Week 4 | Data Dive — Sampling and Drawing Conclusions

Introduction

This analysis explores how random sampling affects conclusions using the Social Media and Entertainment Dataset. We aim to:
- Generate 5 random samples (with replacement) to simulate real-world data collection.
- Analyze differences and consistencies between samples.
- Identify anomalies and trends in categorical and numeric data.
- Understand how sampling impacts conclusions for future analyses.

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Sampling Data

We create 5 random samples, each covering 50% of the dataset.

set.seed(123)  # Ensures reproducibility

# Create 5 samples (with replacement)
samples <- map(1:5, ~ data %>% sample_frac(size = 0.5, replace = TRUE))

# Store each sample in a separate dataframe
df_1 <- samples[[1]]
df_2 <- samples[[2]]
df_3 <- samples[[3]]
df_4 <- samples[[4]]
df_5 <- samples[[5]]

# Check sample sizes
sapply(samples, nrow)
## [1] 150000 150000 150000 150000 150000

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Sample Statistics

We calculate average age, time spent on social media, and most common platform for each sample.

sample_summaries <- map(samples, ~ .x %>%
  summarize(
    Avg_Age = mean(Age, na.rm = TRUE),
    Avg_TimeSpent = mean(`Daily Social Media Time (hrs)`, na.rm = TRUE),
    Platform_Mode = names(sort(table(`Primary Platform`), decreasing = TRUE))[1]
  ))

# Combine results
sample_summaries_df <- bind_rows(sample_summaries, .id = "Sample_ID")

# Display
sample_summaries_df
## # A tibble: 5 × 4
##   Sample_ID Avg_Age Avg_TimeSpent Platform_Mode
##   <chr>       <dbl>         <dbl> <chr>        
## 1 1            38.5          4.26 TikTok       
## 2 2            38.5          4.26 Facebook     
## 3 3            38.5          4.26 Twitter      
## 4 4            38.5          4.25 TikTok       
## 5 5            38.6          4.26 Twitter

Insight:

• The most popular platform varies across samples, suggesting fluctuations in platform engagement.
• Avg. social media time is stable (~4.25 hrs), indicating consistent user behavior across samples.
• Avg. age differs slightly, which could influence trends in media consumption.

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Detecting Outliers

We identify users with extreme social media usage (top 5%) in each sample.

anomalies <- map(samples, ~ .x %>%
  filter(`Daily Social Media Time (hrs)` > quantile(`Daily Social Media Time (hrs)`, 0.95, na.rm = TRUE)))

# Display anomalies count
anomalies_count <- sapply(anomalies, nrow)
anomalies_count
## [1] 7487 7483 7369 7415 7307

Insight:

• The number of extreme users fluctuates across samples (~7,300–7,500).
• A user classified as an outlier in one sample may not be in another, highlighting the instability of anomaly detection in small samples.
• This impacts strategies for identifying high-usage users in marketing or intervention studies.

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Consistency Across Samples

We check whether platform and gender distributions remain stable.

# Count occurrences of (Primary Platform, Gender) in each sample
platform_gender_counts <- map(samples, ~ .x %>%
  count(`Primary Platform`, Gender) %>%
  rename(Count = n))

# Identify common platform-gender pairs appearing in all 5 samples
common_platform_gender <- Reduce(function(x, y) inner_join(x, y, by = c("Primary Platform", "Gender")), 
                                 platform_gender_counts)

# Display how many common platform-gender pairs exist
nrow(common_platform_gender)
## [1] 15

Insight:

• Only 15 platform-gender pairs remain consistent across all samples, showing that rare demographics may not always appear in every sample.
• This highlights potential sampling bias, where some groups are overrepresented or underrepresented.

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Monte Carlo Simulation

We simulate 1,000 repeated samples to estimate the true mean of social media time.

set.seed(42)
mc_samples <- replicate(1000, mean(sample(data$`Daily Social Media Time (hrs)`, size = 0.5 * nrow(data), replace = TRUE), na.rm = TRUE))

# Plot the distribution
ggplot(data.frame(mc_samples), aes(x = mc_samples)) +
  geom_histogram(fill = "lightgreen", bins = 30, alpha = 0.7) +
  labs(title = "Monte Carlo Simulation: Average Time Spent",
       x = "Estimated Mean (hrs)",
       y = "Frequency") +
  theme_minimal()

Insight:

• The estimated mean remains centered around ~4.25 hrs, meaning repeated sampling provides stable estimates.
• Single random samples may misrepresent the true mean, but Monte Carlo methods help reduce uncertainty.

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Final Insights and Next Steps

1. Sample Variability: Different samples yield slightly different conclusions, affecting how we generalize findings.
2. Anomaly Instability: Outliers vary across samples, making them difficult to define consistently.
3. Demographic Representation: Not all user groups appear in every sample, indicating potential biases in data collection.
4. Monte Carlo Stability: Repeated sampling reduces uncertainty in estimating true population values.

Next Steps:

• Use stratified sampling to ensure balanced representation of all groups.
• Apply confidence intervals to quantify uncertainty in estimates.
• Explore trend stability over time by incorporating time-based sampling.

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