SROVNÁNÍ DVOU PRŮMĚRŮ A
JEDNODUCHÁ ANALÝZA
SOUVISLOSTI
Vít Gabrhel
vit.gabrhel@mail.muni.cz
FSS MU,
10. 10. 2016
Harmonogram
0. Rekapitulace předchozí hodiny
1. Deskriptivní statistiky - doplnění
2. Srovnání dvou průměrů
3. Chí-kvadrát
4. Korelace
Rekapitulace
Skript
# Jakou třídu (class) tvoří obě proměnné?
class(alco_1$Country)
class(alco_1$Litry)
lapply(Alco, class)
# Změňte tuto hodnotu na "NA"
alco_1$Litry[alco_1$Litry == "-99"] <- NA
Alco$Litry <- str_replace(Alco$Litry,-
99.00, "NA")
Alco[46,2] = NA
# Jedna z hodnot je evidentně špatně
evidovaná. O jakou hodnotu se jedná
?
chyby = subset(alco, subset = (Litry
< 0))
# V této nové matici ať jsou všechny země
napsané velkými písmeny.
Alco_2 [,"Stát"] = toupper(Alco_2[,"Stát"])
Deskriptivní statistiky
Rozšiřující možnosti
setwd()
library("readxl")
talent_scores_sheets = excel_sheets("talent_scores.xlsx")
talent_scores = read_excel("talent_scores.xlsx", sheet = 1)
# Compute the mean of the scores for each student individually
rowMeans(talent_scores[, 2:6])
# Compute the mean of the scores for each course individually
colMeans(talent_scores[, 2:6])
# Compute the score each student has gained for all his courses
rowSums(talent_scores[, 2:6])
# Compute the total score that is gained by the students on each course
colSums(talent_scores[, 2:6])
Deskriptivní statistiky
Rozšiřující možnosti
wm = read.csv2("wm.csv", header = TRUE)
mean(wm$gain) # function: computes the arithmetic mean
mean(wm$gain, na.rm = TRUE) # function: computes the arithmetic mean
median(wm$gain) # function: computes the median
var(wm$gain) # function: computes the variance
sd(wm$gain) # function: computes the standard deviation
min(wm$gain) # function: return the minimum
max(wm$gain) # function: return the maximum
# Summary statistics for all variables - 5 digits
summary(wm, digits = 5)
# Summary statistics for all variables - 10 digits
summary(wm, digits = 10)
Deskriptivní statistiky
Rozšiřující možnosti
library("dplyr")
# Calculate summary statistics for variables containing "ai". Calculate the statistics to 4 significant digits
summary(select(wm, contains("ai")))
# Alternatively, the numSummary() function might be used to obtain some summary statistics. The function computes:
mean= the mean
sd = the standard deviation
iqr = the interquartile range
0% = the minimum
25% = the 1st quantile or the lower quartile
50% = the median
75% = the 3rd quantile or the upper quartile
100%= the maximum
n = the number of observations
library("Rcmdr")
numSummary(wm$gain)
library("Hmisc")
describe(wm)
Korelace
Úvod (dle Pearson product-moment correlation coefficient, n.d.)
Pearson product-moment correlation coeficient
Předpoklady použití:
Alespoň intervalová úroveň měření proměnných
Normálně rozložená data
Homoskedascita
Korelace
base
# Read the variables names
names(talent_scores)
# Create a subset of the dataframe talent, talent_selected, containing reading, english and
math (in that order)
talent_selected <- subset(talent_scores, select = c(reading, english, math))
# Předpoklady pro použití
hist(talent_selected$english, main="Histogram for English scores", xlab="Students",
border="blue", col="green", xlim=c(0,120), breaks=20)
plot(talent_selected$english, talent_selected$math, main="Scatterplot of Grades",
xlab="English ", ylab="Math", pch=19)
qqnorm(talent_selected$math)
Korelace
base
# Compute the correlations among reading, english and math
cor(talent_selected)
#The cor() function does not calculate p-values to test for significance, but the cor.test()
function does.
cor.test(talent_selected$english, talent_selected$reading, use = pairwise)
cor.test(talent_selected$reading, talent_selected$math, use = pairwise)
cor.test(talent_selected$english, talent_selected$math, use = pairwise)
Korelace
Rcmdr
# The rcorr.adjust() function of the Rmcdr package computes the correlations with the
pairwise p-values among the correlations.
library("Rcmdr")
# Two types of p-values are computed: the ordinary p-values and the adjusted p-values.
?rcorr.adjust
rcorr.adjust(talent_selected)
# Test the significance of the correlations among `english` and `math`
cor.test(talent_selected$english, talent_selected$math, use = pairwise)
Srovnání dvou průměrů (dle Conway, n.d.)
Dependent t-test - úvod
Předpoklady použití:
The sampling distribution is normally distributed. In the dependent ttest
this means that the sampling distribution of the differences between
scores should be normal, not the scores themselves.
Data are measured at least at the interval level.
Srovnání dvou průměrů
Dependent t-test - base - argumenty
# Data
wm_t <- subset(wm, wm$train == "1")
# In the case of our dependent t-test, we need to specify these
arguments to t.test():
?t.test
# x: Column of wm_t containing post-training intelligence scores
# y: Column of wm_t containing pre-training intelligence scores
# paired: Whether we're doing a dependent (i.e. paired) t-test or # #
independent t-test. In this example, it's TRUE
# Note that t.test() carries out a two-sided t-test by default
Srovnání dvou průměrů
Dependent t-test - base - kód
# Conduct a paired t-test using the t.test function
t.test(wm_t$post, wm_t$pre, paired = TRUE)
Output:
Paired t-test
data: wm_t$post and wm_t$pre
t = 14.492, df = 79, p-value < 2.2e-16
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
3.008511 3.966489
sample estimates:
mean of the differences
3.4875
Srovnání dvou průměrů (dle Conway, n.d.)
Dependent t-test - Cohenovo d
Srovnání dvou průměrů
Dependent t-test - Cohenovo d - lsr - argumenty
library("lsr")
# For cohensD(), we'll need to specify three arguments:
# x: Column of wm_t containing post-training intelligence scores
# y: Column of wm_t containing pre-training intelligence scores
# method: Version of Cohen's d to compute, which should be "paired" in this case
?cohensD()
Srovnání dvou průměrů
Dependent t-test - Cohenovo d - lsr - output
# Calculate Cohen's d
cohensD(wm_t$post, wm_t$pre, method = "paired")
[1] 1.620297
Srovnání dvou průměrů
Dependent t-test - Cohenovo d - effsize - argumenty
library("effsize")
cohen.d(x, y, pooled=TRUE, paired=TRUE,
na.rm=FALSE, hedges.correction=FALSE,
conf.level=0.95, noncentral=FALSE)
?cohen.d()
Srovnání dvou průměrů
Dependent t-test - Cohenovo d - effsize - příklad
library("effsize")
cohen.d(wm_t$post,wm_t$pre,pooled=TRUE,paired=TRUE,
na.rm=FALSE, hedges.correction=FALSE,
conf.level=0.95,noncentral=FALSE)
Srovnání dvou průměrů (dle Conway, n.d.)
Independent t-test - úvod
Předpoklady použití:
The sampling distribution is normally distributed.
Data are measured at least at the interval level.
Homogeneity of variance.
Scores are independent (because they come from different people).
Srovnání dvou průměrů
Independent t-test - data
# View the wm_t dataset
wm_t
# Create subsets for each training time
wm_t08 <- subset(wm_t, subset = (wm_t$cond == "t08"))
wm_t12 <- subset(wm_t, subset = (wm_t$cond == "t12"))
wm_t17 <- subset(wm_t, subset = (wm_t$cond == "t17"))
wm_t19 <- subset(wm_t, subset = (wm_t$cond == "t19"))
# Summary statistics for the change in training scores before and after training
describe(wm_t08)
describe(wm_t12)
describe(wm_t17)
describe(wm_t19)
# Create a boxplot of the different training times
ggplot(wm_t, aes(x = cond, y = gain, fill = cond)) + geom_boxplot()
# Levene's test
leveneTest(wm_t$gain ~ wm_t$cond)
Srovnání dvou průměrů
Independent t-test - base
# Conduct an independent t-test
t.test(wm_t19$gain, wm_t08$gain, var.equal = FALSE)
Welch Two Sample t-test
data: wm_t19$gain and wm_t08$gain
t = 8.9677, df = 34.248, p-value = 1.647e-10
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
3.287125 5.212875
sample estimates:
mean of x mean of y
5.60 1.35
Srovnání dvou průměrů (dle Conway, n.d.)
Independent t-test - Cohen's d
Srovnání dvou průměrů
Independent t-test - effsize
# Calculate Cohen's d
cohen.d(wm_t19$gain, wm_t08$gain,pooled=TRUE,paired=FALSE,
na.rm=FALSE, hedges.correction=FALSE,
conf.level=0.95,noncentral=FALSE)
Cohen's d
d estimate: 2.835822 (large)
95 percent confidence interval:
inf sup
1.893561 3.778083
Chí-kvadrát (dle Pearson's chi-squared test, n.d.)
Úvod
Předpoklady použití:
Ne méně než 20 % buněk v rámci kontigenční tabulky s hodnotou méně než 5
Nenulová hodnota v každé z buněk v rámci kontingenční tabulky
Chí-kvadrát
Data a gmodels
# Data
gedu_sheets = excel_sheets("gedu.xlsx")
gedu = read_excel("gedu.xlsx", sheet = 1)
gedu$Gender = as.factor(gedu$Gender)
gedu$Edu = as.factor(gedu$Edu)
gedu$Edu2 = as.factor(gedu$Edu2)
levels(gedu$Gender) = c("Muž", "Žena")
levels(gedu$Edu) = c("ZŠ", "SŠ bez maturity", "SŠ s maturitou", "VŠ")
levels(gedu$Edu2) = c("Nižší než VŠ", "VŠ")
# gmodels
library("gmodels")
?CrossTable()
Chí-kvadrát
Kontingenční tabulky
# Generate a cross table of gender and education
Gedu_CT_01 <- CrossTable(gedu$Edu, gedu$Gender)
# Generate a crosstable for gender and education in which only the results
for the chi-square test are included, and the row proportions.
Gedu_CT_02 = CrossTable(gedu$Edu, gedu$Gender, prop.c = FALSE, prop.t
= FALSE, chisq = TRUE, prop.chisq = FALSE)
# Generate a cross table of gender and fulltime in SPSS format
Gedu_CT_03 = CrossTable(gedu$Edu, gedu$Gender, format = "SPSS")
Chí-kvadrát
Velikost účinku - phí (dle Phi coefficient, n.d.)
library("psych")
Gen = gedu$Gender
Edu2 = gedu$Edu2
table_phi = table(Gen, Edu2)
phi(table_phi, digits = 2)
Chí-kvadrát
Velikost účinku - Cramerovo V (dle Cramér's V, n.d.)
library("psych")
Gen = gedu$Gender
Edu = gedu$Edu
table_CV = table(Gen, Edu)
cramersV(table_CV)
Zdroje
Conway, A. (n.d.) Intro to Statistics with R: Student's T-test. Dostupné online na: https://www.datacamp.com/courses/intro-to-statistics-with-r-
students-t-test
Cramér's V. (n.d.). In Wikipedia: Staženo dne 10. 10. 2016 z https://en.wikipedia.org/wiki/Cram%C3%A9r%27s_V
Effect size (n.d.). In Wikipedia: Staženo dne 10. 10. 2016 z https://en.wikipedia.org/wiki/Effect_size
Pearson's chi-squared test (n.d.). In Wikipedia: Staženo dne 10. 10. 2016 z https://en.wikipedia.org/wiki/Pearson%27s_chi-squared_test
Pearson product-moment correlation coefficient (n.d.). In Wikipedia: Staženo dne 10. 10. 2016 z https://en.wikipedia.org/wiki/Pearson_product-
moment_correlation_coefficient
Phi coefficient (n.d.). In Wikipedia: Staženo dne 10. 10. 2016 z https://en.wikipedia.org/wiki/Phi_coefficient
Sampling distribution (n.d.). In Wikipedia: Staženo dne 10. 10. 2016 z https://en.wikipedia.org/wiki/Sampling_distribution
Standard error (n.d.). In Wikipedia: Staženo dne 10. 10. 2016 z https://en.wikipedia.org/wiki/Standard_error
Student's t-test (n.d.). In Wikipedia: Staženo dne 10. 10. 2016 z https://en.wikipedia.org/wiki/Student%27s_t-test