Homework 2 - Hypothesis Testing
Leong Jia Qian
2025-03-30
Airline Passenger Satisfaction Data Set
Data Source: Kaggle.com (2025)
Link: https://www.kaggle.com/datasets/teejmahal20/airline-passenger-satisfaction/data
1) Raw Data Importation
#train.csv will be used as it is 80% of the full dataset
raw_cloudrate <- read.table("./train.csv", header = TRUE, sep = ",", dec = ".")
head(raw_cloudrate)## X id Gender Customer.Type Age Type.of.Travel Class
## 1 0 70172 Male Loyal Customer 13 Personal Travel Eco Plus
## 2 1 5047 Male disloyal Customer 25 Business travel Business
## 3 2 110028 Female Loyal Customer 26 Business travel Business
## 4 3 24026 Female Loyal Customer 25 Business travel Business
## 5 4 119299 Male Loyal Customer 61 Business travel Business
## 6 5 111157 Female Loyal Customer 26 Personal Travel Eco
## Flight.Distance Inflight.wifi.service Departure.Arrival.time.convenient
## 1 460 3 4
## 2 235 3 2
## 3 1142 2 2
## 4 562 2 5
## 5 214 3 3
## 6 1180 3 4
## Ease.of.Online.booking Gate.location Food.and.drink Online.boarding
## 1 3 1 5 3
## 2 3 3 1 3
## 3 2 2 5 5
## 4 5 5 2 2
## 5 3 3 4 5
## 6 2 1 1 2
## Seat.comfort Inflight.entertainment On.board.service Leg.room.service
## 1 5 5 4 3
## 2 1 1 1 5
## 3 5 5 4 3
## 4 2 2 2 5
## 5 5 3 3 4
## 6 1 1 3 4
## Baggage.handling Checkin.service Inflight.service Cleanliness
## 1 4 4 5 5
## 2 3 1 4 1
## 3 4 4 4 5
## 4 3 1 4 2
## 5 4 3 3 3
## 6 4 4 4 1
## Departure.Delay.in.Minutes Arrival.Delay.in.Minutes satisfaction
## 1 25 18 neutral or dissatisfied
## 2 1 6 neutral or dissatisfied
## 3 0 0 satisfied
## 4 11 9 neutral or dissatisfied
## 5 0 0 satisfied
## 6 0 0 neutral or dissatisfiedExplanation of Raw Data
Target population: All airline passengers
Sample size: Passengers who took part in the airline passengers satisfaction survey (Total = 103,904 observations)
Unit of observation: 1 of the 103904 passengers who participated in the survey
Number of variables: 25 (after cleaning = 23 variables)
Definition & unit of measurement of all initial variables (before clean-up)
id (categorical - nominal): Customer unique identification number
Gender (categorical - nominal): Gender of the passengers - “Female” or “Male”
Customer.Type (categorical - nominal): Customer type - “Loyal” or “disloyal” customer
Age (numerical - ratio): The actual age of the passengers
Type.of.Travel (categorical - nominal): Purpose of the flight of the passengers - “Personal Travel” or “Business Travel”
Class (categorical - ordinal): Travel class in the plane of the passengers - “Business”, “Eco”, “Eco Plus”
Flight.distance (numerical - ratio): The flight distance of this journey
Inflight.wifi.service (numerical - interval): Satisfaction level of the inflight wifi service (0:Not Applicable; 1-5: Satisfaction level)
Departure/Arrival time convenient (numerical - interval): Satisfaction level of Departure/Arrival time convenient
Ease of Online booking (numerical - interval): Satisfaction level of online booking
Gate location (numerical - interval): Satisfaction level of Gate location
Food and drink (numerical - interval): Satisfaction level of Food and drink
Online boarding (numerical - interval): Satisfaction level of online boarding
Seat comfort (numerical - interval): Satisfaction level of Seat comfort
Inflight entertainment (numerical - interval): Satisfaction level of inflight entertainment
On-board service (numerical - interval): Satisfaction level of On-board service
Leg room service (numerical - interval): Satisfaction level of Leg room service
Baggage handling (numerical - interval): Satisfaction level of baggage handling
Check-in service (numerical - interval): Satisfaction level of Check-in service
Inflight service (numerical - interval): Satisfaction level of inflight service
Cleanliness (numerical - interval): Satisfaction level of Cleanliness
Departure Delay in Minutes (numerical - ratio): Minutes delayed when departure
Arrival Delay in Minutes (numerical - ratio): Minutes delayed when Arrival
Satisfaction (categorical - ordinal): Airline satisfaction level - “Satisfaction”, or “Neutral or dissatisfaction”)
2) Data Manipulation / Cleaning
- Load dplyr & tidyr packages
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, unionlibrary(tidyr)- Initial cleaning of raw data
raw_cloudrate <- raw_cloudrate %>%
select(-1, -Customer.Type) #Remove the first column (serial number) and Customer.Type column- Cleaning observations
raw_cloudrate <- raw_cloudrate %>% drop_na() #Drop all observations with NA values in their records
raw_cloudrate$id <- sprintf("%06d", raw_cloudrate$id) #Make ID values to be consistent at 6 digits- Rename variables
raw_cloudrate <- raw_cloudrate %>%
rename (cust_id = id,
gender = Gender,
age = Age,
travel_type = Type.of.Travel,
class = Class,
flight_dist = Flight.Distance,
plane_wifi = Inflight.wifi.service,
dep_arr_conv = Departure.Arrival.time.convenient,
online_book = Ease.of.Online.booking,
gate_loc = Gate.location,
food_drink = Food.and.drink,
online_board = Online.boarding,
seat_comf = Seat.comfort,
plane_ent = Inflight.entertainment,
onboard_srv = On.board.service,
legroom = Leg.room.service,
baggage = Baggage.handling,
checkin_srv = Checkin.service,
plane_srv = Inflight.service,
clean = Cleanliness,
dep_delay = Departure.Delay.in.Minutes,
arr_delay = Arrival.Delay.in.Minutes,
overall_sat = satisfaction)- Converting categorical variables into factor variables
raw_cloudrate <- raw_cloudrate %>%
mutate(
gender = factor(gender, levels = c("Female", "Male"), labels = c("F", "M")),
travel_type = factor(travel_type, levels = c("Personal Travel", "Business travel"), labels = c("Personal", "Work-related")),
class = factor(class, levels = c("Business", "Eco", "Eco Plus"), labels = c("Business", "Eco/EcoPlus", "Eco/EcoPlus")), #Combining both Eco and Eco Plus classes, as Eco Plus class is observed to only have relatively less count to make comparisons
overall_sat = factor(overall_sat, levels = c("neutral or dissatisfied", "satisfied"))
)- Create new dataframes & variables/columns based on conditions
#Create age group column
raw_cloudrate <- raw_cloudrate %>%
mutate(age_grp = cut(age, breaks = seq(0, max(90), by = 10), right = FALSE, labels = FALSE))
raw_cloudrate <- raw_cloudrate %>% select(1:3, age_grp, everything())
raw_cloudrate <- raw_cloudrate %>%
mutate(age_grp = factor(age_grp,
levels = c("1", "2", "3", "4", "5", "6", "7", "8", "9"),
labels = c("0-9", "10-19", "20-29", "30-39", "40-49", "50-59", "60-69", "70-79", "80-89")))
#Inflight Services Ratings By Passengers
indiv_inflight_ratings <- raw_cloudrate %>%
select(cust_id, starts_with("plane"), onboard_srv, seat_comf, legroom) %>%
mutate(avg_score = round(rowMeans(select(., -cust_id), na.rm = TRUE), 2))
#Average Inflight Services Rating Based on Class
avg_inflight_srv_ratings <- raw_cloudrate %>%
group_by(class) %>%
summarise(class_count = n(),
across(c("plane_wifi", "seat_comf", "food_drink",
"plane_ent", "onboard_srv", "legroom"),
~ round(mean(.x, na.rm = TRUE), 2)))
#Delay Statistics Based on Class and Travel Type
delay_stats_class = raw_cloudrate %>%
group_by (class, travel_type) %>%
summarise(avg_dep_delay = mean(dep_delay, na.rm = TRUE),
avg_arr_delay = mean(arr_delay, na.rm = TRUE),
.groups = "drop")
#Satisfaction Breakdown Based on Travel Type
satisfaction_travel <- raw_cloudrate %>%
group_by(travel_type, overall_sat) %>%
summarise(count = n(), .groups = "drop") %>%
mutate(percentage = count / sum(count) * 100)3) Descriptive Statistics
#Load psych package
library(psych)
#Overall summary of the raw database (after data manipulation)
summary(raw_cloudrate)## cust_id gender age age_grp
## Length:103594 F:52576 Min. : 7.00 40-49 :23632
## Class :character M:51018 1st Qu.:27.00 20-29 :20854
## Mode :character Median :40.00 30-39 :20593
## Mean :39.38 50-59 :19053
## 3rd Qu.:51.00 60-69 : 8313
## Max. :85.00 10-19 : 7896
## (Other): 3253
## travel_type class flight_dist plane_wifi
## Personal :32129 Business :49533 Min. : 31 Min. :0.00
## Work-related:71465 Eco/EcoPlus:54061 1st Qu.: 414 1st Qu.:2.00
## Median : 842 Median :3.00
## Mean :1189 Mean :2.73
## 3rd Qu.:1743 3rd Qu.:4.00
## Max. :4983 Max. :5.00
##
## dep_arr_conv online_book gate_loc food_drink online_board
## Min. :0.00 Min. :0.000 Min. :0.000 Min. :0.000 Min. :0.00
## 1st Qu.:2.00 1st Qu.:2.000 1st Qu.:2.000 1st Qu.:2.000 1st Qu.:2.00
## Median :3.00 Median :3.000 Median :3.000 Median :3.000 Median :3.00
## Mean :3.06 Mean :2.757 Mean :2.977 Mean :3.202 Mean :3.25
## 3rd Qu.:4.00 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:4.00
## Max. :5.00 Max. :5.000 Max. :5.000 Max. :5.000 Max. :5.00
##
## seat_comf plane_ent onboard_srv legroom baggage
## Min. :0.00 Min. :0.000 Min. :0.000 Min. :0.000 Min. :1.000
## 1st Qu.:2.00 1st Qu.:2.000 1st Qu.:2.000 1st Qu.:2.000 1st Qu.:3.000
## Median :4.00 Median :4.000 Median :4.000 Median :4.000 Median :4.000
## Mean :3.44 Mean :3.358 Mean :3.383 Mean :3.351 Mean :3.632
## 3rd Qu.:5.00 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:5.000
## Max. :5.00 Max. :5.000 Max. :5.000 Max. :5.000 Max. :5.000
##
## checkin_srv plane_srv clean dep_delay
## Min. :0.000 Min. :0.000 Min. :0.000 Min. : 0.00
## 1st Qu.:3.000 1st Qu.:3.000 1st Qu.:2.000 1st Qu.: 0.00
## Median :3.000 Median :4.000 Median :3.000 Median : 0.00
## Mean :3.304 Mean :3.641 Mean :3.286 Mean : 14.75
## 3rd Qu.:4.000 3rd Qu.:5.000 3rd Qu.:4.000 3rd Qu.: 12.00
## Max. :5.000 Max. :5.000 Max. :5.000 Max. :1592.00
##
## arr_delay overall_sat
## Min. : 0.00 neutral or dissatisfied:58697
## 1st Qu.: 0.00 satisfied :44897
## Median : 0.00
## Mean : 15.18
## 3rd Qu.: 13.00
## Max. :1584.00
## #Selected a few estimates of parameters
raw_cloudrate %>%
select(age, flight_dist, dep_delay, arr_delay, plane_wifi, food_drink, seat_comf, onboard_srv) %>%
describeBy()## Warning in describeBy(.): no grouping variable requested## vars n mean sd median trimmed mad min max range
## age 1 103594 39.38 15.11 40 39.40 17.79 7 85 78
## flight_dist 2 103594 1189.33 997.30 842 1042.61 766.50 31 4983 4952
## dep_delay 3 103594 14.75 38.12 0 5.79 0.00 0 1592 1592
## arr_delay 4 103594 15.18 38.70 0 6.09 0.00 0 1584 1584
## plane_wifi 5 103594 2.73 1.33 3 2.70 1.48 0 5 5
## food_drink 6 103594 3.20 1.33 3 3.25 1.48 0 5 5
## seat_comf 7 103594 3.44 1.32 4 3.55 1.48 0 5 5
## onboard_srv 8 103594 3.38 1.29 4 3.48 1.48 0 5 5
## skew kurtosis se
## age 0.00 -0.72 0.05
## flight_dist 1.11 0.27 3.10
## dep_delay 6.77 101.46 0.12
## arr_delay 6.60 94.53 0.12
## plane_wifi 0.04 -0.85 0.00
## food_drink -0.15 -1.15 0.00
## seat_comf -0.48 -0.92 0.00
## onboard_srv -0.42 -0.89 0.00Explanation of Some Parameters:
- age (median): 50% of the sample size are aged 40 and below, while the remaining 50% are aged above 40.
- dep_delay (mean): Passengers experienced an average 14.75 minutes delay in their departure flights.
- arr_delay (mean): Passengers experienced an average 15.18 minutes delay upon their estimated arrival time.
- onboard_srv (mean): Passengers rated an average of 3.38 out of 5 on their on-board service experience in their flights.
- flight_dist (sd): There is significant variability among the flight distances, with a standard deviation of 997.30km. With its median lower than the mean, implies that there is a right-skewed distribution. This suggests that while many flights have shorter distances, a few long-distance flights are pulling the mean higher.
4) Hypothesis Testing
#Load the necessary packages for hypothesis testing
library(ggplot2)##
## Attaching package: 'ggplot2'## The following objects are masked from 'package:psych':
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## %+%, alphalibrary(ggpubr)
library(car)## Loading required package: carData##
## Attaching package: 'car'## The following object is masked from 'package:psych':
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## logit## The following object is masked from 'package:dplyr':
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## recodelibrary(pastecs)##
## Attaching package: 'pastecs'## The following object is masked from 'package:tidyr':
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## extract## The following objects are masked from 'package:dplyr':
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## first, lastlibrary(rstatix)##
## Attaching package: 'rstatix'## The following object is masked from 'package:stats':
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## filterlibrary(effectsize)##
## Attaching package: 'effectsize'## The following objects are masked from 'package:rstatix':
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## cohens_d, eta_squared## The following object is masked from 'package:psych':
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## phi#Convert satisfaction levels into a binary numeric variable (1 = Satisfied, 0 = Neutral or Dissatisfied)
raw_cloudrate$sat_binary <- ifelse(raw_cloudrate$overall_sat == "satisfied", 1, 0)
#Convert class into binary numeric variable and rearrange column
raw_cloudrate$class_binary <- ifelse(raw_cloudrate$class == "Business", 1, 0)
raw_cloudrate <- raw_cloudrate %>% select(1:6, class_binary, everything())
#Create sample size due to large dataset (for Shapiro Test; n <= 5000)
set.seed(123)
sample_size <- raw_cloudrate[sample(nrow(raw_cloudrate), 500), ]Paired T-test
Conditions & Assumptions:
Variable is numeric
Variable on the population is normally distributed
Research Question: Is there a significant difference between departure delays(dd) and arrival delays(ad)?
Research Hypotheses:
H0: No significant difference between departure and arrival delays (mean dd = mean ad = 0)
H1: Departure and arrival delays significantly differ (mean dd =/ mean ad)
#--------------------------------------
#Create a separate dataframe
paired_t_data <- sample_size %>%
select(c(dep_delay, arr_delay)) %>%
mutate(difference = dep_delay - arr_delay)
describeBy(paired_t_data)## Warning in describeBy(paired_t_data): no grouping variable requested## vars n mean sd median trimmed mad min max range skew
## dep_delay 1 500 15.53 37.93 0 6.17 0.00 0 310 310 4.23
## arr_delay 2 500 15.30 37.69 0 6.10 0.00 0 307 307 4.30
## difference 3 500 0.23 9.61 0 0.58 1.48 -62 37 99 -1.23
## kurtosis se
## dep_delay 21.66 1.70
## arr_delay 21.87 1.69
## difference 7.76 0.43#Visualisation for normality check
ggplot(paired_t_data, aes(x=difference)) +
geom_histogram(binwidth = 10, color = "black") +
xlab("Differences") +
ylab("Count")
Explanation of Histogram
At a glance, most of the differences between departure delays and arrival delays are clustered around 0. This suggest that for many pairs, there is little to no difference. The distribution appears somewhat symmetric but slightly left-skewed, which may indicate that although the differences are centered around zero, there exist some larger positive and negative differences in the data as well. While this histogram may suggest normality to some extent, a Shapiro-Wilk test would provide a more accurate assessment.
#Using Shapiro Test
shapiro.test(paired_t_data$difference)##
## Shapiro-Wilk normality test
##
## data: paired_t_data$difference
## W = 0.80737, p-value < 2.2e-16Explanation of Shapiro Test
We reject null hypothesis (H0) that the data is normally distributed as p-value is <0.0001. Hence, we can conclude that the data did not meet the normality requirement to continue with T-test. A non-parametric testing would be more appropriate.
#T-test
t.test(paired_t_data$dep_delay, paired_t_data$arr_delay,
paired = TRUE,
alternative = "two.sided")##
## Paired t-test
##
## data: paired_t_data$dep_delay and paired_t_data$arr_delay
## t = 0.53493, df = 499, p-value = 0.5929
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -0.6147604 1.0747604
## sample estimates:
## mean difference
## 0.23Explanation of T-test (Assuming there is normality)
If we were to assume normality is met: We fail to reject null hypothesis (H0) as p-value > 0.05. This suggests that departure delays and arrival delay have no significant difference and that its observed mean difference of 23 minutes is not statisically significant too.
#Wilcoxon Signed Rank Test (Non-parametric Test)
wilcox_rank <- wilcox.test(paired_t_data$dep_delay, paired_t_data$arr_delay,
paired = TRUE,
correct = FALSE,
exact = FALSE,
alternative = "two.sided")
wilcox_rank##
## Wilcoxon signed rank test
##
## data: paired_t_data$dep_delay and paired_t_data$arr_delay
## V = 20331, p-value = 0.08863
## alternative hypothesis: true location shift is not equal to 0Explanation of Wilcoxon Signed Rank Test
Going back to the actual test that the data did not meet the normality requirement, we fail to reject null hypothesis as the p-value is > 0.05. There is no significant evidence to show that the median difference between departure delays and arrival delays is different from 0. Even though the observed differences may still exist in the data, they are not statistically significant at 0.05 level.
With Wilcoxon signed-rank test being more robust to non-normality, this result further confirms the hypothesis that there is no significant difference between departure and arrival delays as it is consistent with the paired t-test above.
#Calculating effect size
effectsize(wilcox_rank)## r (rank biserial) | 95% CI
## ---------------------------------
## 0.12 | [-0.03, 0.27]interpret_rank_biserial(0.12, rules = "funder2019")## [1] "small"
## (Rules: funder2019)Interpretation of effect size
According to Funder (2019), the effect size value is 0.12 which is considered small. While there may be some difference between the groups, it is not very strong and an indication that the difference between the groups is minor. With its confidence interval ranging from -0.03 to 0.27, it could suggest that the effect might not be statistically meaningful as the interval includes zero.
Going back to the research question (1)
Is there a significant difference between departure delays(dd) and arrival delays(ad)?
No, with the statistical results from the paired t-test, it shows sufficient evidence that there is little to no significant difference between departure delays and arrival delays that indicates to affect satisfaction level of passengers.
Independent T-test
Conditions & Assumptions:
Variable is numeric
Distribution of the variable is normal in both population
Variable has the same variance. If it is violated, Welch correction to be applied.
Research Question: Does on-board service ratings differ significantly between satisfied and dissatisfied passengers?
Research Hypotheses:
H0: No significant difference in on-board service ratings between satisfied and dissatisfied passengers
H1: Satisfied passengers rate on-board service significantly higher than dissatisfied passengers
#Create a separate dataframe
indep_test <- sample_size %>%
select(c(onboard_srv, overall_sat))
describeBy(indep_test$onboard_srv, indep_test$overall_sat)##
## Descriptive statistics by group
## group: neutral or dissatisfied
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 294 2.95 1.29 3 2.94 1.48 1 5 4 -0.15 -1.13 0.07
## ------------------------------------------------------------
## group: satisfied
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 206 3.82 1.11 4 3.96 1.48 1 5 4 -0.87 0.14 0.08#Visualisation for normality check
ggqqplot(indep_test,
"onboard_srv",
facet.by = "overall_sat")
Explanation of graph
In the Q-Q plot above for both groups (“neutral or dissatisfied” and “satisfied”), there are noticeable deviations from the diagonal line, especially at the ends. This may suggest that the distributions have some skewness or heavy tails, not perfectly follow a normal diagonal reference pattern. Additionally, the stepped trend in the middle clearly indicates that the data may be discrete rather than smoothly continuous due to the data collected being interval numeric. There are also outliers as seen on both graphs, further confirms that the data deviates from normality.
Hence, from the visualisation, it can be seen that the variables do not follow a normal distribution and violated normality. In this case, a non-parametric test would be more suitable to continue on our statistical analysis.
#Using Shapiro Test
indep_test %>%
group_by(overall_sat) %>%
shapiro_test(onboard_srv)## # A tibble: 2 × 4
## overall_sat variable statistic p
## <fct> <chr> <dbl> <dbl>
## 1 neutral or dissatisfied onboard_srv 0.897 2.85e-13
## 2 satisfied onboard_srv 0.848 2.12e-13Explanation of Shapiro Test
We reject null hypothesis (H0) that the data is normally distributed as p-value is <0.0001. This suggest that on-board service ratings are not normally distributed in either of the satisfaction groups (i.e. “satisfied” and “neutral or dissatisfied”), not meeting to the normality requirement to continue with usual T-test. Since normality s violated, a non-parametric testing would be more appropriate.
#Test for same variance
leveneTest(indep_test$onboard_srv, indep_test$overall_sat)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 1 13.082 0.0003285 ***
## 498
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Explanation of Levene’s Test
We reject null hypothesis as the p-value < 0.0001. This suggests that the variances of both groups are significantly not equal, not meeting up to the requirement of having same variance to continue with the parametric t-test. Hence, we should use non-parametric testing for better analysis.
#Independent T-test (For parametric testing)
t.test(indep_test$onboard_srv ~ indep_test$overall_sat,
var.equal = TRUE,
alternative = "two.sided")##
## Two Sample t-test
##
## data: indep_test$onboard_srv by indep_test$overall_sat
## t = -7.8751, df = 498, p-value = 2.148e-14
## alternative hypothesis: true difference in means between group neutral or dissatisfied and group satisfied is not equal to 0
## 95 percent confidence interval:
## -1.0888137 -0.6540038
## sample estimates:
## mean in group neutral or dissatisfied mean in group satisfied
## 2.948980 3.820388Explanation of Independent T-test
If we were to assume normality & same variance is met: We reject null hypothesis that the onboard service ratings between satisfied and dissatisfied passengers are equal as the p-value < 0.0001. Hence, there is a strong evidence that passengers who are satisfied rated significantly higher onboard service score as compared to passengers who are neutral or dissatisfied.
#Wilcoxon Rank Sum Test (For non-parametric testing)
wilcox.test(indep_test$onboard_srv ~ indep_test$overall_sat,
correct = FALSE,
exact = FALSE,
altenative = "two.sided")##
## Wilcoxon rank sum test
##
## data: indep_test$onboard_srv by indep_test$overall_sat
## W = 18691, p-value = 6.25e-14
## alternative hypothesis: true location shift is not equal to 0Explanation of Wilcoxon Rank Sum Test
Going back to the actual test that the data did not meet the normality requirement, we reject null hypothesis as the p-value < 0.0001 which indicates that there is a significant difference in the ratings of onboard service ratings between satisfied and dissatisfied groups. As the Wilcoxon test do not assume normality, it further reinforces the result from the usual T-test above that there is a significant difference in the onboard service ratings between both satisfaction level groups.
#Calculating effect size
effectsize::cohens_d(indep_test$onboard_srv ~ indep_test$overall_sat,
pooled_sd = FALSE)## Cohen's d | 95% CI
## --------------------------
## -0.72 | [-0.91, -0.54]
##
## - Estimated using un-pooled SD.interpret_cohens_d(0.72, rules = "sawilowsky2009")## [1] "medium"
## (Rules: sawilowsky2009)Interpretation of effect size
According to Sawilowsky (2009), the effect size of 0.72 suggests a moderate to large difference in onboard service ratings between the 2 satisfaction groups. We can infer that the passengers who are “satisfied” would tend to give notably higher onboard service ratings as compared to those who are “neutral or dissatisfied”. Even though the effect is not huge, it is substantially significant to indicate that onboard service does have an impact on passenger satisfaction level.
Going back to the research question (2)
Does on-board service ratings differ significantly between satisfied and dissatisfied passengers?
Yes, with the statistical results from the independent t-test, it shows sufficient evidence that on-board service ratings differ significantly between satisfied and dissatisfied passengers.
Conclusion
Based on both hypotheses, I believe that non-parametric methods would be more appropriate for my dataset. This is because the data is closely related to social factors, such as satisfaction, which can vary greatly from person to person depending on individual priorities and needs.