Mung Bean Chlorophyll over Time (Repeated Measures, Simulated)

Simulated repeated measurements of leaf chlorophyll (SPAD) on the same plots at 25, 35, 45 and 55 days after sowing, for four foliar spray treatments in four randomized complete blocks. Errors within a plot follow a first-order autoregressive process.

Usage

mungbean_repeated

Format

A data frame with 64 rows and 5 variables:

block: Factor, block (R1-R4).
treatment: Factor, foliar spray treatment.
das: Days after sowing (25, 35, 45, 55).
plot: Factor, plot identifier (block-treatment).
spad: SPAD chlorophyll meter reading.

Source

Simulated with data-raw/make_datasets.R (seed 2026). Not real experimental data.

Examples

data(mungbean_repeated)
anova_repeated(mungbean_repeated, "spad", "treatment", "das",
               block = "block")
#> 
#> ======================================================================
#>  REPEATED MEASURES ANOVA (SPLIT-PLOT IN TIME)
#> ======================================================================
#>  Response  : spad
#>  Treatment : treatment
#>  Time      : das
#>  Units     : 16
#>  Times     : 4
#> 
#>  Univariate analysis of variance
#>         Source Df  Sum Sq Mean Sq F value Pr(>F)    
#>  block          3   48.65   16.22   5.124 0.0244   *
#>  treatment      3   87.91   29.30   9.259 0.0041  **
#>  Error(a)       9   28.48    3.16                   
#>  das            3 1203.91  401.30 417.333 0.0000 ***
#>  block:das      9   14.89    1.65   1.721 0.1326  NS
#>  treatment:das  9   40.66    4.52   4.698 0.0008 ***
#>  Error(b)      27   25.96    0.96                   
#>  Total         63 1450.47                           
#>  Signif. codes: *** p < 0.001, ** p < 0.01, * p < 0.05, NS not significant
#> 
#>  Grand mean = 38.202   CV(a) = 4.66%   CV(b) = 2.57%
#> 
#>  Mauchly's test of sphericity: W = 0.5414, p = 0.4518
#>  Greenhouse-Geisser epsilon = 0.7684   Huynh-Feldt epsilon = 1.0000
#> 
#>  Within-unit tests with corrected p-values
#>         Source Df F_value p_uncorrected      p_GG      p_HF recommended
#>            das  3 417.333     1.013e-22 6.414e-18 1.013e-22   1.013e-22
#>  treatment:das  9   4.698     8.219e-04 2.793e-03 8.219e-04   8.219e-04
#> 
#>  Mixed models: covariance structures (lower AIC is better)
#>  Structure Parameters    AIC    BIC logLik
#>         CS         21 238.70 276.63 -98.35
#>        AR1         21 230.72 268.66 -94.36
#>         UN         29 238.50 290.90 -90.25
#> 
#>  F-tests with the AR1 structure (residual df; for treatment, the univariate test above is exact)
#>               numDF F-value   p-value
#> block             3   3.971 1.357e-02
#> treatment         3   7.060 5.465e-04
#> das               3 349.707 3.510e-31
#> treatment:das     9   3.268 3.867e-03
#> 
#>  SEm, SEd and CD (alpha = 0.05)
#>  Comparison                                    SEm   SEd   CD    Error    
#>  treatment means                               0.445 0.629 1.423 E(a)     
#>  das means                                     0.245 0.347 0.711 E(b)     
#>  treatment levels at the same or different das 0.615 0.870 1.880 E(a)+E(b)
#>  das levels at the same treatment              0.490 0.693 1.423 E(b)     
#> 
#>  Treatment x time means
#>                25    35    45    55
#> Control     31.50 38.03 41.33 38.48
#> Water spray 30.62 38.00 41.58 37.48
#> Urea 2%     31.60 39.35 45.98 42.67
#> ZnSO4 0.5%  31.40 38.85 43.80 40.58
#> 
#>  Analysis at each time
#>  Time  Mean F_value p_value Sig   CV   SEm    CD
#>    25 31.28   0.446 0.72600  NS 4.26 0.666 2.132
#>    35 38.56   2.108 0.16900  NS 2.36 0.455 1.455
#>    45 43.17  10.450 0.00273  ** 3.12 0.673 2.154
#>    55 39.80  13.088 0.00124  ** 3.21 0.639 2.044