describe.augmentedRCBD computes descriptive statistics from the adjusted means in an object of class augmentedRCBD.

describe.augmentedRCBD(aug)

## Arguments

aug

An object of class augmentedRCBD.

## Value

A list with the following descriptive statistics:

Count

The number of treatments/genotypes.

Mean

The mean value.

Std.Error

The standard error.

Std.Deviation

The standard deviation.

Min

The minimum value

Max

The maximum value

Skewness(statistic)

The skewness estimator.

Skewness(p.value)

The p-value from D'Agostino test of skewness.

Kurtosis(statistic)

The kurtosis estimator.

Kurtosis(p.value)

The p-value from Anscombe-Glynn test of kurtosis.

## Details

describe.augmentedRCBD computes the following descriptive statistics from the adjusted means in an object of class augmentedRCBD.

• Count

• Mean

• Standard deviation

• Standard error

• Minimum

• Maximum

• Skewness statistic along with p-value from D'Agostino test of skewness (D'Agostino, 1970).

• Kurtosis statistic along with p-value from Anscombe-Glynn test of kurtosis (Anscombe and Glynn, 1983).

## References

D'Agostino RB (1970). “Transformation to normality of the null distribution of g1.” Biometrika, 57(3), 679--681.

Anscombe FJ, Glynn WJ (1983). “Distribution of the kurtosis statistic b2 for normal samples.” Biometrika, 70(1), 227--234.

augmentedRCBD

## Examples

# Example data
blk <- c(rep(1,7),rep(2,6),rep(3,7))
trt <- c(1, 2, 3, 4, 7, 11, 12, 1, 2, 3, 4, 5, 9, 1, 2, 3, 4, 8, 6, 10)
y1 <- c(92, 79, 87, 81, 96, 89, 82, 79, 81, 81, 91, 79, 78, 83, 77, 78, 78,
70, 75, 74)
y2 <- c(258, 224, 238, 278, 347, 300, 289, 260, 220, 237, 227, 281, 311, 250,
240, 268, 287, 226, 395, 450)
data <- data.frame(blk, trt, y1, y2)
# Convert block and treatment to factors
data$blk <- as.factor(data$blk)
data$trt <- as.factor(data$trt)
# Results for variable y1
out1 <- augmentedRCBD(data$blk, data$trt, data$y1, method.comp = "lsd", alpha = 0.05, group = TRUE, console = TRUE) #> #> Augmented Design Details #> ======================== #> #> Number of blocks "3" #> Number of treatments "12" #> Number of check treatments "4" #> Number of test treatments "8" #> Check treatments "1, 2, 3, 4" #> #> #> ANOVA, Treatment Adjusted #> ========================= #> Df Sum Sq Mean Sq F value Pr(>F) #> Block (ignoring Treatments) 2 360.1 180.04 6.675 0.0298 * #> Treatment (eliminating Blocks) 11 285.1 25.92 0.961 0.5499 #> Treatment: Check 3 52.9 17.64 0.654 0.6092 #> Treatment: Test and Test vs. Check 8 232.2 29.02 1.076 0.4779 #> Residuals 6 161.8 26.97 #> --- #> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 #> #> ANOVA, Block Adjusted #> ===================== #> Df Sum Sq Mean Sq F value Pr(>F) #> Treatment (ignoring Blocks) 11 575.7 52.33 1.940 0.215 #> Treatment: Check 3 52.9 17.64 0.654 0.609 #> Treatment: Test 7 505.9 72.27 2.679 0.125 #> Treatment: Test vs. Check 1 16.9 16.87 0.626 0.459 #> Block (eliminating Treatments) 2 69.5 34.75 1.288 0.342 #> Residuals 6 161.8 26.97 #> #> Coefficient of Variation #> ======================== #> 6.372367 #> #> Overall Adjusted Mean #> ===================== #> 81.0625 #> #> Standard Errors #> =============== #> Std. Error of Diff. CD (5%) #> Control Treatment Means 4.240458 10.37603 #> Two Test Treatments (Same Block) 7.344688 17.97180 #> Two Test Treatments (Different Blocks) 8.211611 20.09309 #> A Test Treatment and a Control Treatment 6.704752 16.40594 #> #> Treatment Means #> =============== #> Treatment Block Means SE r Min Max Adjusted Means #> 1 84.67 3.84 3 79.00 92.00 84.67 #> 10 3 74.00 <NA> 1 74.00 74.00 77.25 #> 11 1 89.00 <NA> 1 89.00 89.00 86.50 #> 12 1 82.00 <NA> 1 82.00 82.00 79.50 #> 2 79.00 1.15 3 77.00 81.00 79.00 #> 3 82.00 2.65 3 78.00 87.00 82.00 #> 4 83.33 3.93 3 78.00 91.00 83.33 #> 5 2 79.00 <NA> 1 79.00 79.00 78.25 #> 6 3 75.00 <NA> 1 75.00 75.00 78.25 #> 7 1 96.00 <NA> 1 96.00 96.00 93.50 #> 8 3 70.00 <NA> 1 70.00 70.00 73.25 #> 9 2 78.00 <NA> 1 78.00 78.00 77.25 #> #> #> Comparisons #> =========== #> #> Method : lsd #> #> contrast estimate SE df t.ratio p.value sig #> treatment1 - treatment2 5.67 4.24 6 1.336 0.230 #> treatment1 - treatment3 2.67 4.24 6 0.629 0.553 #> treatment1 - treatment4 1.33 4.24 6 0.314 0.764 #> treatment1 - treatment5 6.42 6.36 6 1.009 0.352 #> treatment1 - treatment6 6.42 6.36 6 1.009 0.352 #> treatment1 - treatment7 -8.83 6.36 6 -1.389 0.214 #> treatment1 - treatment8 11.42 6.36 6 1.795 0.123 #> treatment1 - treatment9 7.42 6.36 6 1.166 0.288 #> treatment1 - treatment10 7.42 6.36 6 1.166 0.288 #> treatment1 - treatment11 -1.83 6.36 6 -0.288 0.783 #> treatment1 - treatment12 5.17 6.36 6 0.812 0.448 #> treatment2 - treatment3 -3.00 4.24 6 -0.707 0.506 #> treatment2 - treatment4 -4.33 4.24 6 -1.022 0.346 #> treatment2 - treatment5 0.75 6.36 6 0.118 0.910 #> treatment2 - treatment6 0.75 6.36 6 0.118 0.910 #> treatment2 - treatment7 -14.50 6.36 6 -2.280 0.063 #> treatment2 - treatment8 5.75 6.36 6 0.904 0.401 #> treatment2 - treatment9 1.75 6.36 6 0.275 0.792 #> treatment2 - treatment10 1.75 6.36 6 0.275 0.792 #> treatment2 - treatment11 -7.50 6.36 6 -1.179 0.283 #> treatment2 - treatment12 -0.50 6.36 6 -0.079 0.940 #> treatment3 - treatment4 -1.33 4.24 6 -0.314 0.764 #> treatment3 - treatment5 3.75 6.36 6 0.590 0.577 #> treatment3 - treatment6 3.75 6.36 6 0.590 0.577 #> treatment3 - treatment7 -11.50 6.36 6 -1.808 0.121 #> treatment3 - treatment8 8.75 6.36 6 1.376 0.218 #> treatment3 - treatment9 4.75 6.36 6 0.747 0.483 #> treatment3 - treatment10 4.75 6.36 6 0.747 0.483 #> treatment3 - treatment11 -4.50 6.36 6 -0.707 0.506 #> treatment3 - treatment12 2.50 6.36 6 0.393 0.708 #> treatment4 - treatment5 5.08 6.36 6 0.799 0.455 #> treatment4 - treatment6 5.08 6.36 6 0.799 0.455 #> treatment4 - treatment7 -10.17 6.36 6 -1.598 0.161 #> treatment4 - treatment8 10.08 6.36 6 1.585 0.164 #> treatment4 - treatment9 6.08 6.36 6 0.956 0.376 #> treatment4 - treatment10 6.08 6.36 6 0.956 0.376 #> treatment4 - treatment11 -3.17 6.36 6 -0.498 0.636 #> treatment4 - treatment12 3.83 6.36 6 0.603 0.569 #> treatment5 - treatment6 0.00 8.21 6 0.000 1.000 #> treatment5 - treatment7 -15.25 8.21 6 -1.857 0.113 #> treatment5 - treatment8 5.00 8.21 6 0.609 0.565 #> treatment5 - treatment9 1.00 7.34 6 0.136 0.896 #> treatment5 - treatment10 1.00 8.21 6 0.122 0.907 #> treatment5 - treatment11 -8.25 8.21 6 -1.005 0.354 #> treatment5 - treatment12 -1.25 8.21 6 -0.152 0.884 #> treatment6 - treatment7 -15.25 8.21 6 -1.857 0.113 #> treatment6 - treatment8 5.00 7.34 6 0.681 0.521 #> treatment6 - treatment9 1.00 8.21 6 0.122 0.907 #> treatment6 - treatment10 1.00 7.34 6 0.136 0.896 #> treatment6 - treatment11 -8.25 8.21 6 -1.005 0.354 #> treatment6 - treatment12 -1.25 8.21 6 -0.152 0.884 #> treatment7 - treatment8 20.25 8.21 6 2.466 0.049 * #> treatment7 - treatment9 16.25 8.21 6 1.979 0.095 #> treatment7 - treatment10 16.25 8.21 6 1.979 0.095 #> treatment7 - treatment11 7.00 7.34 6 0.953 0.377 #> treatment7 - treatment12 14.00 7.34 6 1.906 0.105 #> treatment8 - treatment9 -4.00 8.21 6 -0.487 0.643 #> treatment8 - treatment10 -4.00 7.34 6 -0.545 0.606 #> treatment8 - treatment11 -13.25 8.21 6 -1.614 0.158 #> treatment8 - treatment12 -6.25 8.21 6 -0.761 0.475 #> treatment9 - treatment10 0.00 8.21 6 0.000 1.000 #> treatment9 - treatment11 -9.25 8.21 6 -1.126 0.303 #> treatment9 - treatment12 -2.25 8.21 6 -0.274 0.793 #> treatment10 - treatment11 -9.25 8.21 6 -1.126 0.303 #> treatment10 - treatment12 -2.25 8.21 6 -0.274 0.793 #> treatment11 - treatment12 7.00 7.34 6 0.953 0.377 #> #> Treatment Groups #> ================ #> #> Method : lsd #> #> Treatment Adjusted Means SE df lower.CL upper.CL Group #> 8 73.25 5.61 6 59.52 86.98 1 #> 9 77.25 5.61 6 63.52 90.98 12 #> 10 77.25 5.61 6 63.52 90.98 12 #> 5 78.25 5.61 6 64.52 91.98 12 #> 6 78.25 5.61 6 64.52 91.98 12 #> 2 79.00 3.00 6 71.66 86.34 12 #> 12 79.50 5.61 6 65.77 93.23 12 #> 3 82.00 3.00 6 74.66 89.34 12 #> 4 83.33 3.00 6 76.00 90.67 12 #> 1 84.67 3.00 6 77.33 92.00 12 #> 11 86.50 5.61 6 72.77 100.23 12 #> 7 93.50 5.61 6 79.77 107.23 2 # Results for variable y2 out2 <- augmentedRCBD(data$blk, data$trt, data$y2, method.comp = "lsd",
alpha = 0.05, group = TRUE, console = TRUE)
#>
#> Augmented Design Details
#> ========================
#>
#> Number of blocks           "3"
#> Number of treatments       "12"
#> Number of check treatments "4"
#> Number of test treatments  "8"
#> Check treatments           "1, 2, 3, 4"
#>
#>
#> =========================
#>                                      Df Sum Sq Mean Sq F value   Pr(>F)
#> Block (ignoring Treatments)           2   7019    3510  12.261 0.007597 **
#> Treatment (eliminating Blocks)       11  58965    5360  18.727 0.000920 ***
#>   Treatment: Check                    3   2150     717   2.504 0.156116
#>   Treatment: Test and Test vs. Check  8  56815    7102  24.810 0.000473 ***
#> Residuals                             6   1718     286
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> =====================
#>                                Df Sum Sq Mean Sq F value   Pr(>F)
#> Treatment (ignoring Blocks)    11  64708    5883  20.550 0.000707 ***
#>   Treatment: Check              3   2150     717   2.504 0.156116
#>   Treatment: Test               7  34863    4980  17.399 0.001366 **
#>   Treatment: Test vs. Check     1  27694   27694  96.749 6.36e-05 ***
#> Block (eliminating Treatments)  2   1277     639   2.231 0.188645
#> Residuals                       6   1717     286
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Coefficient of Variation
#> ========================
#> 6.057617
#>
#> =====================
#> 298.4792
#>
#> Standard Errors
#> ===============
#>                                          Std. Error of Diff.  CD (5%)
#> Control Treatment Means                             13.81424 33.80224
#> Two Test Treatments (Same Block)                    23.92697 58.54719
#> Two Test Treatments (Different Blocks)              26.75117 65.45775
#> A Test Treatment and a Control Treatment            21.84224 53.44603
#>
#> Treatment Means
#> ===============
#>  Treatment Block  Means    SE r    Min    Max Adjusted Means
#>          1       256.00  3.06 3 250.00 260.00         256.00
#>         10     3 450.00  <NA> 1 450.00 450.00         437.67
#>         11     1 300.00  <NA> 1 300.00 300.00         299.42
#>         12     1 289.00  <NA> 1 289.00 289.00         288.42
#>          2       228.00  6.11 3 220.00 240.00         228.00
#>          3       247.67 10.17 3 237.00 268.00         247.67
#>          4       264.00 18.68 3 227.00 287.00         264.00
#>          5     2 281.00  <NA> 1 281.00 281.00         293.92
#>          6     3 395.00  <NA> 1 395.00 395.00         382.67
#>          7     1 347.00  <NA> 1 347.00 347.00         346.42
#>          8     3 226.00  <NA> 1 226.00 226.00         213.67
#>          9     2 311.00  <NA> 1 311.00 311.00         323.92
#>
#>
#> Comparisons
#> ===========
#>
#> Method : lsd
#>
#>                   contrast estimate    SE df t.ratio p.value sig
#>    treatment1 - treatment2    28.00 13.81  6   2.027   0.089
#>    treatment1 - treatment3     8.33 13.81  6   0.603   0.568
#>    treatment1 - treatment4    -8.00 13.81  6  -0.579   0.584
#>    treatment1 - treatment5   -37.92 20.72  6  -1.830   0.117
#>    treatment1 - treatment6  -126.67 20.72  6  -6.113   0.001 ***
#>    treatment1 - treatment7   -90.42 20.72  6  -4.363   0.005  **
#>    treatment1 - treatment8    42.33 20.72  6   2.043   0.087
#>    treatment1 - treatment9   -67.92 20.72  6  -3.278   0.017   *
#>   treatment1 - treatment10  -181.67 20.72  6  -8.767   0.000 ***
#>   treatment1 - treatment11   -43.42 20.72  6  -2.095   0.081
#>   treatment1 - treatment12   -32.42 20.72  6  -1.564   0.169
#>    treatment2 - treatment3   -19.67 13.81  6  -1.424   0.204
#>    treatment2 - treatment4   -36.00 13.81  6  -2.606   0.040   *
#>    treatment2 - treatment5   -65.92 20.72  6  -3.181   0.019   *
#>    treatment2 - treatment6  -154.67 20.72  6  -7.464   0.000 ***
#>    treatment2 - treatment7  -118.42 20.72  6  -5.715   0.001  **
#>    treatment2 - treatment8    14.33 20.72  6   0.692   0.515
#>    treatment2 - treatment9   -95.92 20.72  6  -4.629   0.004  **
#>   treatment2 - treatment10  -209.67 20.72  6 -10.118   0.000 ***
#>   treatment2 - treatment11   -71.42 20.72  6  -3.447   0.014   *
#>   treatment2 - treatment12   -60.42 20.72  6  -2.916   0.027   *
#>    treatment3 - treatment4   -16.33 13.81  6  -1.182   0.282
#>    treatment3 - treatment5   -46.25 20.72  6  -2.232   0.067
#>    treatment3 - treatment6  -135.00 20.72  6  -6.515   0.001 ***
#>    treatment3 - treatment7   -98.75 20.72  6  -4.766   0.003  **
#>    treatment3 - treatment8    34.00 20.72  6   1.641   0.152
#>    treatment3 - treatment9   -76.25 20.72  6  -3.680   0.010   *
#>   treatment3 - treatment10  -190.00 20.72  6  -9.169   0.000 ***
#>   treatment3 - treatment11   -51.75 20.72  6  -2.497   0.047   *
#>   treatment3 - treatment12   -40.75 20.72  6  -1.967   0.097
#>    treatment4 - treatment5   -29.92 20.72  6  -1.444   0.199
#>    treatment4 - treatment6  -118.67 20.72  6  -5.727   0.001  **
#>    treatment4 - treatment7   -82.42 20.72  6  -3.977   0.007  **
#>    treatment4 - treatment8    50.33 20.72  6   2.429   0.051
#>    treatment4 - treatment9   -59.92 20.72  6  -2.892   0.028   *
#>   treatment4 - treatment10  -173.67 20.72  6  -8.381   0.000 ***
#>   treatment4 - treatment11   -35.42 20.72  6  -1.709   0.138
#>   treatment4 - treatment12   -24.42 20.72  6  -1.178   0.283
#>    treatment5 - treatment6   -88.75 26.75  6  -3.318   0.016   *
#>    treatment5 - treatment7   -52.50 26.75  6  -1.963   0.097
#>    treatment5 - treatment8    80.25 26.75  6   3.000   0.024   *
#>    treatment5 - treatment9   -30.00 23.93  6  -1.254   0.257
#>   treatment5 - treatment10  -143.75 26.75  6  -5.374   0.002  **
#>   treatment5 - treatment11    -5.50 26.75  6  -0.206   0.844
#>   treatment5 - treatment12     5.50 26.75  6   0.206   0.844
#>    treatment6 - treatment7    36.25 26.75  6   1.355   0.224
#>    treatment6 - treatment8   169.00 23.93  6   7.063   0.000 ***
#>    treatment6 - treatment9    58.75 26.75  6   2.196   0.070
#>   treatment6 - treatment10   -55.00 23.93  6  -2.299   0.061
#>   treatment6 - treatment11    83.25 26.75  6   3.112   0.021   *
#>   treatment6 - treatment12    94.25 26.75  6   3.523   0.012   *
#>    treatment7 - treatment8   132.75 26.75  6   4.962   0.003  **
#>    treatment7 - treatment9    22.50 26.75  6   0.841   0.433
#>   treatment7 - treatment10   -91.25 26.75  6  -3.411   0.014   *
#>   treatment7 - treatment11    47.00 23.93  6   1.964   0.097
#>   treatment7 - treatment12    58.00 23.93  6   2.424   0.052
#>    treatment8 - treatment9  -110.25 26.75  6  -4.121   0.006  **
#>   treatment8 - treatment10  -224.00 23.93  6  -9.362   0.000 ***
#>   treatment8 - treatment11   -85.75 26.75  6  -3.205   0.018   *
#>   treatment8 - treatment12   -74.75 26.75  6  -2.794   0.031   *
#>   treatment9 - treatment10  -113.75 26.75  6  -4.252   0.005  **
#>   treatment9 - treatment11    24.50 26.75  6   0.916   0.395
#>   treatment9 - treatment12    35.50 26.75  6   1.327   0.233
#>  treatment10 - treatment11   138.25 26.75  6   5.168   0.002  **
#>  treatment10 - treatment12   149.25 26.75  6   5.579   0.001  **
#>  treatment11 - treatment12    11.00 23.93  6   0.460   0.662
#>
#> Treatment Groups
#> ================
#>
#> Method : lsd
#>
#>  Treatment Adjusted Means    SE df lower.CL upper.CL    Group
#>          8         213.67 18.27  6   168.95   258.38  12
#>          2         228.00  9.77  6   204.10   251.90  1
#>          3         247.67  9.77  6   223.76   271.57  123
#>          1         256.00  9.77  6   232.10   279.90  1234
#>          4         264.00  9.77  6   240.10   287.90   234
#>         12         288.42 18.27  6   243.70   333.13    345
#>          5         293.92 18.27  6   249.20   338.63    345
#>         11         299.42 18.27  6   254.70   344.13     45
#>          9         323.92 18.27  6   279.20   368.63      56
#>          7         346.42 18.27  6   301.70   391.13      56
#>          6         382.67 18.27  6   337.95   427.38       67
#>         10         437.67 18.27  6   392.95   482.38        7

# Descriptive statistics
describe.augmentedRCBD(out1)
#> $Count #> [1] 12 #> #>$Mean
#> [1] 81.0625
#>
#> $Std.Error #> [1] 1.547002 #> #>$Std.Deviation
#> [1] 5.358973
#>
#> $Min #> [1] 73.25 #> #>$Max
#> [1] 93.5
#>
#> $Skewness(statistic) #> skew z #> 0.9250344 1.6745760 #> #>$Skewness(p.value)
#> [1] 0.09401746
#>
#> $Kurtosis(statistic) #> kurt z #> 3.522807 1.282305 #> #>$Kurtosis(p.value)
#> [1] 0.1997357
#>
describe.augmentedRCBD(out2)
#> $Count #> [1] 12 #> #>$Mean
#> [1] 298.4792
#>
#> $Std.Error #> [1] 18.92257 #> #>$Std.Deviation
#> [1] 65.5497
#>
#> $Min #> [1] 213.6667 #> #>$Max
#> [1] 437.6667
#>
#> $Skewness(statistic) #> skew z #> 0.7449405 1.3680211 #> #>$Skewness(p.value)
#> [1] 0.1713055
#>
#> $Kurtosis(statistic) #> kurt z #> 2.787997 0.536812 #> #>$Kurtosis(p.value)
#> [1] 0.5913975
#>