Hypothesis testing

library(readxl)
mydata <- read_xlsx("./Mobile phone.xlsx")
mydata <- as.data.frame(mydata)

mydata$Gender <- factor(mydata$Gender,
                        levels = c("M", "F"),
                        labels = c("M", "F"))

head(mydata)

##   ID Mobile Gender
## 1  1     10      M
## 2  2     11      M
## 3  3     15      F
## 4  4     14      F
## 5  5     12      F
## 6  6     13      F

Description of variables:

• ID: ID of a person
• Mobile: The number of pick-ups of mobile phone in 1 working day
• Gender: M, F

library(ggplot2)

Male <- ggplot(mydata[mydata$Gender == "M",  ], aes(x = Mobile)) +
               theme_linedraw() +
               geom_histogram(binwidth = 1, colour = "black", fill = "darkblue") +
               ylab("Frequency") +
               scale_x_continuous(breaks = seq(0, 20, 2), limits = c(-1, 21)) +
               ggtitle("Male")

Female <- ggplot(mydata[mydata$Gender == "F",  ], aes(x = Mobile)) +
                 theme_linedraw() + 
                 geom_histogram(binwidth = 1, colour = "black", fill = "darkred") +
                 ylab("Frequency") +
                 scale_x_continuous(breaks = seq(0, 20, 2), limits = c(-1, 21)) +
                 ggtitle("Female")

library(ggpubr)
ggarrange(Male, Female,
          ncol = 2, nrow = 1)

## Warning: Removed 2 rows containing missing values or values outside the scale
## range (`geom_bar()`).
## Removed 2 rows containing missing values or values outside the scale
## range (`geom_bar()`).

library(dplyr)

## 
## Attaching package: 'dplyr'

## The following objects are masked from 'package:stats':
## 
##     filter, lag

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

library(rstatix)

## 
## Attaching package: 'rstatix'

## The following object is masked from 'package:stats':
## 
##     filter

mydata %>%
  group_by(Gender) %>%
  shapiro_test(Mobile)

## # A tibble: 2 × 4
##   Gender variable statistic       p
##   <fct>  <chr>        <dbl>   <dbl>
## 1 M      Mobile       0.916 0.00439
## 2 F      Mobile       0.977 0.326

library(psych)

## 
## Attaching package: 'psych'

## The following objects are masked from 'package:ggplot2':
## 
##     %+%, alpha

describeBy(mydata$Mobile, mydata$Gender)

## 
##  Descriptive statistics by group 
## group: M
##    vars  n  mean   sd median trimmed  mad min max range  skew
## X1    1 42 11.45 3.09     11   11.47 2.97   0  18    18 -0.74
##    kurtosis   se
## X1     2.81 0.48
## ---------------------------------------------------- 
## group: F
##    vars  n  mean   sd median trimmed  mad min max range  skew
## X1    1 58 12.45 2.68   12.5   12.44 2.22   7  18    11 -0.03
##    kurtosis   se
## X1    -0.74 0.35

wilcox.test(mydata$Mobile ~ mydata$Gender, 
            correct = FALSE,
            exact = FALSE,
            alternative = "two.sided")

## 
##  Wilcoxon rank sum test
## 
## data:  mydata$Mobile by mydata$Gender
## W = 982.5, p-value = 0.09786
## alternative hypothesis: true location shift is not equal to 0

library(ggplot2)
ggplot(mydata, aes(x = Mobile, fill = Gender)) +
  geom_histogram(position = position_dodge(width = 0.5), binwidth = 1, colour = "Black") +
  scale_x_continuous(breaks = seq(0, 20, 1)) +
  ylab("Frequency") +
  labs(fill = "Group")

ggplot(mydata, aes(x = Mobile, linetype = Gender)) +
  geom_freqpoly(binwidth = 1,
                size = 1,
                colour = "black") +
  scale_x_continuous(breaks = seq(0, 20, 1)) +
  ylab("Frequency") +
  labs(linetype = "Group")

## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## This warning is displayed once per session.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning
## was generated.

ggplot(mydata, aes(x = Mobile)) +
  geom_histogram(binwidth = 1,
                 colour = "black",
                 fill = "grey80",
                 boundary = 0) +
  scale_x_continuous(breaks = seq(0, 20, 1)) +
  ylab("Frequency") +
  facet_wrap(~ Gender, ncol = 1)

library(effectsize)

## 
## Attaching package: 'effectsize'

## The following object is masked from 'package:psych':
## 
##     phi

## The following objects are masked from 'package:rstatix':
## 
##     cohens_d, eta_squared, omega_squared

effectsize(wilcox.test(mydata$Mobile ~ mydata$Gender, 
           correct = FALSE,
           exact = FALSE,
           alternative = "two.sided"))

## r (rank biserial) |        95% CI
## ---------------------------------
## -0.19             | [-0.40, 0.03]

library(effectsize)
interpret_rank_biserial(0.19)

## [1] "small"
## (Rules: funder2019)