# Examples

## Completely Randomized Design

Single factor CRD is equivalent to One-Way ANOVA.

### Example 1 - CRD

```py
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

```py
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

```py
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

```python
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

```python
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

```python
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

```python
import doex
exp = 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

```python
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

```py
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")`.

```py
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

```py
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    |                     |             |         |
+---------------------+-----+----------------+---------------------+-------------+---------+
```