Introduction
The case study named “Guys have more pocket money than Gals” is an exploration of difference in money spend (from their pocket money) among guys and gals in the student population across various MAHE colleges.
Importing Packages
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✔ ggplot2 3.5.1 ✔ tibble 3.2.1
✔ lubridate 1.9.3 ✔ tidyr 1.3.1
✔ purrr 1.0.2
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Loading required package: ggridges
New to ggformula? Try the tutorials:
learnr::run_tutorial("introduction", package = "ggformula")
learnr::run_tutorial("refining", package = "ggformula")
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library (broom)library (infer)
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library (nortest)library (dplyr)library (crosstable)
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Dataset: Pocket Money
<- read_csv ("../../data/PocketMoney.csv" )
Rows: 82 Columns: 4
── Column specification ────────────────────────────────────────────────────────
Delimiter: ","
chr (2): Name, Gender
dbl (2): Sr no, MS
ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
# A tibble: 82 × 4
`Sr no` Name Gender MS
<dbl> <chr> <chr> <dbl>
1 1 Aagam Male 150
2 2 Aakash Male 240
3 3 Aarushi Female 382
4 4 Abheeta Female 60
5 5 Adithya Male 68
6 6 Aditya Male 300
7 7 Akanksha Female 270
8 8 Amruta Female 190
9 9 Anaaya Female 300
10 10 Anish Male 0
# ℹ 72 more rows
Rows: 82
Columns: 4
$ `Sr no` <dbl> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18,…
$ Name <chr> "Aagam", "Aakash", "Aarushi", "Abheeta", "Adithya", "Aditya", …
$ Gender <chr> "Male", "Male", "Female", "Female", "Male", "Male", "Female", …
$ MS <dbl> 150, 240, 382, 60, 68, 300, 270, 190, 300, 0, 250, 85, 700, 14…
categorical variables:
name class levels n missing
1 Name character 82 82 0
2 Gender character 2 82 0
distribution
1 Aagam (1.2%), Aakash (1.2%) ...
2 Female (50%), Male (50%)
quantitative variables:
name class min Q1 median Q3 max mean sd n missing
1 Sr no numeric 1 21.25 41.5 61.75 82 41.5000 23.81526 82 0
2 MS numeric 0 100.00 264.5 596.25 13000 720.9634 1835.72169 82 0
Factorization
<- pm %>% mutate (Gender = as_factor (Gender)
# A tibble: 82 × 4
`Sr no` Name Gender MS
<dbl> <chr> <fct> <dbl>
1 1 Aagam Male 150
2 2 Aakash Male 240
3 3 Aarushi Female 382
4 4 Abheeta Female 60
5 5 Adithya Male 68
6 6 Aditya Male 300
7 7 Akanksha Female 270
8 8 Amruta Female 190
9 9 Anaaya Female 300
10 10 Anish Male 0
# ℹ 72 more rows
Rows: 82
Columns: 4
$ `Sr no` <dbl> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18,…
$ Name <chr> "Aagam", "Aakash", "Aarushi", "Abheeta", "Adithya", "Aditya", …
$ Gender <fct> Male, Male, Female, Female, Male, Male, Female, Female, Female…
$ MS <dbl> 150, 240, 382, 60, 68, 300, 270, 190, 300, 0, 250, 85, 700, 14…
categorical variables:
name class levels n missing
1 Name character 82 82 0
2 Gender factor 2 82 0
distribution
1 Aagam (1.2%), Aakash (1.2%) ...
2 Male (50%), Female (50%)
quantitative variables:
name class min Q1 median Q3 max mean sd n missing
1 Sr no numeric 1 21.25 41.5 61.75 82 41.5000 23.81526 82 0
2 MS numeric 0 100.00 264.5 596.25 13000 720.9634 1835.72169 82 0
Data summary
Name
pm
Number of rows
82
Number of columns
4
_______________________
Column type frequency:
character
1
factor
1
numeric
2
________________________
Group variables
None
Variable type: character
Variable type: factor
Gender
0
1
FALSE
2
Mal: 41, Fem: 41
Variable type: numeric
Sr no
0
1
41.50
23.82
1
21.25
41.5
61.75
82
▇▇▇▇▇
MS
0
1
720.96
1835.72
0
100.00
264.5
596.25
13000
▇▁▁▁▁
Crosstable
%>% crosstable (MS~ Gender) %>% as_flextable
label
variable
Gender
Male
Female
MS
Min / Max
0 / 1.0e+04
0 / 1.3e+04
Med [IQR]
250.0 [150.0;842.0]
280.0 [85.0;500.0]
Mean (std)
748.6 (1636.5)
693.3 (2035.8)
N (NA)
41 (0)
41 (0)
Visualization.
gf_boxplot (MS~ Gender, data = pm) %>% gf_labs (title = "Money Spend by each Gender" ,x = "Gender" ,y = "Amount"
Males spent between 0 and 10,000, while females spent between 0 and 13,000. On average, males spent 748.6 with a standard deviation of 1636.5, indicating a wide variation in spending. For females, the average spending was 693.3, with an even larger standard deviation of 2035.8, showing that some females spent significantly higher amounts than others. The median spending for males was 250, and for females, it was slightly higher at 280. This suggests that, while the typical spending amounts or median are relatively close, with only a few women spending more, resulting in a higher maximum and larger variance in female spending.
Data Dictionary
Quantitative Variables
MS: It is money spend by each individual.
Qualitative Variables
Gender: Indicates the gender of individuals.
Gender
Histogram
gf_histogram (~ MS,fill = ~ Gender, data= pm)%>% gf_facet_wrap (vars (Gender)) %>% gf_labs (title= "Who spends more pocket money" )
The histogram shows pocket money spending by gender, with most individuals in both groups spending less than 1,000 units. Males tend to have lower spending amounts overall, though a few outliers spent significantly more, creating a rightward skew in the male distribution. For females, the spending distribution is slightly more spread out, with some females also spending higher amounts. While both genders have most individuals spending under 1,000, the female group shows a few more instances of individuals spending amounts above this range, including higher outliers around or above 10,000. Overall, spending patterns vary within each gender, but both groups have a significant number of lower spenders.
Null Hypothesis
There is no difference between pocket money for men and women.
Density Graph
%>% gf_density (~ MS, title= "People who spend more" )%>% gf_fitdistr (dist= "dnorm" )
The normal distribution line overlaid on this plot shows that most spending is clustered around lower amounts, but there’s a significant rightward tail due to a few individuals with much higher spending, making the actual distribution more right-skewed than the fitted normal line.
%>% gf_density (~ MS, fill= ~ Gender, alpha= 0.5 , title= "Who has more Pocket Money?" )%>% gf_facet_grid (~ Gender) %>% gf_fitdistr (dist= "dnorm" )
For males, the distribution has a sharp peak at lower spending values, with the normal line deviating slightly to capture this peak, though the rightward tail makes the actual spending pattern skewed. In contrast, the female distribution is a bit more spread out, as shown by a slightly flatter normal curve, indicating a wider range of spending amounts. Both genders display spending concentrated at lower levels, but females show slightly greater variability. The normal distribution lines emphasize these differences, with the male line showing a more pronounced peak, while the female line is broader, reflecting more diverse spending patterns within the group.
T-Test
:: t_test (MS~ Gender, data= pm) %>% :: tidy ()
# A tibble: 1 × 10
estimate estimate1 estimate2 statistic p.value parameter conf.low conf.high
<dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 55.3 749. 693. 0.136 0.893 76.5 -757. 868.
# ℹ 2 more variables: method <chr>, alternative <chr>
The test results show that the mean spending for males is approximately 748.61, while for females it’s around 693.32. The estimated difference between the two groups is 55.29, which is quite small. The p-value is 0.89 indicating that there is no statistically significant difference in spending between males and females. The confidence interval for the difference ranges from -757.07 to 867.66, which is wide and includes zero, which again shows that any observed difference in spending between genders is likely due to random variation.
Making separate columns
%>% filter (Gender== "Female" ) %>% select (MS)-> FM
# A tibble: 41 × 1
MS
<dbl>
1 382
2 60
3 270
4 190
5 300
6 85
7 700
8 140
9 1070
10 1200
# ℹ 31 more rows
%>% filter (Gender== "Male" ) %>% select (MS)-> M
# A tibble: 41 × 1
MS
<dbl>
1 150
2 240
3 68
4 300
5 0
6 250
7 1143
8 100
9 10000
10 1433
# ℹ 31 more rows
Shapiro Test
Shapiro-Wilk normality test
data: FM$MS
W = 0.29606, p-value = 8.961e-13
Shapiro-Wilk normality test
data: M$MS
W = 0.40726, p-value = 1.136e-11
Using the Shapiro test, it is understood that the Money Spend amounts for both female and male students do not follow a normal distribution, as seen by the extremely low p-values for both groups- 8.961 x 10 to the power of negative 13 for females and 1.136 x 10 to the power of negative 11 for males. This result suggests that any analysis or statistical tests requiring normality may not be suitable for this data, which is when we switch to doing tests such as the Wilcoxon Test.
Wilcoxon Test
wilcox.test (MS ~ Gender, data = pm,conf.int = TRUE ,conf.level = 0.95 ) %>% :: tidy ()
Warning in wilcox.test.default(x = DATA[[1L]], y = DATA[[2L]], ...): cannot
compute exact p-value with ties
Warning in wilcox.test.default(x = DATA[[1L]], y = DATA[[2L]], ...): cannot
compute exact confidence intervals with ties
# A tibble: 1 × 7
estimate statistic p.value conf.low conf.high method alternative
<dbl> <dbl> <dbl> <dbl> <dbl> <chr> <chr>
1 55.0 936. 0.381 -70.0 180. Wilcoxon rank sum t… two.sided
The test provided a p-value of 0.3807, indicating that there is no statistically significant difference in MS amounts between the two groups as it is significantly higher than 0.05. The 95% confidence interval ranges from -69.99998 to 180. This wide confidence interval, which includes zero, further supporting that the observed difference is likely due to chance rather than a consistent and realistic difference in spending behavior between female and male students. This result shows that the Null Hypothesis cannot be rejected.
Permutation Test
<- diffmean (MS~ Gender, data = pm)
<- do (4999 ) * diffmean (data = pm, ~ shuffle (Gender))
diffmean
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### prop1 (~ diffmean <= obs_mean, data = null_dist)### gf_histogram (data = null_dist, ~ diffmean, bins = 25 ) %>% gf_vline (xintercept = obs_mean, colour = "red" , linewidth = 1 ,title = "Null Distribution by Permutation for Gender" ) %>% gf_labs (x = "Difference in Means" )
The calculated observed mean difference in Money Spend amounts between genders from the permutation test is -55.29268, meaning that, on average, females spent 55.29 units less than males. When this observed difference is compared to the distribution of differences generated from 4,999 permutations, the proportion of differences is 0.4234. This p-value of 0.4234, being much higher than 0.05, suggesting that the observed difference is not statistically significant. Hence, the null hypothesis of no difference in spending behavior between gals and guys, cannot be rejected. The histogram of null distribution further establishes that the observed difference is likely occurred by chance, understood by the marking of the red line on the graph.
Conclusion
The study “Guys have more pocket money than Gals” explored spending differences between male and female students across various MAHE colleges using the amounts they spend. The initial visual analysis with boxplots and histograms revealed that while both genders had a large number of low spenders and at very rare instances a few individuals spent significantly more, resulting in a rightward skew. A t-test was conducted, showing that male students had an average spending of approximately 748.61 while female students spent around 693.32, resulting in a small estimated difference of 55.29. However, the t-test had the p-value as 0.89, which is much higher 0.05, indicating that there is no high difference between the groups.
After this, the Shapiro test indicated that spending data for both genders was not normally distributed, with p-values of 8.961 × 10 to the power of negative 13 for females and 1.136 × 10 to the power of negative 11 for males, leading to the use of the non-parametric methods such as the Wilcoxon Test. This test returned a p-value of 0.3807, with a confidence interval that included zero, indicating no significant difference were found in spending between genders.
A permutation test was then conducted with 4,999 permuted sample datasets to create a null distribution, providing an observed mean difference of -55.29. With a pvalue of 0.4234 it was confirmed that the observed difference is likely due to random chance.
In conclusion, both the Wilcoxon and permutation tests indicate no significant difference in spending between male and female students.
