Testes Não Paramétricos

Resultados

17.24

df <- structure(list(
  trat = c(rep("Controle", 10), rep("Tratada", 10)),
  parcela = c(rep(seq(1:10), 2)),
  resp = c(
    115.4, 121, 112.3, 78.7, 65.6, 213.5, 157.5, 80.7, 142.8, 100.3,
    98.4, 73.6, 65.9, 42.1, 77.2, 104.0, 82.8, 59.4, 102.6, 53.7
  )
),
.Names = c("trat", "parcela", "resp"),
class = "data.frame",
row.names = c(NA, -20L)
)

df$trat <- as.factor(df$trat)

df %>% kable

trat	parcela	resp
Controle	1	115.4
Controle	2	121.0
Controle	3	112.3
Controle	4	78.7
Controle	5	65.6
Controle	6	213.5
Controle	7	157.5
Controle	8	80.7
Controle	9	142.8
Controle	10	100.3
Tratada	1	98.4
Tratada	2	73.6
Tratada	3	65.9
Tratada	4	42.1
Tratada	5	77.2
Tratada	6	104.0
Tratada	7	82.8
Tratada	8	59.4
Tratada	9	102.6
Tratada	10	53.7

ggdensity(df$resp, fill = "lightgray")

ggqqplot(df$resp)

df %>% 
  group_by(trat) %>%
  shapiro_test(resp)  %>% kable

trat	variable	statistic	p
Controle	resp	0.9269365	0.4184447
Tratada	resp	0.9497315	0.6653243

res <- bartlett.test(resp ~ trat, data = df)
res 

    Bartlett test of homogeneity of variances

data:  resp by trat
Bartlett's K-squared = 4.1299, df = 1, p-value = 0.04213

df %>% levene_test(resp ~ trat)  %>% kable

df1	df2	statistic	p
1	18	2.029988	0.1713302

tab <- df %>%
  group_by(trat) %>%
  get_summary_stats(resp, type = "mean_sd") %>%
  as.data.frame()

tab  %>% kable

trat	variable	n	mean	sd
Controle	resp	10	118.78	43.884
Tratada	resp	10	75.97	21.268

tab %>%
  summarise(redução.com.tratamento = paste(round((1 - (min(mean) / max(mean))) * 100, 2), "%")) %>% kable()

redução.com.tratamento
36.04 %

stat.test <- df %>% pairwise_sign_test(resp ~ trat)

stat.test  %>% kable

.y.	group1	group2	n1	n2	statistic	df	p	p.adj	p.adj.signif
resp	Controle	Tratada	10	10	9	10	0.022	0.022	*

bxp <- ggpaired(df,
  x = "trat", y = "resp", color = "trat",
  ylab = "Peso (g) de Plantas Daninhas", xlab = "", label = T, repel = T, palette = "Dark2"
) +
  theme_pubr(legend = "none")


stat.test <- stat.test %>% add_xy_position(x = "trat")

bxp + stat_pvalue_manual(stat.test) +
  labs(subtitle = get_test_label(stat.test, detailed = TRUE))

17.25

df <- data.frame(
  stringsAsFactors = T,
  var = c(
    "A", "A", "A",
    "A", "A", "A", "A", "A", "A", "A", "A", "A",
    "A", "A", "B", "B", "B", "B", "B", "B", "B", "B",
    "B", "B", "B", "B", "B", "B", "B"
  ),
  prod = c(
    4.2, 3.5, 4.2,
    5.8, 2.8, 4.8, 3.3, 5.1, 3.7, 2.5, 4.7, 5.9,
    4.2, 5.2, 4.3, 2.5, 5.1, 1.8, 3.6, 3.8, 3.5, 4,
    4.5, 4.5, 5.2, 4.1, 2.2, 1.7, 5
  )
)


df %>% kable

var	prod
A	4.2
A	3.5
A	4.2
A	5.8
A	2.8
A	4.8
A	3.3
A	5.1
A	3.7
A	2.5
A	4.7
A	5.9
A	4.2
A	5.2
B	4.3
B	2.5
B	5.1
B	1.8
B	3.6
B	3.8
B	3.5
B	4.0
B	4.5
B	4.5
B	5.2
B	4.1
B	2.2
B	1.7
B	5.0

ggdensity(df$prod, fill = "lightgray")

ggqqplot(df$prod) 

df %>% 
  group_by(var) %>%
  shapiro_test(prod)  %>% kable

var	variable	statistic	p
A	prod	0.9700240	0.8769761
B	prod	0.9115877	0.1432172

res <- bartlett.test(prod ~ var, data = df)
res

    Bartlett test of homogeneity of variances

data:  prod by var
Bartlett's K-squared = 0.16488, df = 1, p-value = 0.6847

df %>% levene_test(prod ~ var)  %>% kable

df1	df2	statistic	p
1	27	0.1108677	0.7417302

df %>%
  group_by(var) %>%
  get_summary_stats(prod, type = "median_iqr")  %>% kable

var	variable	n	median	iqr
A	prod	14	4.2	1.475
B	prod	15	4.0	1.500

bxp <- ggboxplot(
  df,
  x = "var", y = "prod", color = "var", palette = "jco",
  ylab = "Produçao (kg)", xlab = "Variedade", add = "jitter", bxp.errorbar = T
)


stat.test <- df %>%
  wilcox_test(prod ~ var) %>%
  add_significance()
stat.test  %>% kable

.y.	group1	group2	n1	n2	statistic	p	p.signif
prod	A	B	14	15	131	0.265	ns

df %>% wilcox_effsize(prod ~ var)  %>% kable

.y.	group1	group2	effsize	n1	n2	magnitude
prod	A	B	0.2109486	14	15	small

stat.test <- stat.test %>% add_xy_position(x = "var")
bxp +
  stat_pvalue_manual(stat.test) +
  labs(subtitle = get_test_label(stat.test, detailed = TRUE)) + theme_pubr(legend = "none")

17.26

df <- data.frame(
  stringsAsFactors = T,
  parcela = c(
    1L, 2L, 3L, 4L, 5L, 6L, 7L, 8L, 1L,
    2L, 3L, 4L, 5L, 6L, 7L, 8L
  ),
  trat = c(
    "controle", "controle", "controle",
    "controle", "controle", "controle",
    "controle", "controle", "tratada", "tratada",
    "tratada", "tratada", "tratada",
    "tratada", "tratada", "tratada"
  ),
  resp = c(
    103.7, 88.5, 75.4, 97.8, 93.2, 81.4,
    78.1, 105.4, 98.7, 112.4, 117.3, 102.5,
    114.3, 116.4, 107.8, 104.3
  )
)


df  %>% kable

parcela	trat	resp
1	controle	103.7
2	controle	88.5
3	controle	75.4
4	controle	97.8
5	controle	93.2
6	controle	81.4
7	controle	78.1
8	controle	105.4
1	tratada	98.7
2	tratada	112.4
3	tratada	117.3
4	tratada	102.5
5	tratada	114.3
6	tratada	116.4
7	tratada	107.8
8	tratada	104.3

tab <- df %>%
  group_by(trat) %>%
  get_summary_stats(resp, type = "common") %>%
  as.data.frame()



ggdensity(df$resp, fill = "lightgray")

ggqqplot(df$resp)

df %>% 
  group_by(trat) %>%
  shapiro_test(resp)  %>% kable

trat	variable	statistic	p
controle	resp	0.9332002	0.5456486
tratada	resp	0.9316795	0.5314870

res <- bartlett.test(resp ~ trat, data = df)
res

    Bartlett test of homogeneity of variances

data:  resp by trat
Bartlett's K-squared = 1.6201, df = 1, p-value = 0.2031

df %>% levene_test(resp ~ trat)  %>% kable

df1	df2	statistic	p
1	14	3.004222	0.1050056

tab  %>% kable

trat	variable	n	min	max	median	iqr	mean	sd	se	ci
controle	resp	8	75.4	105.4	90.85	18.700	90.438	11.498	4.065	9.612
tratada	resp	8	98.7	117.3	110.10	10.975	109.213	6.916	2.445	5.782

tab %>%
  summarise(ganho = paste(round((max(mean) - min(mean)) / min(mean) * 100, 2), "%")) %>%
  kable()

ganho
20.76 %

stat.test <- df %>%
  wilcox_test(resp ~ trat, detailed = T) %>%
  add_significance()
stat.test  %>% kable

estimate	.y.	group1	group2	n1	n2	statistic	p	conf.low	conf.high	method	alternative	p.signif
-19.25	resp	controle	tratada	8	8	5	0.00295	-29.7	-8.7	Wilcoxon	two.sided	**

df %>% wilcox_effsize(resp ~ trat) %>% kable

.y.	group1	group2	effsize	n1	n2	magnitude
resp	controle	tratada	0.7088918	8	8	large

bxp <- ggboxplot(df,
  x = "trat", y = "resp", color = "trat",
  ylab = "Peso (g) Plântula de Milho", xlab = "", add = "jitter",
  palette = "Dark2", bxp.errorbar = T
) + theme_pubr(legend = "none")


stat.test <- stat.test %>% add_xy_position(x = "trat")

bxp + stat_pvalue_manual(stat.test) +
  labs(
    subtitle = get_test_label(stat.test, detailed = TRUE),
    caption = get_pwc_label(stat.test)
  )

17.27

df <- structure(list(
  trat = c(
    "Rizoma 1kg",
    "Rizoma 1kg",
    "Rizoma 1kg",
    "Rizoma 1kg",
    "Rizoma 1kg",
    "Rizoma 2kg",
    "Rizoma 2kg",
    "Rizoma 2kg",
    "Rizoma 2kg",
    "Rizoma 2kg",
    "Rizoma 3kg",
    "Rizoma 3kg",
    "Rizoma 3kg",
    "Rizoma 3kg",
    "Rizoma 3kg"
  ),
  r = c(
    "1",
    "2",
    "3",
    "4",
    "5",
    "1",
    "2",
    "3",
    "4",
    "5",
    "1",
    "2",
    "3",
    "4",
    "5"
  ),
  resp = c(
    7.2,
    8.4,
    8.2,
    8.4,
    7.8,
    8.4,
    8.8,
    8.6,
    9.7,
    9.2,
    9.0,
    9.3,
    9.0,
    9.9,
    10.1
  )
),
.Names = c("trat", "r", "resp"),
class = "data.frame",
row.names = c(NA, -15L)
)
df$trat <- as.factor(df$trat)
df %>% kable

trat	r	resp
Rizoma 1kg	1	7.2
Rizoma 1kg	2	8.4
Rizoma 1kg	3	8.2
Rizoma 1kg	4	8.4
Rizoma 1kg	5	7.8
Rizoma 2kg	1	8.4
Rizoma 2kg	2	8.8
Rizoma 2kg	3	8.6
Rizoma 2kg	4	9.7
Rizoma 2kg	5	9.2
Rizoma 3kg	1	9.0
Rizoma 3kg	2	9.3
Rizoma 3kg	3	9.0
Rizoma 3kg	4	9.9
Rizoma 3kg	5	10.1

df %>%
  group_by(trat) %>%
  get_summary_stats(resp, type = "mean")  %>% kable

trat	variable	n	mean
Rizoma 1kg	resp	5	8.00
Rizoma 2kg	resp	5	8.94
Rizoma 3kg	resp	5	9.46

bxp <- ggboxplot(
  df,
  x = "trat",
  y = "resp",
  color = "trat",
  palette = "jco",
  bxp.errorbar = T, add = "jitter"
)


gghistogram(df,
  x = "resp", y = "..density..",
  fill = "steelblue", bins = 4, add_density = TRUE
)

df %>%
  group_by(trat) %>%
  identify_outliers(resp)  %>% kable

trat	r	resp	is.outlier	is.extreme

df %>%
  group_by(trat) %>%
  shapiro_test(resp) %>% kable

trat	variable	statistic	p
Rizoma 1kg	resp	0.8539288	0.2072593
Rizoma 2kg	resp	0.9494145	0.7330048
Rizoma 3kg	resp	0.8548712	0.2104124

res <- bartlett.test(resp ~ trat, data = df)
res

    Bartlett test of homogeneity of variances

data:  resp by trat
Bartlett's K-squared = 0.00084382, df = 2, p-value = 0.9996

df %>% levene_test(resp ~ trat)  %>% kable

df1	df2	statistic	p
2	12	0.0169014	0.983264

model <- lm(resp ~ trat, data = df)
ggqqplot(residuals(model))

res.kruskal <- df %>%
  kruskal_test(resp ~ trat)

df %>% kruskal_effsize(resp ~ trat)  %>% kable

.y.	n	effsize	method	magnitude
resp	15	0.6674474	eta2[H]	large

ggdensity(df, x = "resp", rug = TRUE, fill = "lightgray") +
  stat_central_tendency(type = "median", color = "red", linetype = "dashed") +
  labs(subtitle = get_test_label(res.kruskal, detailed = TRUE))

pwc2 <- df %>%
  dunn_test(resp ~ trat, p.adjust.method = "bonferroni") %>%
  add_significance()

pwc2 <- pwc2 %>%
  add_xy_position(x = "trat")


bxp + stat_pvalue_manual(pwc2, hide.ns = T) +
  labs(
    subtitle = get_test_label(res.kruskal, detailed = T),
    caption = get_pwc_label(pwc2)
  ) +
  theme_pubr(legend = "none") +
  ylab("Número de pencas por cacho ") +
  xlab("") +
  # stat_compare_means()+
  theme(
    legend.title = element_blank(),
    text = element_text(),
    axis.text.y = element_text(
      angle = 0,
      hjust = 1,
      colour = "black"
    ),
    axis.text.x = element_text(
      angle = 0,
      hjust = 0.5,
      colour = "black"
    )
  )

17.28

df <- data.frame(
  stringsAsFactors = T,
  blo = c(
    "b1", "b2", "b3", "b4", "b5",
    "b6", "b1", "b2", "b3", "b4", "b5", "b6", "b1", "b2", "b3",
    "b4", "b5", "b6", "b1", "b2", "b3", "b4", "b5", "b6"
  ),
  var = c(
    "Co 419", "Co 419", "Co 419",
    "Co 419", "Co 419", "Co 419", "Co 421", "Co 421", "Co 421",
    "Co 421", "Co 421", "Co 421", "CB-4170", "CB-4170",
    "CB-4170", "CB-4170", "CB-4170", "CB-4170", "CB-4176",
    "CB-4176", "CB-4176", "CB-4176", "CB-4176", "CB-4176"
  ),
  resp = c(
    110.6, 119.5, 120.1, 105.3,
    130.8, 138.1, 116.7, 128.4, 131.5, 114.8, 146.8, 155.5,
    140.3, 150, 150.9, 144.7, 153.9, 156.9, 143.4, 153.8, 151.5,
    144.1, 154.6, 159.3
  )
)

df %>% kable

blo	var	resp
b1	Co 419	110.6
b2	Co 419	119.5
b3	Co 419	120.1
b4	Co 419	105.3
b5	Co 419	130.8
b6	Co 419	138.1
b1	Co 421	116.7
b2	Co 421	128.4
b3	Co 421	131.5
b4	Co 421	114.8
b5	Co 421	146.8
b6	Co 421	155.5
b1	CB-4170	140.3
b2	CB-4170	150.0
b3	CB-4170	150.9
b4	CB-4170	144.7
b5	CB-4170	153.9
b6	CB-4170	156.9
b1	CB-4176	143.4
b2	CB-4176	153.8
b3	CB-4176	151.5
b4	CB-4176	144.1
b5	CB-4176	154.6
b6	CB-4176	159.3

df %>%
  group_by(var) %>%
  get_summary_stats(resp, type = "full") %>% kable

var	variable	n	min	max	median	q1	q3	iqr	mad	mean	sd	se	ci
CB-4170	resp	6	140.3	156.9	150.45	146.025	153.150	7.125	6.820	149.450	6.066	2.477	6.366
CB-4176	resp	6	143.4	159.3	152.65	145.950	154.400	8.450	6.375	151.117	6.249	2.551	6.558
Co 419	resp	6	105.3	138.1	119.80	112.825	128.125	15.300	14.974	120.733	12.213	4.986	12.816
Co 421	resp	6	114.8	155.5	129.95	119.625	142.975	23.350	21.053	132.283	16.211	6.618	17.012

res.fried <- df %>% friedman_test(resp ~ var | blo)
res.fried %>% kable

.y.	n	statistic	df	p	method
resp	6	17	3	0.0007067	Friedman test

df %>% friedman_effsize(resp ~ var | blo) %>% kable

.y.	n	effsize	method	magnitude
resp	6	0.9444444	Kendall W	large

pwc <- df %>%
  wilcox_test(resp ~ var, p.adjust.method = "bonferroni") %>%
  add_significance()
pwc %>% kable

.y.	group1	group2	n1	n2	statistic	p	p.adj	p.adj.signif
resp	CB-4170	CB-4176	6	6	15	0.699	1.000	ns
resp	CB-4170	Co 419	6	6	36	0.002	0.013	*
resp	CB-4170	Co 421	6	6	29	0.093	0.559	ns
resp	CB-4176	Co 419	6	6	36	0.002	0.013	*
resp	CB-4176	Co 421	6	6	29	0.093	0.559	ns
resp	Co 419	Co 421	6	6	11	0.310	1.000	ns

pwc <- pwc %>% add_xy_position(x = "blo")
ggboxplot(df, x = "var", y = "resp", add = "jitter", color = "var", palette = "jco", xlab = "", ylab = "Produção (t/ha)") + theme_pubr(legend = "none") +
  stat_pvalue_manual(pwc, hide.ns = T) +
  labs(
    subtitle = get_test_label(res.fried, detailed = TRUE),
    caption = get_pwc_label(pwc))

17.29

df <- data.frame(
  stringsAsFactors = F,
  x = c(
    0.602, 0.636, 0.604, 0.548, 0.59,
    0.592, 0.625, 0.641, 0.606, 0.502, 0.588,
    0.594, 0.626),
  y = c(
    0.619, 0.62, 0.62, 0.538, 0.616,
    0.601, 0.664, 0.652, 0.579, 0.501, 0.59,
    0.622, 0.606))

ggdensity(df$x, fill = "lightgray")

ggqqplot(df$x)

ggdensity(df$y, fill = "lightgray")

ggqqplot(df$y)

df %>%
  cor_test(
    method = "spearman",
    conf.level = 0.95
  ) %>%
  add_significance() %>% kable

var1	var2	cor	statistic	p	method	p.signif
x	y	0.68	115.6586	0.0102	Spearman	*

ggscatter(df,
  x = "x", y = "y",
  add = "reg.line", conf.int = TRUE,
  cor.coef = TRUE, cor.method = "spearman",
  xlab = "DAP (Sonda Pressler)", ylab = "DAP (Seccões transversais do tronco)")

Referência

Essas análises fazem parte dos Exercícios do Livro (Paulo Vanderlei Ferreira 2018), utilizando os pacotes dplyr (Wickham et al. 2020), ggpubr (Kassambara 2020a), rstatix (Kassambara 2020b) e knitr, (Xie 2014)

Kassambara, Alboukadel. 2020a. Ggpubr: ’Ggplot2’ Based Publication Ready Plots. https://CRAN.R-project.org/package=ggpubr.

———. 2020b. Rstatix: Pipe-Friendly Framework for Basic Statistical Tests. https://CRAN.R-project.org/package=rstatix.

Paulo Vanderlei Ferreira. 2018. Estatística Experimental Aplicada às Ciências Agrárias. Edited by Editora UFV. 1st ed. Viçosa, MG.

Wickham, Hadley, Romain François, Lionel Henry, and Kirill Müller. 2020. Dplyr: A Grammar of Data Manipulation. https://CRAN.R-project.org/package=dplyr.

Xie, Yihui. 2014. “Knitr: A Comprehensive Tool for Reproducible Research in R.” In Implementing Reproducible Computational Research, edited by Victoria Stodden, Friedrich Leisch, and Roger D. Peng. Chapman; Hall/CRC. http://www.crcpress.com/product/isbn/9781466561595.