Morphometric analysis of CD68 content in microglia by 63X confocal microscopy

Dependent variables: iba1.vol, cd68.vol, perc.cd68 Unit of measure: n is a cell Fixed Effects: group (MIA, CON), trt (SAL, LPS), region (dorsal striatum (DS) & ventral striatum (VS))

## `summarise()` has grouped output by 'group', 'trt'. You can override using the `.groups` argument.
## # A tibble: 8 x 6
## # Groups:   group, trt [4]
##   group trt   region     n mouse litter
##   <fct> <fct> <fct>  <int> <int>  <int>
## 1 CON   SAL   DS        34     4      4
## 2 CON   SAL   VS        25     4      4
## 3 CON   LPS   DS        33     4      4
## 4 CON   LPS   VS        29     4      4
## 5 MIA   SAL   DS        19     4      3
## 6 MIA   SAL   VS        26     4      3
## 7 MIA   LPS   DS        26     3      2
## 8 MIA   LPS   VS        19     3      2

Plot microglia volume, cd68 volume and % CD68, n= per cell

black = CON, red = MIA

3-way ANOVA (group x region x trt)

Iba1.Vol

# get summary data
data %>%
  group_by(group, region, trt) %>%
  get_summary_stats(iba1.vol, type = "mean_sd")
## # A tibble: 8 x 7
##   group trt   region variable     n  mean    sd
##   <fct> <fct> <fct>  <chr>    <dbl> <dbl> <dbl>
## 1 CON   SAL   DS     iba1.vol    34 1400.  510.
## 2 CON   LPS   DS     iba1.vol    33 1288.  715.
## 3 CON   SAL   VS     iba1.vol    25 1304.  637.
## 4 CON   LPS   VS     iba1.vol    29 1050.  592.
## 5 MIA   SAL   DS     iba1.vol    19 1412.  793.
## 6 MIA   LPS   DS     iba1.vol    26  864.  621.
## 7 MIA   SAL   VS     iba1.vol    26 1620.  952.
## 8 MIA   LPS   VS     iba1.vol    19  611.  540.
# Build the linear model
model  <- lm(iba1.vol ~ group+trt+region+group:trt, data = data)

# Compute Shapiro-Wilk test of normality and levene test for equal variance
data %>% group_by(trt, region, group) %>% shapiro_test(iba1.vol)
## # A tibble: 8 x 6
##   group trt   region variable statistic         p
##   <fct> <fct> <fct>  <chr>        <dbl>     <dbl>
## 1 CON   SAL   DS     iba1.vol     0.985 0.919    
## 2 MIA   SAL   DS     iba1.vol     0.952 0.423    
## 3 CON   SAL   VS     iba1.vol     0.937 0.129    
## 4 MIA   SAL   VS     iba1.vol     0.894 0.0116   
## 5 CON   LPS   DS     iba1.vol     0.794 0.0000248
## 6 MIA   LPS   DS     iba1.vol     0.871 0.00379  
## 7 CON   LPS   VS     iba1.vol     0.862 0.00135  
## 8 MIA   LPS   VS     iba1.vol     0.753 0.000254
data %>% levene_test(iba1.vol ~ group*trt*region)
## # A tibble: 1 x 4
##     df1   df2 statistic     p
##   <int> <int>     <dbl> <dbl>
## 1     7   203     0.858 0.541
res.aov <- data %>% anova_test(iba1.vol ~ group+trt+region+group:trt)
## Coefficient covariances computed by hccm()
res.aov
## ANOVA Table (type II tests)
## 
##      Effect DFn DFd      F        p p<.05   ges
## 1     group   1 206  1.675 1.97e-01       0.008
## 2       trt   1 206 21.972 5.03e-06     * 0.096
## 3    region   1 206  1.295 2.56e-01       0.006
## 4 group:trt   1 206 10.459 1.00e-03     * 0.048
aov.out <- lm(iba1.vol ~ group+trt+region+group:trt, data = data)
Anova(aov.out) 
## Anova Table (Type II tests)
## 
## Response: iba1.vol
##             Sum Sq  Df F value    Pr(>F)    
## group       771716   1  1.6746  0.197099    
## trt       10125827   1 21.9721 5.026e-06 ***
## region      596784   1  1.2950  0.256457    
## group:trt  4819951   1 10.4588  0.001422 ** 
## Residuals 94934962 206                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
data %>%
  group_by(trt, region) %>%
  anova_test(iba1.vol ~ group, error = aov.out)
## Coefficient covariances computed by hccm()
## Coefficient covariances computed by hccm()
## Coefficient covariances computed by hccm()
## Coefficient covariances computed by hccm()
## # A tibble: 4 x 9
##   trt   region Effect   DFn   DFd     F     p `p<.05`       ges
## * <fct> <fct>  <chr>  <dbl> <dbl> <dbl> <dbl> <chr>       <dbl>
## 1 SAL   DS     group      1   206 0.003 0.953 ""      0.0000168
## 2 SAL   VS     group      1   206 2.78  0.097 ""      0.013    
## 3 LPS   DS     group      1   206 5.68  0.018 "*"     0.027    
## 4 LPS   VS     group      1   206 4.81  0.029 "*"     0.023
pwc <- data %>%
  group_by(trt, region) %>%
  emmeans_test(iba1.vol ~ group, p.adjust.method = "fdr")
pwc
## # A tibble: 4 x 11
##   trt   region term  .y.      group1 group2    df statistic      p  p.adj
## * <chr> <chr>  <chr> <chr>    <chr>  <chr>  <dbl>     <dbl>  <dbl>  <dbl>
## 1 LPS   DS     group iba1.vol CON    MIA      203    2.39   0.0179 0.0179
## 2 LPS   VS     group iba1.vol CON    MIA      203    2.20   0.0293 0.0293
## 3 SAL   DS     group iba1.vol CON    MIA      203   -0.0589 0.953  0.953 
## 4 SAL   VS     group iba1.vol CON    MIA      203   -1.67   0.0968 0.0968
## # … with 1 more variable: p.adj.signif <chr>
# posthoc emmeans

data %>% 
  emmeans_test(
    iba1.vol ~ group, p.adjust.method = "fdr", model = model)
## NOTE: Results may be misleading due to involvement in interactions
## # A tibble: 1 x 9
##   term  .y.      group1 group2    df statistic     p p.adj p.adj.signif
## * <chr> <chr>    <chr>  <chr>  <dbl>     <dbl> <dbl> <dbl> <chr>       
## 1 group iba1.vol CON    MIA      206      1.24 0.215 0.215 ns
pwc <- pwc %>% add_xy_position(x = "region")
bxp <- ggboxplot(data, x = "region", y = "iba1.vol", color = "group", palette = "jco", facet.by = "trt",  add.params = list(size=0.5))
bxp +
  stat_pvalue_manual(pwc) +
  labs(
    subtitle = get_test_label(res.aov, detailed = TRUE),
    caption = get_pwc_label(pwc))

Cd68.Vol

# get summary data
data %>%
  group_by(group, region, trt) %>%
  get_summary_stats(cd68.vol, type = "mean_sd")
## # A tibble: 8 x 7
##   group trt   region variable     n  mean    sd
##   <fct> <fct> <fct>  <chr>    <dbl> <dbl> <dbl>
## 1 CON   SAL   DS     cd68.vol    34  50.0  28.7
## 2 CON   LPS   DS     cd68.vol    33  56.2  39.9
## 3 CON   SAL   VS     cd68.vol    25  44.5  35.3
## 4 CON   LPS   VS     cd68.vol    29  41.7  33.3
## 5 MIA   SAL   DS     cd68.vol    19  43.9  32.7
## 6 MIA   LPS   DS     cd68.vol    26  29.3  26.2
## 7 MIA   SAL   VS     cd68.vol    26  37.9  31.2
## 8 MIA   LPS   VS     cd68.vol    19  19.5  23.6
# Build the linear model
model  <- lm(cd68.vol ~ group+trt+region+group:trt, data = data)

# Compute Shapiro-Wilk test of normality and levene test for equal variance
data %>% group_by(trt, region, group) %>% shapiro_test(cd68.vol)
## # A tibble: 8 x 6
##   group trt   region variable statistic         p
##   <fct> <fct> <fct>  <chr>        <dbl>     <dbl>
## 1 CON   SAL   DS     cd68.vol     0.917 0.0130   
## 2 MIA   SAL   DS     cd68.vol     0.896 0.0407   
## 3 CON   SAL   VS     cd68.vol     0.883 0.00784  
## 4 MIA   SAL   VS     cd68.vol     0.841 0.000945 
## 5 CON   LPS   DS     cd68.vol     0.863 0.000669 
## 6 MIA   LPS   DS     cd68.vol     0.838 0.000830 
## 7 CON   LPS   VS     cd68.vol     0.764 0.0000205
## 8 MIA   LPS   VS     cd68.vol     0.712 0.0000772
data %>% levene_test(cd68.vol ~ group*trt*region)
## # A tibble: 1 x 4
##     df1   df2 statistic     p
##   <int> <int>     <dbl> <dbl>
## 1     7   203     0.902 0.506
res.aov <- data %>% anova_test(cd68.vol ~ group+trt+region+group:trt)
## Coefficient covariances computed by hccm()
res.aov
## ANOVA Table (type II tests)
## 
##      Effect DFn DFd      F        p p<.05   ges
## 1     group   1 206 11.934 0.000669     * 0.055
## 2       trt   1 206  1.772 0.185000       0.009
## 3    region   1 206  4.321 0.039000     * 0.021
## 4 group:trt   1 206  4.441 0.036000     * 0.021
aov.out <- lm(cd68.vol ~ group+trt+region+group:trt, data = data)
Anova(aov.out) 
## Anova Table (Type II tests)
## 
## Response: cd68.vol
##           Sum Sq  Df F value    Pr(>F)    
## group      12199   1 11.9340 0.0006691 ***
## trt         1811   1  1.7721 0.1845986    
## region      4417   1  4.3213 0.0388761 *  
## group:trt   4540   1  4.4414 0.0362863 *  
## Residuals 210579 206                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
data %>%
  group_by(trt, region) %>%
  anova_test(cd68.vol ~ group, error = aov.out)
## Coefficient covariances computed by hccm()
## Coefficient covariances computed by hccm()
## Coefficient covariances computed by hccm()
## Coefficient covariances computed by hccm()
## # A tibble: 4 x 9
##   trt   region Effect   DFn   DFd      F     p `p<.05`   ges
## * <fct> <fct>  <chr>  <dbl> <dbl>  <dbl> <dbl> <chr>   <dbl>
## 1 SAL   DS     group      1   206  0.453 0.502 ""      0.002
## 2 SAL   VS     group      1   206  0.535 0.465 ""      0.003
## 3 LPS   DS     group      1   206 10.3   0.002 "*"     0.048
## 4 LPS   VS     group      1   206  5.54  0.02  "*"     0.026
pwc <- data %>%
  group_by(trt, region) %>%
  emmeans_test(cd68.vol ~ group, p.adjust.method = "fdr")
pwc
## # A tibble: 4 x 11
##   trt   region term  .y.      group1 group2    df statistic       p   p.adj
## * <chr> <chr>  <chr> <chr>    <chr>  <chr>  <dbl>     <dbl>   <dbl>   <dbl>
## 1 LPS   DS     group cd68.vol CON    MIA      203     3.19  0.00165 0.00165
## 2 LPS   VS     group cd68.vol CON    MIA      203     2.34  0.0202  0.0202 
## 3 SAL   DS     group cd68.vol CON    MIA      203     0.669 0.504   0.504  
## 4 SAL   VS     group cd68.vol CON    MIA      203     0.727 0.468   0.468  
## # … with 1 more variable: p.adj.signif <chr>
# posthoc
data %>% 
  emmeans_test(
    cd68.vol ~ group, p.adjust.method = "fdr", model = model)
## NOTE: Results may be misleading due to involvement in interactions
## # A tibble: 1 x 9
##   term  .y.      group1 group2    df statistic        p    p.adj p.adj.signif
## * <chr> <chr>    <chr>  <chr>  <dbl>     <dbl>    <dbl>    <dbl> <chr>       
## 1 group cd68.vol CON    MIA      206      3.42 0.000753 0.000753 ***
pwc <- pwc %>% add_xy_position(x = "region")
bxp <- ggboxplot(data, x = "region", y = "cd68.vol", color = "group", palette = "jco", facet.by = "trt",  add.params = list(size=0.5))
bxp +
  stat_pvalue_manual(pwc) +
  labs(
    subtitle = get_test_label(res.aov, detailed = TRUE),
    caption = get_pwc_label(pwc))

Percent CD68

# get summary data
data %>%
  group_by(group, region, trt) %>%
  get_summary_stats(perc.cd68, type = "mean_sd")
## # A tibble: 8 x 7
##   group trt   region variable      n  mean    sd
##   <fct> <fct> <fct>  <chr>     <dbl> <dbl> <dbl>
## 1 CON   SAL   DS     perc.cd68    34  3.60  1.86
## 2 CON   LPS   DS     perc.cd68    33  4.54  2.38
## 3 CON   SAL   VS     perc.cd68    25  3.49  1.88
## 4 CON   LPS   VS     perc.cd68    29  3.97  1.81
## 5 MIA   SAL   DS     perc.cd68    19  3.35  1.82
## 6 MIA   LPS   DS     perc.cd68    26  3.21  1.48
## 7 MIA   SAL   VS     perc.cd68    26  2.56  2.07
## 8 MIA   LPS   VS     perc.cd68    19  2.74  1.44
# Build the linear model
model  <- lm(perc.cd68 ~ group+trt+region+group:trt, data = data)

# Compute Shapiro-Wilk test of normality and levene test for equal variance
data %>% group_by(trt, region, group) %>% shapiro_test(perc.cd68)
## # A tibble: 8 x 6
##   group trt   region variable  statistic       p
##   <fct> <fct> <fct>  <chr>         <dbl>   <dbl>
## 1 CON   SAL   DS     perc.cd68     0.953 0.148  
## 2 MIA   SAL   DS     perc.cd68     0.954 0.463  
## 3 CON   SAL   VS     perc.cd68     0.973 0.729  
## 4 MIA   SAL   VS     perc.cd68     0.873 0.00407
## 5 CON   LPS   DS     perc.cd68     0.960 0.257  
## 6 MIA   LPS   DS     perc.cd68     0.963 0.456  
## 7 CON   LPS   VS     perc.cd68     0.932 0.0608 
## 8 MIA   LPS   VS     perc.cd68     0.943 0.300
data %>% levene_test(perc.cd68 ~ group*trt*region)
## # A tibble: 1 x 4
##     df1   df2 statistic     p
##   <int> <int>     <dbl> <dbl>
## 1     7   203      1.31 0.246
res.aov <- data %>% anova_test(perc.cd68 ~ group+trt+region+group:trt)
## Coefficient covariances computed by hccm()
res.aov
## ANOVA Table (type II tests)
## 
##      Effect DFn DFd      F       p p<.05   ges
## 1     group   1 206 12.812 0.00043     * 0.059
## 2       trt   1 206  2.945 0.08800       0.014
## 3    region   1 206  3.189 0.07600       0.015
## 4 group:trt   1 206  1.737 0.18900       0.008
model  <- lm(perc.cd68 ~ group*trt+region, data = data)
data %>%
  group_by(trt) %>%
  anova_test(perc.cd68 ~ group+region, error = aov.out)
## Coefficient covariances computed by hccm()
## Coefficient covariances computed by hccm()
## # A tibble: 4 x 8
##   trt   Effect   DFn   DFd     F     p `p<.05`       ges
## * <fct> <chr>  <dbl> <dbl> <dbl> <dbl> <chr>       <dbl>
## 1 SAL   group      1   206 0.009 0.926 ""      0.0000422
## 2 SAL   region     1   206 0.004 0.949 ""      0.00002  
## 3 LPS   group      1   206 0.042 0.838 ""      0.000204 
## 4 LPS   region     1   206 0.007 0.933 ""      0.0000348
data %>%
  group_by(region) %>%
  anova_test(perc.cd68 ~ group*trt, error = aov.out)
## Coefficient covariances computed by hccm()
## Coefficient covariances computed by hccm()
## # A tibble: 6 x 8
##   region Effect      DFn   DFd        F     p `p<.05`        ges
## * <fct>  <chr>     <dbl> <dbl>    <dbl> <dbl> <chr>        <dbl>
## 1 DS     group         1   206 0.018    0.893 ""      0.0000884 
## 2 DS     trt           1   206 0.007    0.933 ""      0.0000343 
## 3 DS     group:trt     1   206 0.008    0.931 ""      0.0000365 
## 4 VS     group         1   206 0.027    0.869 ""      0.000133  
## 5 VS     trt           1   206 0.003    0.957 ""      0.000014  
## 6 VS     group:trt     1   206 0.000554 0.981 ""      0.00000269
data %>%
  group_by(trt, region) %>%
  anova_test(perc.cd68 ~ group, error = aov.out)
## Coefficient covariances computed by hccm()
## Coefficient covariances computed by hccm()
## Coefficient covariances computed by hccm()
## Coefficient covariances computed by hccm()
## # A tibble: 4 x 9
##   trt   region Effect   DFn   DFd        F     p `p<.05`        ges
## * <fct> <fct>  <chr>  <dbl> <dbl>    <dbl> <dbl> <chr>        <dbl>
## 1 SAL   DS     group      1   206 0.000739 0.978 ""      0.00000359
## 2 SAL   VS     group      1   206 0.011    0.917 ""      0.0000524 
## 3 LPS   DS     group      1   206 0.025    0.875 ""      0.000121  
## 4 LPS   VS     group      1   206 0.017    0.896 ""      0.0000833
library(emmeans)
pwc <- data %>%
  group_by(trt, region) %>%
  emmeans_test(perc.cd68 ~ group, p.adjust.method = "bh") %>%
  select(-df, -statistic, -p) 

pwc <- data %>%
  group_by(trt, region) %>%
  emmeans_test(perc.cd68 ~ group, p.adjust.method = "fdr")
pwc
## # A tibble: 4 x 11
##   trt   region term  .y.       group1 group2    df statistic       p   p.adj
## * <chr> <chr>  <chr> <chr>     <chr>  <chr>  <dbl>     <dbl>   <dbl>   <dbl>
## 1 LPS   DS     group perc.cd68 CON    MIA      203     2.67  0.00830 0.00830
## 2 LPS   VS     group perc.cd68 CON    MIA      203     2.21  0.0283  0.0283 
## 3 SAL   DS     group perc.cd68 CON    MIA      203     0.458 0.647   0.647  
## 4 SAL   VS     group perc.cd68 CON    MIA      203     1.75  0.0813  0.0813 
## # … with 1 more variable: p.adj.signif <chr>
pwc <- pwc %>% add_xy_position(x = "trt")
bxp <- ggboxplot(data, x = "trt", y = "perc.cd68", color = "group", palette = "jco", facet.by = "region",  add.params = list(size=0.5))
bxp +
  stat_pvalue_manual(pwc) +
  labs(
    subtitle = get_test_label(res.aov, detailed = TRUE),
    caption = get_pwc_label(pwc))

Reproducibility info

## [1] "2021-09-06 14:31:36 EDT"
## ─ Session info ───────────────────────────────────────────────────────────────
##  setting  value                       
##  version  R version 4.0.3 (2020-10-10)
##  os       macOS Big Sur 10.16         
##  system   x86_64, darwin17.0          
##  ui       X11                         
##  language (EN)                        
##  collate  en_US.UTF-8                 
##  ctype    en_US.UTF-8                 
##  tz       America/New_York            
##  date     2021-09-06                  
## 
## ─ Packages ───────────────────────────────────────────────────────────────────
##  package      * version    date       lib source        
##  abind          1.4-5      2016-07-21 [1] CRAN (R 4.0.2)
##  assertthat     0.2.1      2019-03-21 [1] CRAN (R 4.0.2)
##  backports      1.2.1      2020-12-09 [1] CRAN (R 4.0.2)
##  boot           1.3-28     2021-05-03 [1] CRAN (R 4.0.2)
##  broom          0.7.8      2021-06-24 [1] CRAN (R 4.0.2)
##  bslib          0.2.5.1    2021-05-18 [1] CRAN (R 4.0.2)
##  cachem         1.0.5      2021-05-15 [1] CRAN (R 4.0.2)
##  callr          3.7.0      2021-04-20 [1] CRAN (R 4.0.2)
##  car          * 3.0-11     2021-06-27 [1] CRAN (R 4.0.3)
##  carData      * 3.0-4      2020-05-22 [1] CRAN (R 4.0.2)
##  cellranger     1.1.0      2016-07-27 [1] CRAN (R 4.0.2)
##  cli            3.0.0      2021-06-30 [1] CRAN (R 4.0.2)
##  coda           0.19-4     2020-09-30 [1] CRAN (R 4.0.2)
##  codetools      0.2-18     2020-11-04 [1] CRAN (R 4.0.2)
##  colorspace     2.0-2      2021-06-24 [1] CRAN (R 4.0.2)
##  cowplot      * 1.1.1      2020-12-30 [1] CRAN (R 4.0.2)
##  crayon         1.4.1      2021-02-08 [1] CRAN (R 4.0.2)
##  curl           4.3.2      2021-06-23 [1] CRAN (R 4.0.2)
##  data.table     1.14.0     2021-02-21 [1] CRAN (R 4.0.3)
##  DBI            1.1.1      2021-01-15 [1] CRAN (R 4.0.2)
##  dbplyr         2.1.1      2021-04-06 [1] CRAN (R 4.0.2)
##  desc           1.3.0      2021-03-05 [1] CRAN (R 4.0.2)
##  devtools       2.4.2      2021-06-07 [1] CRAN (R 4.0.2)
##  digest         0.6.27     2020-10-24 [1] CRAN (R 4.0.2)
##  dplyr        * 1.0.7      2021-06-18 [1] CRAN (R 4.0.2)
##  ellipsis       0.3.2      2021-04-29 [1] CRAN (R 4.0.2)
##  emmeans      * 1.6.1      2021-06-01 [1] CRAN (R 4.0.2)
##  estimability   1.3        2018-02-11 [1] CRAN (R 4.0.2)
##  evaluate       0.14       2019-05-28 [1] CRAN (R 4.0.1)
##  fansi          0.5.0      2021-05-25 [1] CRAN (R 4.0.3)
##  farver         2.1.0      2021-02-28 [1] CRAN (R 4.0.2)
##  fastmap        1.1.0      2021-01-25 [1] CRAN (R 4.0.2)
##  forcats      * 0.5.1      2021-01-27 [1] CRAN (R 4.0.3)
##  foreign        0.8-81     2020-12-22 [1] CRAN (R 4.0.2)
##  fs             1.5.0      2020-07-31 [1] CRAN (R 4.0.2)
##  generics       0.1.0      2020-10-31 [1] CRAN (R 4.0.2)
##  ggplot2      * 3.3.5      2021-06-25 [1] CRAN (R 4.0.2)
##  ggpubr       * 0.4.0      2020-06-27 [1] CRAN (R 4.0.2)
##  ggsci          2.9        2018-05-14 [1] CRAN (R 4.0.2)
##  ggsignif       0.6.2      2021-06-14 [1] CRAN (R 4.0.2)
##  glue           1.4.2      2020-08-27 [1] CRAN (R 4.0.2)
##  gtable         0.3.0      2019-03-25 [1] CRAN (R 4.0.2)
##  haven          2.4.1      2021-04-23 [1] CRAN (R 4.0.2)
##  highr          0.9        2021-04-16 [1] CRAN (R 4.0.2)
##  hms            1.1.0      2021-05-17 [1] CRAN (R 4.0.2)
##  htmltools      0.5.1.1    2021-01-22 [1] CRAN (R 4.0.2)
##  httr           1.4.2      2020-07-20 [1] CRAN (R 4.0.2)
##  jquerylib      0.1.4      2021-04-26 [1] CRAN (R 4.0.3)
##  jsonlite       1.7.2      2020-12-09 [1] CRAN (R 4.0.2)
##  knitr          1.33       2021-04-24 [1] CRAN (R 4.0.2)
##  labeling       0.4.2      2020-10-20 [1] CRAN (R 4.0.2)
##  lattice        0.20-44    2021-05-02 [1] CRAN (R 4.0.2)
##  lifecycle      1.0.0      2021-02-15 [1] CRAN (R 4.0.2)
##  lme4         * 1.1-27.1   2021-06-22 [1] CRAN (R 4.0.2)
##  lmerTest     * 3.1-3      2020-10-23 [1] CRAN (R 4.0.2)
##  lubridate      1.7.10     2021-02-26 [1] CRAN (R 4.0.2)
##  magrittr       2.0.1      2020-11-17 [1] CRAN (R 4.0.2)
##  MASS         * 7.3-54     2021-05-03 [1] CRAN (R 4.0.2)
##  Matrix       * 1.3-4      2021-06-01 [1] CRAN (R 4.0.2)
##  memoise        2.0.0      2021-01-26 [1] CRAN (R 4.0.2)
##  minqa          1.2.4      2014-10-09 [1] CRAN (R 4.0.2)
##  modelr         0.1.8      2020-05-19 [1] CRAN (R 4.0.2)
##  multcomp     * 1.4-17     2021-04-29 [1] CRAN (R 4.0.2)
##  munsell        0.5.0      2018-06-12 [1] CRAN (R 4.0.2)
##  mvtnorm      * 1.1-2      2021-06-07 [1] CRAN (R 4.0.2)
##  nlme           3.1-152    2021-02-04 [1] CRAN (R 4.0.2)
##  nloptr         1.2.2.2    2020-07-02 [1] CRAN (R 4.0.2)
##  numDeriv       2016.8-1.1 2019-06-06 [1] CRAN (R 4.0.2)
##  openxlsx       4.2.4      2021-06-16 [1] CRAN (R 4.0.2)
##  pillar         1.6.1      2021-05-16 [1] CRAN (R 4.0.2)
##  pkgbuild       1.2.0      2020-12-15 [1] CRAN (R 4.0.3)
##  pkgconfig      2.0.3      2019-09-22 [1] CRAN (R 4.0.2)
##  pkgload        1.2.1      2021-04-06 [1] CRAN (R 4.0.2)
##  plyr           1.8.6      2020-03-03 [1] CRAN (R 4.0.2)
##  prettyunits    1.1.1      2020-01-24 [1] CRAN (R 4.0.2)
##  processx       3.5.2      2021-04-30 [1] CRAN (R 4.0.2)
##  ps             1.6.0      2021-02-28 [1] CRAN (R 4.0.2)
##  purrr        * 0.3.4      2020-04-17 [1] CRAN (R 4.0.2)
##  R6             2.5.0      2020-10-28 [1] CRAN (R 4.0.2)
##  Rcpp           1.0.7      2021-07-07 [1] CRAN (R 4.0.3)
##  readr        * 1.4.0      2020-10-05 [1] CRAN (R 4.0.2)
##  readxl         1.3.1      2019-03-13 [1] CRAN (R 4.0.2)
##  remotes        2.4.0      2021-06-02 [1] CRAN (R 4.0.2)
##  reprex         2.0.0      2021-04-02 [1] CRAN (R 4.0.2)
##  rio            0.5.27     2021-06-21 [1] CRAN (R 4.0.2)
##  rlang          0.4.11     2021-04-30 [1] CRAN (R 4.0.2)
##  rmarkdown      2.9        2021-06-15 [1] CRAN (R 4.0.2)
##  rprojroot      2.0.2      2020-11-15 [1] CRAN (R 4.0.2)
##  rstatix      * 0.7.0      2021-02-13 [1] CRAN (R 4.0.2)
##  rstudioapi     0.13       2020-11-12 [1] CRAN (R 4.0.2)
##  rvest          1.0.0      2021-03-09 [1] CRAN (R 4.0.3)
##  sandwich       3.0-1      2021-05-18 [1] CRAN (R 4.0.2)
##  sass           0.4.0      2021-05-12 [1] CRAN (R 4.0.2)
##  scales         1.1.1      2020-05-11 [1] CRAN (R 4.0.2)
##  sessioninfo    1.1.1      2018-11-05 [1] CRAN (R 4.0.2)
##  stringi        1.6.2      2021-05-17 [1] CRAN (R 4.0.2)
##  stringr      * 1.4.0      2019-02-10 [1] CRAN (R 4.0.2)
##  survival     * 3.2-11     2021-04-26 [1] CRAN (R 4.0.3)
##  testthat       3.0.4      2021-07-01 [1] CRAN (R 4.0.2)
##  TH.data      * 1.0-10     2019-01-21 [1] CRAN (R 4.0.2)
##  tibble       * 3.1.2      2021-05-16 [1] CRAN (R 4.0.2)
##  tidyr        * 1.1.3      2021-03-03 [1] CRAN (R 4.0.2)
##  tidyselect     1.1.1      2021-04-30 [1] CRAN (R 4.0.2)
##  tidyverse    * 1.3.1      2021-04-15 [1] CRAN (R 4.0.2)
##  usethis        2.0.1      2021-02-10 [1] CRAN (R 4.0.2)
##  utf8           1.2.1      2021-03-12 [1] CRAN (R 4.0.3)
##  vctrs          0.3.8      2021-04-29 [1] CRAN (R 4.0.2)
##  withr          2.4.2      2021-04-18 [1] CRAN (R 4.0.2)
##  xfun           0.24       2021-06-15 [1] CRAN (R 4.0.2)
##  xml2           1.3.2      2020-04-23 [1] CRAN (R 4.0.2)
##  xtable         1.8-4      2019-04-21 [1] CRAN (R 4.0.2)
##  yaml           2.2.1      2020-02-01 [1] CRAN (R 4.0.2)
##  zip            2.2.0      2021-05-31 [1] CRAN (R 4.0.2)
##  zoo            1.8-9      2021-03-09 [1] CRAN (R 4.0.3)
## 
## [1] /Library/Frameworks/R.framework/Versions/4.0/Resources/library