9462        0.9634
31        0.9476        0.9644
32        0.9490        0.9652
33        0.9505        0.9661
34        0.9521        0.9671
35        0.9530        0.9678
36        0.9540        0.9686
37        0.9551        0.9693
38        0.9555        0.9700
39        0.9568        0.9704
40        0.9576        0.9712
41        0.9589        0.9719
42        0.9593        0.9723
43        0.9609        0.9730
44        0.9611        0.9734
45        0.9620        0.9739
46        0.9629        0.9744
47        0.9637        0.9748
48        0.9640        0.9753
49        0.9643        0.9758
50        0.9654        0.9761
55        0.9683        0.9781
60        0.9706        0.9797
65        0.9723        0.9809
70        0.9742        0.9822
75        0.9758        0.9831
80        0.9771        0.9841
85        0.9784        0.9850
90        0.9797        0.9857
95        0.9804        0.9864
100        0.9814        0.9869
110        0.9830        0.9881
120        0.9841        0.9889
130        0.9854        0.9897
140        0.9865        0.9904
150        0.9871        0.9909
160        0.9879        0.9915
170        0.9887        0.9919
180        0.9891        0.9923
190        0.9897        0.9927
200        0.9903        0.9930
210        0.9907        0.9933
220        0.9910        0.9936
230        0.9914        0.9939
240        0.9917        0.9941
250        0.9921        0.9943
260        0.9924        0.9945
270        0.9926        0.9947
280        0.9929        0.9949
290        0.9931        0.9951
300        0.9933        0.9952
310        0.9936        0.9954
320        0.9937        0.9955
330        0.9939        0.9956
340        0.9941        0.9957
350        0.9942        0.9958
360        0.9944        0.9959
370        0.9945        0.9960
380        0.9947        0.9961
390        0.9948        0.9962
400        0.9949        0.9963
410        0.9950        0.9964
420        0.9951        0.9965
430        0.9953        0.9966
440        0.9954        0.9966
450        0.9954        0.9967
460        0.9955        0.9968
470        0.9956        0.9968
480        0.9957        0.9969
490        0.9958        0.9969
500        0.9959        0.9970
525        0.9961        0.9972
550        0.9963        0.9973
575        0.9964        0.9974
600        0.9965        0.9975
625        0.9967        0.9976
650        0.9968        0.9977
675        0.9969        0.9977
700        0.9970        0.9978
725        0.9971        0.9979
750        0.9972        0.9980
775        0.9973        0.9980
800        0.9974        0.9981
825        0.9975        0.9981
850        0.9975        0.9982
875        0.9976        0.9982
900        0.9977        0.9983
925        0.9977        0.9983
950        0.9978        0.9984
975        0.9978        0.9984
1000        0.9979        0.9984
```