Tópico 5 Análises inferenciais simples t-testes, ANOVA e regressão simples
Ricardo Primi
26 de abril de 2016
setwd("~/Dropbox/R Stat")Análise de variância simples
- Comparação de médias n grupos
- Pergunta de pesquisa: há diferenças entre as médidas ? Há uma tendência global as pessoas em um dos grupos terem notas mais altas ou mais baixas que outro grupo?
- Os n grupos são amostras de uma distribuição única ou de diferentes distribuições?
Prática com o senna v1: Há diferenças em auto gestão entre alunos de séries diferentes ?
# Abrir banco de dados
load("senna.RData")
# Análise descritivas
library(psych)
describe(sennav1[ , 24:29])## vars n mean sd median trimmed mad min max range skew
## F1.Cons 1 66 3.50 0.85 3.36 3.51 0.86 1.22 5.00 3.78 -0.17
## F2.Extr 2 66 3.41 0.54 3.37 3.40 0.53 2.14 5.00 2.86 0.26
## F3.EmSt 3 66 3.30 0.80 3.16 3.32 1.07 1.12 4.90 3.78 -0.16
## F4.Agre 4 66 3.53 0.57 3.50 3.51 0.54 2.25 4.83 2.58 0.23
## F5.Opns 5 66 3.26 0.64 3.31 3.30 0.64 1.62 4.50 2.88 -0.49
## F6.NVLoc 6 66 2.39 0.58 2.27 2.34 0.44 1.50 4.38 2.88 0.93
## kurtosis se
## F1.Cons -0.27 0.11
## F2.Extr 0.07 0.07
## F3.EmSt -0.63 0.10
## F4.Agre -0.35 0.07
## F5.Opns 0.18 0.08
## F6.NVLoc 0.71 0.07describeBy(sennav1[ , 24:29], group = sennav1$ESCOLARIDADE)## group: 5
## vars n mean sd median trimmed mad min max range skew
## F1.Cons 1 21 4.07 0.83 4.44 4.16 0.82 2.11 5.00 2.89 -0.61
## F2.Extr 2 21 3.61 0.51 3.67 3.63 0.49 2.56 4.56 2.00 -0.25
## F3.EmSt 3 21 3.59 0.86 3.90 3.61 1.19 2.20 4.90 2.70 -0.29
## F4.Agre 4 21 3.74 0.46 3.60 3.71 0.44 3.00 4.70 1.70 0.48
## F5.Opns 5 21 3.37 0.79 3.38 3.45 0.74 1.62 4.50 2.88 -0.69
## F6.NVLoc 6 21 2.38 0.72 2.12 2.27 0.37 1.62 4.38 2.75 1.21
## kurtosis se
## F1.Cons -0.72 0.18
## F2.Extr -0.92 0.11
## F3.EmSt -1.41 0.19
## F4.Agre -0.78 0.10
## F5.Opns -0.24 0.17
## F6.NVLoc 0.79 0.16
## --------------------------------------------------------
## group: 7
## vars n mean sd median trimmed mad min max range skew
## F1.Cons 1 24 3.48 0.56 3.36 3.48 0.62 2.61 4.33 1.72 0.08
## F2.Extr 2 24 3.41 0.55 3.35 3.36 0.41 2.43 5.00 2.57 0.94
## F3.EmSt 3 24 3.38 0.66 3.38 3.37 0.74 2.38 4.56 2.19 0.11
## F4.Agre 4 24 3.49 0.59 3.50 3.46 0.62 2.50 4.75 2.25 0.36
## F5.Opns 5 24 3.35 0.44 3.31 3.35 0.57 2.46 4.23 1.77 -0.07
## F6.NVLoc 6 24 2.41 0.59 2.30 2.39 0.68 1.50 3.50 2.00 0.36
## kurtosis se
## F1.Cons -1.38 0.11
## F2.Extr 1.19 0.11
## F3.EmSt -1.26 0.13
## F4.Agre -0.59 0.12
## F5.Opns -0.77 0.09
## F6.NVLoc -1.16 0.12
## --------------------------------------------------------
## group: 9
## vars n mean sd median trimmed mad min max range skew
## F1.Cons 1 21 2.95 0.81 2.94 2.97 0.41 1.22 4.50 3.28 -0.19
## F2.Extr 2 21 3.21 0.51 3.21 3.22 0.42 2.14 4.07 1.93 -0.10
## F3.EmSt 3 21 2.93 0.76 3.00 2.96 0.83 1.12 4.06 2.94 -0.39
## F4.Agre 4 21 3.37 0.61 3.33 3.34 0.72 2.25 4.83 2.58 0.40
## F5.Opns 5 21 3.07 0.63 3.15 3.07 0.46 1.69 4.23 2.54 -0.22
## F6.NVLoc 6 21 2.36 0.42 2.30 2.35 0.44 1.60 3.10 1.50 0.34
## kurtosis se
## F1.Cons -0.13 0.18
## F2.Extr -0.81 0.11
## F3.EmSt -0.50 0.17
## F4.Agre -0.34 0.13
## F5.Opns -0.50 0.14
## F6.NVLoc -1.09 0.09# Cria escolaridade como uma variável "factor"
sennav1$esc2 <- factor(sennav1$ESCOLARIDADE)
# ANOVA VD: auto gestão VI: escolaridade
fit <- aov(F1.Cons ~ esc2, data = sennav1)
summary(fit)## Df Sum Sq Mean Sq F value Pr(>F)
## esc2 2 13.24 6.619 12.22 3.28e-05 ***
## Residuals 63 34.14 0.542
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# Figura comparando as médias
library(gplots)##
## Attaching package: 'gplots'
##
## The following object is masked from 'package:stats':
##
## lowessplotmeans(F1.Cons ~ esc2, data = sennav1, bars =TRUE, ci.label = TRUE,
mean.labels=TRUE, digits = 2)
# Comparações post-hoc
TukeyHSD(fit)## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = F1.Cons ~ esc2, data = sennav1)
##
## $esc2
## diff lwr upr p adj
## 7-5 -0.5942266 -1.122176 -6.627670e-02 0.0237294
## 9-5 -1.1221600 -1.667424 -5.768957e-01 0.0000179
## 9-7 -0.5279334 -1.055883 1.648671e-05 0.0500088Há diferenças entre generos (t-teste)?
# Cria escolaridade como uma variável "factor"
sennav1$esc2 <- factor(sennav1$ESCOLARIDADE)
t.test(sennav1$F1.Cons~sennav1$SEXO) ##
## Welch Two Sample t-test
##
## data: sennav1$F1.Cons by sennav1$SEXO
## t = -0.3224, df = 54.839, p-value = 0.7484
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.4923841 0.3559214
## sample estimates:
## mean in group 0 mean in group 1
## 3.466825 3.535056t.test(sennav1$m_notas~sennav1$SEXO)##
## Welch Two Sample t-test
##
## data: sennav1$m_notas by sennav1$SEXO
## t = -2.664, df = 62.43, p-value = 0.009814
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -1.3103333 -0.1869573
## sample estimates:
## mean in group 0 mean in group 1
## 6.956650 7.705295t.test(sennav1$F3.EmSt~sennav1$SEXO)##
## Welch Two Sample t-test
##
## data: sennav1$F3.EmSt by sennav1$SEXO
## t = 0.95016, df = 60.293, p-value = 0.3458
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.2060150 0.5788866
## sample estimates:
## mean in group 0 mean in group 1
## 3.395905 3.209470Análise de regressão?
# Cria escolaridade como uma variável "factor"
fit2 <- lm( m_notas ~ F1.Cons , data=sennav1)
summary(fit2) # show results##
## Call:
## lm(formula = m_notas ~ F1.Cons, data = sennav1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.6174 -0.6358 0.0137 0.6415 3.4231
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.9825 0.5480 9.092 4.49e-13 ***
## F1.Cons 0.6682 0.1519 4.400 4.27e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.044 on 63 degrees of freedom
## (1 observation deleted due to missingness)
## Multiple R-squared: 0.235, Adjusted R-squared: 0.2229
## F-statistic: 19.36 on 1 and 63 DF, p-value: 4.267e-05fitted(fit) # predicted values## 1 2 3 4 5 6 7 8
## 4.074074 4.074074 4.074074 4.074074 4.074074 4.074074 4.074074 4.074074
## 9 10 11 12 13 14 15 16
## 4.074074 4.074074 4.074074 4.074074 4.074074 4.074074 4.074074 4.074074
## 17 18 19 20 21 22 23 24
## 4.074074 4.074074 4.074074 4.074074 4.074074 3.479847 3.479847 3.479847
## 25 26 27 28 29 30 31 32
## 3.479847 3.479847 3.479847 3.479847 3.479847 3.479847 3.479847 3.479847
## 33 34 35 36 37 38 39 40
## 3.479847 3.479847 3.479847 3.479847 3.479847 3.479847 3.479847 3.479847
## 41 42 43 44 45 46 47 48
## 3.479847 3.479847 3.479847 3.479847 3.479847 2.951914 2.951914 2.951914
## 49 50 51 52 53 54 55 56
## 2.951914 2.951914 2.951914 2.951914 2.951914 2.951914 2.951914 2.951914
## 57 58 59 60 61 62 63 64
## 2.951914 2.951914 2.951914 2.951914 2.951914 2.951914 2.951914 2.951914
## 65 66
## 2.951914 2.951914residuals(fit) # residuals## 1 2 3 4 5
## -0.851851852 0.703703704 0.592592593 0.370370370 -0.296296296
## 6 7 8 9 10
## 0.592592593 0.925925926 0.370370370 -0.185185185 0.925925926
## 11 12 13 14 15
## -1.962962963 -0.518518519 -1.296296296 -0.629629630 -0.851851852
## 16 17 18 19 20
## 0.370370370 0.703703704 -0.740740741 0.925925926 -0.074074074
## 21 22 23 24 25
## 0.925925926 -0.479847495 -0.313180828 0.020152505 0.575708061
## 26 27 28 29 30
## -0.813180828 -0.257625272 -0.090958606 -0.813180828 0.742374728
## 31 32 33 34 35
## 0.575708061 -0.479847495 -0.868736383 0.814270153 -0.146514161
## 36 37 38 39 40
## -0.646514161 -0.257625272 0.853485839 -0.368736383 0.242374728
## 41 42 43 44 45
## 0.353485839 -0.202069717 0.520152505 0.242374728 0.797930283
## 46 47 48 49 50
## -1.174136321 1.548085901 -0.118580766 1.381419234 -1.729691877
## 51 52 53 54 55
## -0.229691877 -0.451914099 0.103641457 0.159197012 -1.451914099
## 56 57 58 59 60
## 0.048085901 -0.285247432 0.881419234 0.325863679 -0.174136321
## 61 62 63 64 65
## 0.871615313 0.492530345 -0.174136321 -0.063025210 0.048085901
## 66
## -0.007469655library(sjPlot)
sjp.lm(fit2, type = "std")
sjp.lm(fit2, type = "pred")
| Model 1 | ||||||
| B | CI | std. Beta | CI | p | ||
| (Intercept) | 4.98 | 3.89 – 6.08 | <.001 | |||
| F1.Cons | 0.67 | 0.36 – 0.97 | 0.48 | 0.27 – 0.70 | <.001 | |
| Observations | 65 | |||||
| R2 / adj. R2 | .235 / .223 | |||||
Exercício 3
- Faça a ANOVA considerando os fatores restantes do senna (F2 a F6)
- Faça a regressão predizendo faltas a partir dos fatores do senna