Examples¶
Completely Randomized Design¶
Single factor CRD is equivalent to One-Way ANOVA.
Example 1 - CRD¶
import doex
exp = doex.CompletelyRandomizedDesign(
[24, 28, 37, 30], # Treatment 1
[37, 44, 31, 35], # Treatment 2
[42, 47, 52, 38], # Treatment 3
)
+---------------------+-----+----------------+---------------------+-------------+---------+
| Source of Variation | DOF | Sum of Squares | Mean Sum of Squares | F statistic | p value |
+---------------------+-----+----------------+---------------------+-------------+---------+
| Treatments | 2 | 450.6667 | 225.3333 | 7.0356 | 0.0145 |
| Error | 9 | 288.2500 | 32.0278 | | |
| Total | 11 | 738.9167 | | | |
+---------------------+-----+----------------+---------------------+-------------+---------+
Example 2 - OneWayANOVA¶
import doex
exp = doex.OneWayANOVA(
[24, 28, 37, 30], # Treatment 1
[37, 44, 31, 35], # Treatment 2
[42, 47, 52, 38], # Treatment 3
)
Randomized Complete Block Design¶
RCBD is equivalent to Two-Way ANOVA.
Example 1 - RCBD¶
import doex
exp = doex.RandomizedCompleteBlockDesign(
[
[73, 68, 74, 71, 67],
[73, 67, 75, 72, 70],
[75, 68, 78, 73, 68],
[73, 71, 75, 75, 69],
]
)
+---------------------+-----+----------------+---------------------+-------------+---------+
| Source of Variation | DOF | Sum of Squares | Mean Sum of Squares | F statistic | p value |
+---------------------+-----+----------------+---------------------+-------------+---------+
| Treatments | 3 | 12.9500 | 4.3167 | 2.3761 | 0.1211 |
| Blocks | 4 | 157.0000 | 39.2500 | 21.6055 | 0.0000 |
| Error | 12 | 21.8000 | 1.8167 | | |
| Total | 19 | 191.7500 | | | |
+---------------------+-----+----------------+---------------------+-------------+---------+
Example 2 - RCBD¶
import doex
exp = doex.RandomizedCompleteBlockDesign(
[
[9.3, 9.4, 9.6, 10.0],
[9.4, 9.3, 9.8, 9.9],
[9.2, 9.4, 9.5, 9.7],
[9.7, 9.6, 10.0, 10.2],
]
)
+---------------------+-----+----------------+---------------------+-------------+---------+
| Source of Variation | DOF | Sum of Squares | Mean Sum of Squares | F statistic | p value |
+---------------------+-----+----------------+---------------------+-------------+---------+
| Treatments | 3 | 0.3850 | 0.1283 | 14.4375 | 0.0009 |
| Blocks | 3 | 0.8250 | 0.2750 | 30.9375 | 0.0000 |
| Error | 9 | 0.0800 | 0.0089 | | |
| Total | 15 | 1.2900 | | | |
+---------------------+-----+----------------+---------------------+-------------+---------+
Example 3 - TwoWayANOVA¶
import doex
exp = doex.TwoWayANOVA(
[
[9.3, 9.4, 9.6, 10.0],
[9.4, 9.3, 9.8, 9.9],
[9.2, 9.4, 9.5, 9.7],
[9.7, 9.6, 10.0, 10.2],
]
)
Randomized Complete Block Design With Missing Values¶
Missing values must be indicated with float("nan").
Example 1 - RCBD One Value Missing¶
import doex
exp = doex.RandomizedCompleteBlockDesign_MissingValues(
[
[18.5, 11.7, 15.4, 16.5],
[15.7, float("nan"), 16.6, 18.6],
[16.2, 12.9, 15.5, 12.7],
[14.1, 14.4, 20.3, 15.7],
[13.0, 16.9, 18.4, 16.5],
[13.6, 12.5, 41.5, 18.0],
]
)
Data after adjusting for 1 missing value(s)
[[18.5 11.7 15.4 16.5 ]
[15.7 12.92 16.6 18.6 ]
[16.2 12.9 15.5 12.7 ]
[14.1 14.4 20.3 15.7 ]
[13. 16.9 18.4 16.5 ]
[13.6 12.5 41.5 18. ]]
+---------------------+-----+----------------+---------------------+-------------+---------+
| Source of Variation | DOF | Sum of Squares | Mean Sum of Squares | F statistic | p value |
+---------------------+-----+----------------+---------------------+-------------+---------+
| Treatments | 5 | 120.6883 | 24.1377 | 0.7561 | 0.5956 |
| Blocks | 3 | 199.7598 | 66.5866 | 2.0859 | 0.1481 |
| Error | 14 | 446.9110 | 31.9222 | | |
| Total | 23 | 767.3591 | | | |
+---------------------+-----+----------------+---------------------+-------------+---------+
Example 2 - RCBD One Value Missing¶
import doex
exp = doex.RandomizedCompleteBlockDesign_MissingValues(
[
[90.3, 89.2, 98.2, 93.9, 87.4, 97.9],
[92.5, 89.5, 90.6, float("nan"), 87, 95.8],
[85.5, 90.8, 89.6, 86.2, 88, 93.4],
[82.5, 89.5, 85.6, 87.4, 78.9, 90.7],
]
)
Data after adjusting for 1 missing value(s)
[[90.3 89.2 98.2 93.9 87.4 97.9 ]
[92.5 89.5 90.6 91.08 87. 95.8 ]
[85.5 90.8 89.6 86.2 88. 93.4 ]
[82.5 89.5 85.6 87.4 78.9 90.7 ]]
+---------------------+-----+----------------+---------------------+-------------+---------+
| Source of Variation | DOF | Sum of Squares | Mean Sum of Squares | F statistic | p value |
+---------------------+-----+----------------+---------------------+-------------+---------+
| Treatments | 3 | 166.1438 | 55.3813 | 7.6241 | 0.0029 |
| Blocks | 5 | 189.5220 | 37.9044 | 5.2181 | 0.0065 |
| Error | 14 | 101.6960 | 7.2640 | | |
| Total | 23 | 457.3618 | | | |
+---------------------+-----+----------------+---------------------+-------------+---------+
Example 3 - RCBD Two Values Missing¶
import doex
exp = doex.RandomizedCompleteBlockDesign_MissingValues(
[
[[12, 14, 12],
[10, float("nan"), 8],
[float("nan"), 15, 10]]
]
)
Data after adjusting for 2 missing value(s)
[[12. 14. 12.]
[10. 12. 8.]
[12. 15. 10.]]
+---------------------+-----+----------------+---------------------+-------------+---------+
| Source of Variation | DOF | Sum of Squares | Mean Sum of Squares | F statistic | p value |
+---------------------+-----+----------------+---------------------+-------------+---------+
| Treatments | 2 | 12.6667 | 6.3333 | 4.7500 | 0.1739 |
| Blocks | 2 | 20.6667 | 10.3333 | 7.7500 | 0.1143 |
| Error | 2 | 2.6667 | 1.3333 | | |
| Total | 8 | 36.0000 | | | |
+---------------------+-----+----------------+---------------------+-------------+---------+
Latin Square Design¶
Example 1 - LSD¶
import doex
exp = doex.LatinSquare(
[
["A", "B", "D", "C", "E"],
["C", "E", "A", "D", "B"],
["B", "A", "C", "E", "D"],
["D", "C", "E", "B", "A"],
["E", "D", "B", "A", "C"],
],
[
[8, 7, 1, 7, 3],
[11, 2, 7, 3, 8],
[4, 9, 10, 1, 5],
[6, 8, 6, 6, 10],
[4, 2, 3, 8, 8],
],
)
+---------------------+-----+----------------+---------------------+-------------+---------+
| Source of Variation | DOF | Sum of Squares | Mean Sum of Squares | F statistic | p value |
+---------------------+-----+----------------+---------------------+-------------+---------+
| Treatments | 4 | 141.4400 | 35.3600 | 11.3092 | 0.0005 |
| Rows | 4 | 15.4400 | 3.8600 | 1.2345 | 0.3476 |
| Columns | 4 | 12.2400 | 3.0600 | 0.9787 | 0.4550 |
| Error | 12 | 37.5200 | 3.1267 | | |
| Total | 24 | 206.6400 | | | |
+---------------------+-----+----------------+---------------------+-------------+---------+
Example 2 - LSD With Missing Value¶
Missing values must be indicated with float("nan").
import doex
exp = doex.LatinSquare(
[
["A", "C", "B", "D"],
["C", "B", "D", "A"],
["B", "D", "A", "C"],
["D", "A", "C", "B"],
],
[
[12, 19, 10, 8],
[18, 12, 6, float("nan")],
[22, 10, 5, 21],
[12, 7, 27, 17],
]
)
Treatment values after handling 1 missing value at (1, 3):
[[12. 19. 10. 8.]
[18. 12. 6. 2.]
[22. 10. 5. 21.]
[12. 7. 27. 17.]]
+---------------------+-----+----------------+---------------------+-------------+---------+
| Source of Variation | DOF | Sum of Squares | Mean Sum of Squares | F statistic | p value |
+---------------------+-----+----------------+---------------------+-------------+---------+
| Treatments | 3 | 525.5000 | 175.1667 | 12.5119 | 0.0092 |
| Rows | 3 | 90.5000 | 30.1667 | 2.1548 | 0.2119 |
| Columns | 3 | 48.0000 | 16.0000 | 1.1429 | 0.4168 |
| Error | 5 | 70.0000 | 14.0000 | | |
| Total | 15 | 734.0000 | | | |
+---------------------+-----+----------------+---------------------+-------------+---------+
Graeco-Latin Square Design¶
import doex
exp = doex.GraecoLatinSquare(
latin=[
["A", "B", "C", "D", "E"],
["B", "C", "D", "E", "A"],
["C", "D", "E", "A", "B"],
["D", "E", "A", "B", "C"],
["E", "A", "B", "C", "D"],
],
greek=[
["a", "g", "e", "b", "d"],
["b", "d", "a", "g", "e"],
["g", "e", "b", "d", "a"],
["d", "a", "g", "e", "b"],
["e", "b", "d", "a", "g"],
],
treatments_values=[
[-1, -5, -6, -1, -1],
[-8, -1, 5, 2, 11],
[-7, 13, 1, 2, -4],
[1, 6, 1, -2, -3],
[-3, 5, -5, 4, 6],
],
)
+---------------------+-----+----------------+---------------------+-------------+---------+
| Source of Variation | DOF | Sum of Squares | Mean Sum of Squares | F statistic | p value |
+---------------------+-----+----------------+---------------------+-------------+---------+
| Latin treatments | 4 | 330.0000 | 82.5000 | 10.0000 | 0.0033 |
| Greek treatments | 4 | 62.0000 | 15.5000 | 1.8788 | 0.2076 |
| Rows | 4 | 68.0000 | 17.0000 | 2.0606 | 0.1783 |
| Columns | 4 | 150.0000 | 37.5000 | 4.5455 | 0.0329 |
| Error | 8 | 66.0000 | 8.2500 | | |
| Total | 24 | 676.0000 | | | |
+---------------------+-----+----------------+---------------------+-------------+---------+