Chi-Square Distribution and p value
Chi-Square Distribution and p value, Understanding Chi-Square Statistics and Shaded Regions in Tables
In various statistical analyses, tables often display chi-square (χ²) statistics to represent the differences between observed and expected values.
The shaded region in these tables signifies the column indexes and holds significance in interpreting the results.
The chi-square distribution is a probability distribution used to determine the critical and p-values associated with these statistics.
Normal Distribution in R » Data Science Tutorials
Critical values help identify the significance level at which the observed results deviate from the expected values, while p-values quantify the probability of observing such deviations by chance.
By understanding the chi-square distribution and its relationship with shaded regions in tables, researchers can better assess the statistical significance of their findings and draw more informed conclusions from their data.
| df | A=0.005 | 0.010 | 0.025 | 0.05 | 0.10 | 0.25 | 0.50 | 0.75 | 0.90 | 0.95 | 0.975 | 0.99 | 0.995 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 0.000039 | 0.00016 | 0.00098 | 0.0039 | 0.0158 | 0.102 | 0.455 | 1.32 | 2.71 | 3.84 | 5.02 | 6.63 | 7.88 |
| 2 | 0.0100 | 0.0201 | 0.0506 | 0.103 | 0.211 | 0.575 | 1.39 | 2.77 | 4.61 | 5.99 | 7.38 | 9.21 | 10.6 |
| 3 | 0.0717 | 0.115 | 0.216 | 0.352 | 0.584 | 1.21 | 2.37 | 4.11 | 6.25 | 7.81 | 9.35 | 11.3 | 12.8 |
| 4 | 0.207 | 0.297 | 0.484 | 0.711 | 1.06 | 1.92 | 3.36 | 5.39 | 7.78 | 9.49 | 11.1 | 13.3 | 14.9 |
| 5 | 0.412 | 0.554 | 0.831 | 1.15 | 1.61 | 2.67 | 4.35 | 6.63 | 9.24 | 11.1 | 12.8 | 15.1 | 16.7 |
| 6 | 0.676 | 0.872 | 1.24 | 1.64 | 2.20 | 3.45 | 5.35 | 7.84 | 10.6 | 12.6 | 14.4 | 16.8 | 18.5 |
| 7 | 0.989 | 1.24 | 1.69 | 2.17 | 2.83 | 4.25 | 6.35 | 9.04 | 12.0 | 14.1 | 16.0 | 18.5 | 20.3 |
| 8 | 1.34 | 1.65 | 2.18 | 2.73 | 3.49 | 5.07 | 7.34 | 10.2 | 13.4 | 15.5 | 17.5 | 20.1 | 22.0 |
| 9 | 1.73 | 2.09 | 2.70 | 3.33 | 4.17 | 5.9 | 8.34 | 11.4 | 14.7 | 16.9 | 19.0 | 21.7 | 23.6 |
| 10 | 2.16 | 2.56 | 3.25 | 3.94 | 4.87 | 6.74 | 9.34 | 12.5 | 16.0 | 18.3 | 20.5 | 23.2 | 25.2 |
| 11 | 2.60 | 3.05 | 3.82 | 4.57 | 5.58 | 7.58 | 10.3 | 13.7 | 17.3 | 19.7 | 21.9 | 24.7 | 26.8 |
| 12 | 3.07 | 3.57 | 4.40 | 5.23 | 6.30 | 8.44 | 11.3 | 14.8 | 18.5 | 21.0 | 23.3 | 26.2 | 28.3 |
| 13 | 3.57 | 4.11 | 5.01 | 5.89 | 7.04 | 9.3 | 12.3 | 16.0 | 19.8 | 22.4 | 24.7 | 27.7 | 29.8 |
| 14 | 4.07 | 4.66 | 5.63 | 6.57 | 7.79 | 10.2 | 13.3 | 17.1 | 21.1 | 23.7 | 26.1 | 29.1 | 31.3 |
| 15 | 4.60 | 5.23 | 6.26 | 7.26 | 8.55 | 11.0 | 14.3 | 18.2 | 22.3 | 25.0 | 27.5 | 30.6 | 32.8 |
| 16 | 5.14 | 5.81 | 6.91 | 7.96 | 9.31 | 11.9 | 15.3 | 19.4 | 23.5 | 26.3 | 28.8 | 32.0 | 34.3 |
| 17 | 5.70 | 6.41 | 7.56 | 8.67 | 10.1 | 12.8 | 16.3 | 20.5 | 24.8 | 27.6 | 30.2 | 33.4 | 35.7 |
| 18 | 6.26 | 7.01 | 8.23 | 9.39 | 10.9 | 13.7 | 17.3 | 21.6 | 26.0 | 28.9 | 31.5 | 34.8 | 37.2 |
| 19 | 6.84 | 7.63 | 8.91 | 10.1 | 11.7 | 14.6 | 18.3 | 22.7 | 27.2 | 30.1 | 32.9 | 36.2 | 38.6 |
| 20 | 7.43 | 8.26 | 9.59 | 10.9 | 12.4 | 15.5 | 19.3 | 23.8 | 28.4 | 31.4 | 34.2 | 37.6 | 40.0 |
| 21 | 8.03 | 8.90 | 10.3 | 11.6 | 13.2 | 16.3 | 20.3 | 24.9 | 29.6 | 32.7 | 35.5 | 38.9 | 41.4 |
| 22 | 8.64 | 9.54 | 11.0 | 12.3 | 14.0 | 17.2 | 21.3 | 26.0 | 30.8 | 33.9 | 36.8 | 40.3 | 42.8 |
| 23 | 9.26 | 10.2 | 11.7 | 13.1 | 14.8 | 18.1 | 22.3 | 27.1 | 32.0 | 35.2 | 38.1 | 41.6 | 44.2 |
| 24 | 9.89 | 10.9 | 12.4 | 13.8 | 15.7 | 19.0 | 23.3 | 28.2 | 33.2 | 36.4 | 39.4 | 43.0 | 45.6 |
| 25 | 10.5 | 11.5 | 13.1 | 14.6 | 16.5 | 19.9 | 24.3 | 29.3 | 34.4 | 37.7 | 40.6 | 44.3 | 46.9 |
| 26 | 11.2 | 12.2 | 13.8 | 15.4 | 17.3 | 20.8 | 25.3 | 30.4 | 35.6 | 38.9 | 41.9 | 45.6 | 48.3 |
| 27 | 11.8 | 12.9 | 14.6 | 16.2 | 18.1 | 21.7 | 26.3 | 31.5 | 36.7 | 40.1 | 43.2 | 47.0 | 49.6 |
| 28 | 12.5 | 13.6 | 15.3 | 16.9 | 18.9 | 22.7 | 27.3 | 32.6 | 37.9 | 41.3 | 44.5 | 48.3 | 51.0 |
| 29 | 13.1 | 14.3 | 16.0 | 17.7 | 19.8 | 23.6 | 28.3 | 33.7 | 39.1 | 42.6 | 45.7 | 49.6 | 52.3 |
| 30 | 13.8 | 15.0 | 16.8 | 18.5 | 20.6 | 24.5 | 29.3 | 34.8 | 40.3 | 43.8 | 47.0 | 50.9 | 53.7 |
| 31 | 14.5 | 15.7 | 17.5 | 19.3 | 21.4 | 25.4 | 30.3 | 35.9 | 41.4 | 45.0 | 48.2 | 52.2 | 55.0 |
| 32 | 15.1 | 16.4 | 18.3 | 20.1 | 22.3 | 26.3 | 31.3 | 37.0 | 42.6 | 46.2 | 49.5 | 53.5 | 56.3 |
| 33 | 15.8 | 17.1 | 19.0 | 20.9 | 23.1 | 27.2 | 32.3 | 38.1 | 43.7 | 47.4 | 50.7 | 54.8 | 57.6 |
| 34 | 16.5 | 17.8 | 19.8 | 21.7 | 24.0 | 28.1 | 33.3 | 39.1 | 44.9 | 48.6 | 52.0 | 56.1 | 59.0 |
| 35 | 17.2 | 18.5 | 20.6 | 22.5 | 24.8 | 29.1 | 34.3 | 40.2 | 46.1 | 49.8 | 53.2 | 57.3 | 60.3 |
| 36 | 17.9 | 19.2 | 21.3 | 23.3 | 25.6 | 30.0 | 35.3 | 41.3 | 47.2 | 51.0 | 54.4 | 58.6 | 61.6 |
| 37 | 18.6 | 20.0 | 22.1 | 24.1 | 26.5 | 30.9 | 36.3 | 42.4 | 48.4 | 52.2 | 55.7 | 59.9 | 62.9 |
| 38 | 19.3 | 20.7 | 22.9 | 24.9 | 27.3 | 31.8 | 37.3 | 43.5 | 49.5 | 53.4 | 56.9 | 61.2 | 64.2 |
| 39 | 20.0 | 21.4 | 23.7 | 25.7 | 28.2 | 32.7 | 38.3 | 44.5 | 50.7 | 54.6 | 58.1 | 62.4 | 65.5 |
| 40 | 20.7 | 22.2 | 24.4 | 26.5 | 29.1 | 33.7 | 39.3 | 45.6 | 51.8 | 55.8 | 59.3 | 63.7 | 66.8 |
| 41 | 21.4 | 22.9 | 25.2 | 27.3 | 29.9 | 34.6 | 40.3 | 46.7 | 52.9 | 56.9 | 60.6 | 65.0 | 68.1 |
| 42 | 22.1 | 23.7 | 26.0 | 28.1 | 30.8 | 35.5 | 41.3 | 47.8 | 54.1 | 58.1 | 61.8 | 66.2 | 69.3 |
| 43 | 22.9 | 24.4 | 26.8 | 29.0 | 31.6 | 36.4 | 42.3 | 48.8 | 55.2 | 59.3 | 63.0 | 67.5 | 70.6 |
| 44 | 23.6 | 25.1 | 27.6 | 29.8 | 32.5 | 37.4 | 43.3 | 49.9 | 56.4 | 60.5 | 64.2 | 68.7 | 71.9 |
| 45 | 24.3 | 25.9 | 28.4 | 30.6 | 33.4 | 38.3 | 44.3 | 51.0 | 57.5 | 61.7 | 65.4 | 70.0 | 73.2 |
| df | A=0.005 | 0.010 | 0.025 | 0.05 | 0.10 | 0.25 | 0.50 | 0.75 | 0.90 | 0.95 | 0.975 | 0.99 | 0.995 |
Causal Conclusions and Control of Confounding Variables (finnstats.com)
