Результат анализа данных в пакете Statgraphics.
One-Variable Analysis - d17
Data variable: d17
11006 values ranging from 1.0 to 81.0
The StatAdvisor
This procedure is designed to summarize a single sample of data. It will calculate various statistics and graphs. Also included in the procedure are confidence intervals and hypothesis tests.
Summary Statistics for d17
Count |
11006 |
Average |
1.54207 |
Median |
1.0 |
Mode |
1.0 |
Variance |
2.8936 |
Standard deviation |
1.70106 |
Coeff. of variation |
110.31% |
Range |
80.0 |
Skewness |
19.0631 |
Stnd. skewness |
816.457 |
Kurtosis |
738.472 |
Stnd. kurtosis |
15814.1 |
The StatAdvisor
This table shows summary statistics for d17. It includes measures of central tendency, measures of variability, and measures of shape. Of particular interest here are the standardized skewness and standardized kurtosis, which can be used to determine whether the sample comes from a normal distribution. Values of these statistics outside the range of -2 to +2 indicate significant departures from normality, which would tend to invalidate any statistical test regarding the standard deviation. In this case, the standardized skewness value is not within the range expected for data from a normal distribution. The standardized kurtosis value is not within the range expected for data from a normal distribution.
Frequency Tabulation for d17
|
Lower |
Upper |
|
|
Relative |
Cumulative |
Cum. Rel. |
Class |
Limit |
Limit |
Midpoint |
Frequency |
Frequency |
Frequency |
Frequency |
|
at or below |
-3.0 |
|
0 |
0.0000 |
0 |
0.0000 |
1 |
-3.0 |
-0.560976 |
-1.78049 |
0 |
0.0000 |
0 |
0.0000 |
2 |
-0.560976 |
1.87805 |
0.658537 |
8081 |
0.7342 |
8081 |
0.7342 |
3 |
1.87805 |
4.31707 |
3.09756 |
2575 |
0.2340 |
10656 |
0.9682 |
4 |
4.31707 |
6.7561 |
5.53659 |
199 |
0.0181 |
10855 |
0.9863 |
5 |
6.7561 |
9.19512 |
7.97561 |
100 |
0.0091 |
10955 |
0.9954 |
6 |
9.19512 |
11.6341 |
10.4146 |
21 |
0.0019 |
10976 |
0.9973 |
7 |
11.6341 |
14.0732 |
12.8537 |
13 |
0.0012 |
10989 |
0.9985 |
8 |
14.0732 |
16.5122 |
15.2927 |
2 |
0.0002 |
10991 |
0.9986 |
9 |
16.5122 |
18.9512 |
17.7317 |
4 |
0.0004 |
10995 |
0.9990 |
10 |
18.9512 |
21.3902 |
20.1707 |
5 |
0.0005 |
11000 |
0.9995 |
11 |
21.3902 |
23.8293 |
22.6098 |
2 |
0.0002 |
11002 |
0.9996 |
12 |
23.8293 |
26.2683 |
25.0488 |
2 |
0.0002 |
11004 |
0.9998 |
13 |
26.2683 |
28.7073 |
27.4878 |
0 |
0.0000 |
11004 |
0.9998 |
14 |
28.7073 |
31.1463 |
29.9268 |
0 |
0.0000 |
11004 |
0.9998 |
15 |
31.1463 |
33.5854 |
32.3659 |
0 |
0.0000 |
11004 |
0.9998 |
16 |
33.5854 |
36.0244 |
34.8049 |
0 |
0.0000 |
11004 |
0.9998 |
17 |
36.0244 |
38.4634 |
37.2439 |
0 |
0.0000 |
11004 |
0.9998 |
18 |
38.4634 |
40.9024 |
39.6829 |
0 |
0.0000 |
11004 |
0.9998 |
19 |
40.9024 |
43.3415 |
42.122 |
0 |
0.0000 |
11004 |
0.9998 |
20 |
43.3415 |
45.7805 |
44.561 |
0 |
0.0000 |
11004 |
0.9998 |
21 |
45.7805 |
48.2195 |
47.0 |
0 |
0.0000 |
11004 |
0.9998 |
22 |
48.2195 |
50.6585 |
49.439 |
0 |
0.0000 |
11004 |
0.9998 |
23 |
50.6585 |
53.0976 |
51.878 |
0 |
0.0000 |
11004 |
0.9998 |
24 |
53.0976 |
55.5366 |
54.3171 |
0 |
0.0000 |
11004 |
0.9998 |
25 |
55.5366 |
57.9756 |
56.7561 |
0 |
0.0000 |
11004 |
0.9998 |
26 |
57.9756 |
60.4146 |
59.1951 |
0 |
0.0000 |
11004 |
0.9998 |
27 |
60.4146 |
62.8537 |
61.6341 |
0 |
0.0000 |
11004 |
0.9998 |
28 |
62.8537 |
65.2927 |
64.0732 |
0 |
0.0000 |
11004 |
0.9998 |
29 |
65.2927 |
67.7317 |
66.5122 |
0 |
0.0000 |
11004 |
0.9998 |
30 |
67.7317 |
70.1707 |
68.9512 |
0 |
0.0000 |
11004 |
0.9998 |
31 |
70.1707 |
72.6098 |
71.3902 |
0 |
0.0000 |
11004 |
0.9998 |
32 |
72.6098 |
75.0488 |
73.8293 |
1 |
0.0001 |
11005 |
0.9999 |
33 |
75.0488 |
77.4878 |
76.2683 |
0 |
0.0000 |
11005 |
0.9999 |
34 |
77.4878 |
79.9268 |
78.7073 |
0 |
0.0000 |
11005 |
0.9999 |
35 |
79.9268 |
82.3659 |
81.1463 |
1 |
0.0001 |
11006 |
1.0000 |
36 |
82.3659 |
84.8049 |
83.5854 |
0 |
0.0000 |
11006 |
1.0000 |
37 |
84.8049 |
87.2439 |
86.0244 |
0 |
0.0000 |
11006 |
1.0000 |
38 |
87.2439 |
89.6829 |
88.4634 |
0 |
0.0000 |
11006 |
1.0000 |
39 |
89.6829 |
92.122 |
90.9024 |
0 |
0.0000 |
11006 |
1.0000 |
40 |
92.122 |
94.561 |
93.3415 |
0 |
0.0000 |
11006 |
1.0000 |
41 |
94.561 |
97.0 |
95.7805 |
0 |
0.0000 |
11006 |
1.0000 |
|
above |
97.0 |
|
0 |
0.0000 |
11006 |
1.0000 |
Mean = 1.54207 Standard deviation = 1.70106
The StatAdvisor
This option performs a frequency tabulation by dividing the range of d17 into equal width intervals and counting the number of data values in each interval. The frequencies show the number of data values in each interval, while the relative frequencies show the proportions in each interval. You can change the definition of the intervals by pressing the alternate mouse button and selecting Pane Options. You can see the results of the tabulation graphically by selecting Frequency Histogram from the list of Graphical Options.
Percentiles for d17
|
Percentiles |
1.0% |
1.0 |
5.0% |
1.0 |
10.0% |
1.0 |
25.0% |
1.0 |
50.0% |
1.0 |
75.0% |
2.0 |
90.0% |
3.0 |
95.0% |
4.0 |
99.0% |
7.0 |
Confidence Intervals for d17
95.0% confidence interval for mean: 1.54207 +/- 0.0317799 [1.51029, 1.57385]
95.0% confidence interval for standard deviation: [1.67888, 1.72383]
The StatAdvisor
This pane displays 95.0% confidence intervals for the mean and standard deviation of d17. The classical interpretation of these intervals is that, in repeated sampling, these intervals will contain the true mean or standard deviation of the population from which the data come 95.0% of the time. In practical terms, we can state with 95.0% confidence that the true mean d17 is somewhere between 1.51029 and 1.57385, while the true standard deviation is somewhere between 1.67888 and 1.72383.
Both intervals assume that the population from which the sample comes can be represented by a normal distribution. While the confidence interval for the mean is quite robust and not very sensitive to violations of this assumption, the confidence interval for the standard deviation is quite sensitive. If the data do not come from a normal distribution, the interval for the standard deviation may be incorrect. To check whether the data come from a normal distribution, select Summary Statistics from the list of Tabular Options, or choose Normal Probability Plot from the list of Graphical Options.
Hypothesis Tests for d17
Sample mean = 1.54207
Sample median = 1.0
Sample standard deviation = 1.70106
t-test
Null hypothesis: mean = 0
Alternative: not equal
Computed t statistic = 95.1041
P-Value = 0
Reject the null hypothesis for alpha = 0.05.
sign test
Null hypothesis: median = 0
Alternative: not equal
Number of values below hypothesized median: 0
Number of values above hypothesized median: 11006
Large sample test statistic = 104.9 (continuity correction applied)
P-Value = 0
Reject the null hypothesis for alpha = 0.05.
signed rank test
Null hypothesis: median = 0
Alternative: not equal
Average rank of values below hypothesized median: 0
Average rank of values above hypothesized median: 5503.5
Large sample test statistic = (continuity correction applied)
P-Value = 0
Reject the null hypothesis for alpha = 0.05.
chi-square test
Null hypothesis: sigma = 1.0
Alternative: not equal
Computed chi-square statistic = 31844.0
P-Value = 0
Reject the null hypothesis for alpha = 0.05.
The StatAdvisor
This pane displays the results of tests concerning the population from which the sample of d17 comes. The t-test tests the null hypothesis that the mean d17 equals 0.0 versus the alternative hypothesis that the mean d17 is not equal to 0.0. Since the P-value for this test is less than 0.05, we can reject the null hypothesis at the 95.0% confidence level. The sign test tests the null hypothesis that the median d17 equals 0.0 versus the alternative hypothesis that the median d17 is not equal to 0.0. It is based on counting the number of values above and below the hypothesized median. Since the P-value for this test is less than 0.05, we can reject the null hypothesis at the 95.0% confidence level. The signed rank test tests the null hypothesis that the median d17 equals 0.0 versus the alternative hypothesis that the median d17 is not equal to 0.0. It is based on comparing the average ranks of values above and below the hypothesized median. Since the P-value for this test is less than 0.05, we can reject the null hypothesis at the 95.0% confidence level. The sign and signed rank tests are less sensitive to the presence of outliers but are somewhat less powerful than the t-test if the data all come from a single normal distribution.
The chi-square test tests the null hypothesis that the standard deviation of d17 equals 1.0 versus the alternative hypothesis that the standard deviation of d17 is not equal to 1.0. Since the P-value for this test is less than 0.05, we can reject the null hypothesis at the 95.0% confidence level.
Как видно, результаты программы на Python совпадают с результатами из Statgraphics.