Mixed model ANOVA
Very straightforward.
#load packages library(tidyverse) ## ── Attaching packages ─────────────────────────────────────── tidyverse 1.3.1 ── ## ✓ ggplot2 3.3.3 ✓ purrr 0.3.4 ## ✓ tibble 3.1.2 ✓ dplyr 1.0.6 ## ✓ tidyr 1.1.3 ✓ stringr 1.4.0 ## ✓ readr 1.4.0 ✓ forcats 0.5.1 ## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ── ## x dplyr::filter() masks stats::filter() ## x dplyr::lag() masks stats::lag() library(lme4) ## Loading required package: Matrix ## ## Attaching package: 'Matrix' ## The following objects are masked from 'package:tidyr': ## ## expand, pack, unpack flum <- read_csv("http://rstats4ag.org/data/FlumiBeans.csv") ## ## ── Column specification ──────────────────────────────────────────────────────── ## cols( ## year = col_double(), ## treatment = col_character(), ## block = col_double(), ## population.4wk = col_double() ## ) head(flum) ## # A tibble: 6 x 4 ## year treatment block population.4wk ## <dbl> <chr> <dbl> <dbl> ## 1 2009 Nontreated 1 55757 ## 2 2009 Nontreated 2 45302 ## 3 2009 Nontreated 3 38333 ## 4 2009 flumioxazin + trifluralin 1 13939 ## 5 2009 flumioxazin + trifluralin 2 27878 ## 6 2009 flumioxazin + trifluralin 3 31363 str(flum) ## spec_tbl_df [77 × 4] (S3: spec_tbl_df/tbl_df/tbl/data.frame) ## $ year : num [1:77] 2009 2009 2009 2009 2009 ... ## $ treatment : chr [1:77] "Nontreated" "Nontreated" "Nontreated" "flumioxazin + trifluralin" ... ## $ block : num [1:77] 1 2 3 1 2 3 1 2 3 1 ... ## $ population.4wk: num [1:77] 55757 45302 38333 13939 27878 ... ## - attr(*, "spec")= ## .. cols( ## .. year = col_double(), ## .. treatment = col_character(), ## .. block = col_double(), ## .. population.4wk = col_double() ## .. ) flum <- flum %>% mutate(yrblock = with(flum, factor(year):factor(block))) head(flum) ## # A tibble: 6 x 5 ## year treatment block population.4wk yrblock ## <dbl> <chr> <dbl> <dbl> <fct> ## 1 2009 Nontreated 1 55757 2009:1 ## 2 2009 Nontreated 2 45302 2009:2 ## 3 2009 Nontreated 3 38333 2009:3 ## 4 2009 flumioxazin + trifluralin 1 13939 2009:1 ## 5 2009 flumioxazin + trifluralin 2 27878 2009:2 ## 6 2009 flumioxazin + trifluralin 3 31363 2009:3
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