Context and Data Preparation

Analysis Overview and Data Quality

OV

Analysis Overview

Mann-Whitney U Test Configuration

Analysis overview and configuration

Mann Whitney
Marketing Analytics Team
Compare ad exposure between treatment groups using non-parametric test
Module Configuration
alternative two.sided
confidence_level 0.95
exact_test auto
Processing ID
mann_whitney_test_20260307_231158
analysis type: Mann Whitney
company: Marketing Analytics Team
objective: Compare ad exposure between treatment groups using non-parametric test
IN

Key Insights

Analysis Overview

Purpose

This analysis compares ad exposure levels between two treatment groups—an advertisement group (ad) and a public service announcement group (psa)—using a Mann-Whitney U test. The non-parametric approach was selected to avoid assumptions about data distribution, making it appropriate for comparing exposure metrics that may be skewed or non-normally distributed across unequal sample sizes.

Key Findings

  • Sample Size Imbalance: Ad group contains 475 observations versus psa group with only 25, creating a 19:1 ratio that affects statistical power and interpretation
  • Median Exposure Difference: Ad group median of 79 is more than double the psa group median of 35, indicating substantially higher exposure in the ad treatment
  • Statistical Significance: P-value of 0.008 (below α = 0.05) confirms the difference is statistically significant, not due to random chance
  • Effect Size: Rank-biserial correlation of -0.315 represents a medium effect, with 95% confidence interval (-0.547 to -0.083) excluding zero
  • Distribution Similarity: Both groups exhibit similar distribution shapes, validating the median comparison as the appropriate focus

Interpretation

The ad group demonstrates significantly higher exposure than the psa group. The U statistic of 7807.5 and mean rank difference (

IN

Key Insights

Analysis Overview

Purpose

This analysis compares ad exposure levels between two treatment groups—an advertisement group (ad) and a public service announcement group (psa)—using a Mann-Whitney U test. The non-parametric approach was selected to avoid assumptions about data distribution, making it appropriate for comparing exposure metrics that may be skewed or non-normally distributed across unequal sample sizes.

Key Findings

  • Sample Size Imbalance: Ad group contains 475 observations versus psa group with only 25, creating a 19:1 ratio that affects statistical power and interpretation
  • Median Exposure Difference: Ad group median of 79 is more than double the psa group median of 35, indicating substantially higher exposure in the ad treatment
  • Statistical Significance: P-value of 0.008 (below α = 0.05) confirms the difference is statistically significant, not due to random chance
  • Effect Size: Rank-biserial correlation of -0.315 represents a medium effect, with 95% confidence interval (-0.547 to -0.083) excluding zero
  • Distribution Similarity: Both groups exhibit similar distribution shapes, validating the median comparison as the appropriate focus

Interpretation

The ad group demonstrates significantly higher exposure than the psa group. The U statistic of 7807.5 and mean rank difference (

PP

Data Preprocessing

Data Quality & Completeness

500
Final Observations

Data preprocessing and column mapping

Data Pipeline
500
Initial Records
500
Clean Records
Column Mapping
group_var
→
test group
value_var
→
total ads
500 Records
MCP Analytics
500 Records
IN

Key Insights

Data Preprocessing

Purpose

This section documents the data preprocessing pipeline for the Mann-Whitney U test comparing ad exposure between treatment groups. Perfect data retention (100%) indicates no rows were removed during cleaning, meaning all 500 observations proceeded to statistical analysis without filtering or exclusion.

Key Findings

  • Initial Rows: 500 observations collected across both groups (ad: 475, psa: 25)
  • Final Rows: 500 observations retained with zero removals
  • Retention Rate: 100% - no data loss during preprocessing
  • Train/Test Split: Not applicable; full dataset used for non-parametric hypothesis testing

Interpretation

The complete data retention reflects a clean dataset requiring no exclusions for missing values, outliers, or data quality issues. This preserves the full sample size advantage for the Mann-Whitney U test, which relies on rank-based comparisons across all observations. The imbalanced group sizes (475 vs. 25) remain intact, which is appropriate for this non-parametric test that doesn’t assume equal variances or normal distributions.

Context

No transformations or filtering were applied, so the analysis operates on raw exposure values. The absence of preprocessing decisions means observed differences in medians (79 vs. 35) and rank distributions reflect genuine group variation rather than artifacts of data cleaning.

IN

Key Insights

Data Preprocessing

Purpose

This section documents the data preprocessing pipeline for the Mann-Whitney U test comparing ad exposure between treatment groups. Perfect data retention (100%) indicates no rows were removed during cleaning, meaning all 500 observations proceeded to statistical analysis without filtering or exclusion.

Key Findings

  • Initial Rows: 500 observations collected across both groups (ad: 475, psa: 25)
  • Final Rows: 500 observations retained with zero removals
  • Retention Rate: 100% - no data loss during preprocessing
  • Train/Test Split: Not applicable; full dataset used for non-parametric hypothesis testing

Interpretation

The complete data retention reflects a clean dataset requiring no exclusions for missing values, outliers, or data quality issues. This preserves the full sample size advantage for the Mann-Whitney U test, which relies on rank-based comparisons across all observations. The imbalanced group sizes (475 vs. 25) remain intact, which is appropriate for this non-parametric test that doesn’t assume equal variances or normal distributions.

Context

No transformations or filtering were applied, so the analysis operates on raw exposure values. The absence of preprocessing decisions means observed differences in medians (79 vs. 35) and rank distributions reflect genuine group variation rather than artifacts of data cleaning.

Executive Summary

Key Findings and Recommendations

TLDR

Executive Summary

Key Findings & Recommendations

500
P-Value

Key Performance Indicators

Total observations
500
P value
0.8%
Effect size
-0.31
Significant
Yes

Key Findings

Key findings

Finding Value
Test Result Significant (p=0.0079)
Effect Size -0.315 (Medium)
Group 1 Median 79.00 (n=475)
Group 2 Median 35.00 (n=25)

Executive Summary

Bottom Line: Compared ad (n=475) vs psa (n=25) using Mann-Whitney U test. Significant difference found (p=0.0079, effect size r=-0.315).

Key Findings:
• Median ad: 79.00
• Median psa: 35.00
• Effect magnitude: Medium

Recommendation: Groups differ meaningfully - take action based on context

Executive Summary
Key Insights
Statistical Results
IN

Key Insights

Executive Summary

Purpose

This analysis compared ad exposure levels between two treatment groups (ad vs. psa) using a non-parametric Mann-Whitney U test. The objective was to determine whether statistically and practically meaningful differences exist in ad exposure between these groups, with results informing campaign strategy decisions.

Key Findings

  • Median Ad Exposure: 79 units vs. PSA median of 35 units—a 126% difference favoring the ad group
  • Statistical Significance: p-value of 0.008 indicates the difference is unlikely due to chance (well below α=0.05 threshold)
  • Effect Size: Rank-biserial r of -0.315 represents a medium effect, with 95% confidence interval (-0.547 to -0.083) excluding zero
  • Sample Composition: Highly imbalanced groups (475 ad vs. 25 psa observations), though Mann-Whitney U is robust to this disparity
  • Distribution Shape: Both groups exhibit similar distributional shapes, validating median comparison as appropriate

Interpretation

The ad group received substantially higher exposure than the psa group, and this difference is both statistically significant and practically meaningful. The medium effect size indicates this is not merely a trivial statistical artifact. The analysis successfully achieved its objective: demonstrating a clear, defensible distinction in ad exposure between treatment

IN

Key Insights

Executive Summary

Purpose

This analysis compared ad exposure levels between two treatment groups (ad vs. psa) using a non-parametric Mann-Whitney U test. The objective was to determine whether statistically and practically meaningful differences exist in ad exposure between these groups, with results informing campaign strategy decisions.

Key Findings

  • Median Ad Exposure: 79 units vs. PSA median of 35 units—a 126% difference favoring the ad group
  • Statistical Significance: p-value of 0.008 indicates the difference is unlikely due to chance (well below α=0.05 threshold)
  • Effect Size: Rank-biserial r of -0.315 represents a medium effect, with 95% confidence interval (-0.547 to -0.083) excluding zero
  • Sample Composition: Highly imbalanced groups (475 ad vs. 25 psa observations), though Mann-Whitney U is robust to this disparity
  • Distribution Shape: Both groups exhibit similar distributional shapes, validating median comparison as appropriate

Interpretation

The ad group received substantially higher exposure than the psa group, and this difference is both statistically significant and practically meaningful. The medium effect size indicates this is not merely a trivial statistical artifact. The analysis successfully achieved its objective: demonstrating a clear, defensible distinction in ad exposure between treatment

Statistical Test Results

Mann-Whitney U Test Statistics

TR

Test Results

U Statistic and P-Value

7808
U statistic

Mann-Whitney U test statistical results

7808
u statistic
0.008
p value
Significant
significance
Mann-Whitney U
Statistical Significance
IN

Key Insights

Test Results

Purpose

This section presents the statistical test results from a Mann-Whitney U test comparing ad exposure between the treatment (ad) and control (psa) groups. The test determines whether observed differences in ad exposure distributions are statistically significant or due to random variation, directly addressing the analysis objective of comparing exposure between groups.

Key Findings

  • U Statistic: 7807.50 - Represents the rank-based test statistic; the PSA group has a smaller rank sum, indicating lower exposure values
  • P-value: 0.0079 - Falls below the 0.05 significance threshold, confirming a statistically significant difference exists between groups
  • Effect Size: -0.315 (medium effect) - Quantifies the practical magnitude of the difference; the negative value indicates the PSA group ranks lower in exposure
  • Confidence Level: 95% (α = 0.05) - The result is reliable at standard statistical confidence thresholds

Interpretation

The Mann-Whitney U test confirms that ad exposure differs significantly between groups. The ad group (median = 79) demonstrates substantially higher exposure than the psa group (median = 35). With a p-value of 0.0079, this difference is unlikely due to chance. The medium effect size (-0.315) indicates this is not merely a statistical artifact but represents a meaningful practical difference in

IN

Key Insights

Test Results

Purpose

This section presents the statistical test results from a Mann-Whitney U test comparing ad exposure between the treatment (ad) and control (psa) groups. The test determines whether observed differences in ad exposure distributions are statistically significant or due to random variation, directly addressing the analysis objective of comparing exposure between groups.

Key Findings

  • U Statistic: 7807.50 - Represents the rank-based test statistic; the PSA group has a smaller rank sum, indicating lower exposure values
  • P-value: 0.0079 - Falls below the 0.05 significance threshold, confirming a statistically significant difference exists between groups
  • Effect Size: -0.315 (medium effect) - Quantifies the practical magnitude of the difference; the negative value indicates the PSA group ranks lower in exposure
  • Confidence Level: 95% (α = 0.05) - The result is reliable at standard statistical confidence thresholds

Interpretation

The Mann-Whitney U test confirms that ad exposure differs significantly between groups. The ad group (median = 79) demonstrates substantially higher exposure than the psa group (median = 35). With a p-value of 0.0079, this difference is unlikely due to chance. The medium effect size (-0.315) indicates this is not merely a statistical artifact but represents a meaningful practical difference in

Group Comparison

Distribution of Values by Group

GC

Group Comparison

Distribution by Group

Visual comparison of group distributions

Box Plot
Medians
Outliers
IN

Key Insights

Group Comparison

Purpose

This section visualizes the raw distribution of ad exposure values across the two treatment groups to establish whether observed differences are meaningful. The box plot enables direct comparison of central tendency, spread, and outlier patterns between the ad group (n=475) and psa group (n=25), providing context for the Mann-Whitney U test results.

Key Findings

  • Ad Group Median: 79.00 — substantially higher exposure compared to psa group
  • PSA Group Median: 35.00 — lower central tendency, suggesting reduced ad exposure in this treatment
  • Median Difference: 44-unit gap (126% higher in ad group) indicates a notable practical separation
  • Distribution Shape: Both groups show right-skewed patterns with similar shape ratios (0.098 vs 0.282), validating the non-parametric test choice

Interpretation

The ad group demonstrates consistently higher ad exposure values across the distribution, with a median nearly 2.5 times that of the psa group. This visual separation aligns with the Mann-Whitney U test’s statistically significant finding (p=0.008) and supports the medium effect size (r=-0.315). The similar distribution shapes confirm that differences reflect genuine exposure disparities rather than structural artifacts.

Context

The substantial sample size imbalance (475 vs 25

IN

Key Insights

Group Comparison

Purpose

This section visualizes the raw distribution of ad exposure values across the two treatment groups to establish whether observed differences are meaningful. The box plot enables direct comparison of central tendency, spread, and outlier patterns between the ad group (n=475) and psa group (n=25), providing context for the Mann-Whitney U test results.

Key Findings

  • Ad Group Median: 79.00 — substantially higher exposure compared to psa group
  • PSA Group Median: 35.00 — lower central tendency, suggesting reduced ad exposure in this treatment
  • Median Difference: 44-unit gap (126% higher in ad group) indicates a notable practical separation
  • Distribution Shape: Both groups show right-skewed patterns with similar shape ratios (0.098 vs 0.282), validating the non-parametric test choice

Interpretation

The ad group demonstrates consistently higher ad exposure values across the distribution, with a median nearly 2.5 times that of the psa group. This visual separation aligns with the Mann-Whitney U test’s statistically significant finding (p=0.008) and supports the medium effect size (r=-0.315). The similar distribution shapes confirm that differences reflect genuine exposure disparities rather than structural artifacts.

Context

The substantial sample size imbalance (475 vs 25

Rank Distribution

Rank Analysis Across Groups

RD

Rank Distribution

Rank Comparison Across Groups

Distribution of ranks across groups

Ranks
Violin Plot
IN

Key Insights

Rank Distribution

Purpose

This section reveals how the Mann-Whitney test transforms raw ad exposure values into ranks for statistical comparison. By analyzing rank distributions, we can understand whether one group systematically occupies higher or lower positions in the overall exposure hierarchy, independent of actual exposure magnitudes. This rank-based approach is particularly valuable when data contains outliers or skewness.

Key Findings

  • Ad Group Mean Rank: 254.4 - Substantially higher than the overall mean (250.5), indicating the ad group tends to occupy higher-ranked positions in exposure distribution
  • PSA Group Mean Rank: 175.7 - Notably lower, suggesting the psa group clusters toward lower exposure values
  • Rank Separation: A difference of 78.7 ranks between groups demonstrates clear stratification in the exposure hierarchy
  • Distribution Symmetry: Near-zero skewness (0.03) confirms ranks are evenly distributed across the full range, validating test assumptions

Interpretation

The ad group’s higher mean rank (254.4 vs. 175.7) directly explains the statistically significant Mann-Whitney result (p=0.008). This 31% rank differential indicates the ad group consistently receives greater ad exposure than the psa group. The rank-based comparison neutralizes the impact of extreme outliers while preserving the ordinal relationship between observations, making this finding robust regardless

IN

Key Insights

Rank Distribution

Purpose

This section reveals how the Mann-Whitney test transforms raw ad exposure values into ranks for statistical comparison. By analyzing rank distributions, we can understand whether one group systematically occupies higher or lower positions in the overall exposure hierarchy, independent of actual exposure magnitudes. This rank-based approach is particularly valuable when data contains outliers or skewness.

Key Findings

  • Ad Group Mean Rank: 254.4 - Substantially higher than the overall mean (250.5), indicating the ad group tends to occupy higher-ranked positions in exposure distribution
  • PSA Group Mean Rank: 175.7 - Notably lower, suggesting the psa group clusters toward lower exposure values
  • Rank Separation: A difference of 78.7 ranks between groups demonstrates clear stratification in the exposure hierarchy
  • Distribution Symmetry: Near-zero skewness (0.03) confirms ranks are evenly distributed across the full range, validating test assumptions

Interpretation

The ad group’s higher mean rank (254.4 vs. 175.7) directly explains the statistically significant Mann-Whitney result (p=0.008). This 31% rank differential indicates the ad group consistently receives greater ad exposure than the psa group. The rank-based comparison neutralizes the impact of extreme outliers while preserving the ordinal relationship between observations, making this finding robust regardless

Effect Size Analysis

Practical Significance Assessment

ES

Effect Size

Rank-Biserial Correlation with CI

-0.315
Effect Size

Effect size and practical significance

-0.315
effect size
-0.547
ci lower
-0.082
ci upper
effect size: -0.315
ci lower: -0.547
ci upper: -0.082
IN

Key Insights

Effect Size

Purpose

This section quantifies the practical magnitude of the difference in ad exposure between treatment groups. While the p-value (0.008) confirms statistical significance, effect size reveals whether this difference is practically meaningful. This bridges the gap between statistical significance and real-world impact for comparing ad versus PSA exposure.

Key Findings

  • Rank-Biserial Correlation (r): -0.315 - A medium negative effect indicating the ad group has meaningfully higher exposure values than the PSA group
  • 95% Confidence Interval: [-0.547, -0.083] - The true effect likely falls in this range; the interval excludes zero, reinforcing the significant difference
  • Effect Magnitude Classification: Medium - Falls at the boundary between small (|r| < 0.3) and medium (0.3-0.5), indicating a substantive practical difference beyond chance

Interpretation

The negative coefficient reflects that the ad group occupies higher ranks (median: 79) compared to the PSA group (median: 35). This medium effect size demonstrates the ad exposure difference is not only statistically significant but also practically substantial. The confidence interval’s width suggests reasonable precision, though the lower bound approaches small-effect territory, indicating some uncertainty in the exact magnitude.

Context

Effect size interpretation depends on domain context; medium effects may be trivial or important depending on

IN

Key Insights

Effect Size

Purpose

This section quantifies the practical magnitude of the difference in ad exposure between treatment groups. While the p-value (0.008) confirms statistical significance, effect size reveals whether this difference is practically meaningful. This bridges the gap between statistical significance and real-world impact for comparing ad versus PSA exposure.

Key Findings

  • Rank-Biserial Correlation (r): -0.315 - A medium negative effect indicating the ad group has meaningfully higher exposure values than the PSA group
  • 95% Confidence Interval: [-0.547, -0.083] - The true effect likely falls in this range; the interval excludes zero, reinforcing the significant difference
  • Effect Magnitude Classification: Medium - Falls at the boundary between small (|r| < 0.3) and medium (0.3-0.5), indicating a substantive practical difference beyond chance

Interpretation

The negative coefficient reflects that the ad group occupies higher ranks (median: 79) compared to the PSA group (median: 35). This medium effect size demonstrates the ad exposure difference is not only statistically significant but also practically substantial. The confidence interval’s width suggests reasonable precision, though the lower bound approaches small-effect territory, indicating some uncertainty in the exact magnitude.

Context

Effect size interpretation depends on domain context; medium effects may be trivial or important depending on

Summary Statistics

Group Descriptive Statistics

SS

Summary Statistics

Group Descriptive Statistics

Descriptive statistics by group

Sample Size
Median
Mean Rank
IN

Key Insights

Summary Statistics

Purpose

This section provides the foundational statistics needed to understand the Mann-Whitney U test comparison between ad and PSA groups. The rank-based metrics (mean rank and sum of ranks) are the core calculations that drive the statistical test, making this table essential for interpreting whether ad exposure differs significantly between treatment groups.

Key Findings

  • Sample Size Imbalance: Ad group (N=475) vastly outnumbers PSA group (N=25), a 19:1 ratio that reflects the experimental design but affects statistical power for the smaller group.
  • Median Ad Exposure: Ad group median of 79 is more than double the PSA group median of 35, suggesting higher typical exposure in the ad condition.
  • Mean Rank Differential: Ad group mean rank (254.44) substantially exceeds PSA group mean rank (175.70), indicating ad observations tend to occupy higher positions in the overall ranking distribution.
  • Rank Sum Disparity: Ad group sum of ranks (120,858) dwarfs PSA group (4,392), reflecting both the larger sample size and higher individual ranks.

Interpretation

The descriptive statistics reveal a clear central tendency difference: the ad group exhibits both higher median values and higher average ranks, suggesting greater ad exposure overall. The rank sums directly feed into the U statistic calculation; the ad group’s substantially

IN

Key Insights

Summary Statistics

Purpose

This section provides the foundational statistics needed to understand the Mann-Whitney U test comparison between ad and PSA groups. The rank-based metrics (mean rank and sum of ranks) are the core calculations that drive the statistical test, making this table essential for interpreting whether ad exposure differs significantly between treatment groups.

Key Findings

  • Sample Size Imbalance: Ad group (N=475) vastly outnumbers PSA group (N=25), a 19:1 ratio that reflects the experimental design but affects statistical power for the smaller group.
  • Median Ad Exposure: Ad group median of 79 is more than double the PSA group median of 35, suggesting higher typical exposure in the ad condition.
  • Mean Rank Differential: Ad group mean rank (254.44) substantially exceeds PSA group mean rank (175.70), indicating ad observations tend to occupy higher positions in the overall ranking distribution.
  • Rank Sum Disparity: Ad group sum of ranks (120,858) dwarfs PSA group (4,392), reflecting both the larger sample size and higher individual ranks.

Interpretation

The descriptive statistics reveal a clear central tendency difference: the ad group exhibits both higher median values and higher average ranks, suggesting greater ad exposure overall. The rank sums directly feed into the U statistic calculation; the ad group’s substantially

Distribution Shape Assessment

Distribution Similarity Check

DC

Distribution Check

Shape Similarity Assessment

0

Distribution shape similarity assessment

Distribution Shape
Interpretation
IN

Key Insights

Distribution Check

Purpose

This section validates whether the Mann-Whitney U test is appropriately applied by assessing distribution shape similarity between the ad and psa groups. Since non-parametric tests assume similar distributional shapes, confirming this assumption justifies comparing medians directly rather than relying on rank comparisons alone.

Key Findings

  • Shape Ratio (ad): 0.098 – Indicates a relatively compact distribution with smaller spread relative to range
  • Shape Ratio (psa): 0.282 – Shows a slightly more dispersed distribution, but still comparable to the ad group
  • Assessment Conclusion: Similar shapes confirmed – medians can be compared directly across groups
  • IQR Comparison: Ad group (129.50) vs. psa group (94.00) – Both show moderate interquartile spreads despite different sample sizes

Interpretation

The shape ratios (0.098 vs. 0.282) are sufficiently close to confirm distributional similarity, validating the Mann-Whitney U test’s core assumption. This means the observed median difference (ad: 79 vs. psa: 35) reflects a genuine difference in ad exposure between groups rather than an artifact of different distribution shapes. The similar shapes support the statistical significance finding (p = 0.008) as a reliable comparison of central tendency.

Context

This assessment assumes I

IN

Key Insights

Distribution Check

Purpose

This section validates whether the Mann-Whitney U test is appropriately applied by assessing distribution shape similarity between the ad and psa groups. Since non-parametric tests assume similar distributional shapes, confirming this assumption justifies comparing medians directly rather than relying on rank comparisons alone.

Key Findings

  • Shape Ratio (ad): 0.098 – Indicates a relatively compact distribution with smaller spread relative to range
  • Shape Ratio (psa): 0.282 – Shows a slightly more dispersed distribution, but still comparable to the ad group
  • Assessment Conclusion: Similar shapes confirmed – medians can be compared directly across groups
  • IQR Comparison: Ad group (129.50) vs. psa group (94.00) – Both show moderate interquartile spreads despite different sample sizes

Interpretation

The shape ratios (0.098 vs. 0.282) are sufficiently close to confirm distributional similarity, validating the Mann-Whitney U test’s core assumption. This means the observed median difference (ad: 79 vs. psa: 35) reflects a genuine difference in ad exposure between groups rather than an artifact of different distribution shapes. The similar shapes support the statistical significance finding (p = 0.008) as a reliable comparison of central tendency.

Context

This assessment assumes I

Interpretation & Recommendations

Statistical and Business Interpretation

IN

Interpretation

Statistical and Business Interpretation

0

Statistical and business interpretation

Summary findings

Component Result
Statistical Significance Significant (p=0.0079)
Effect Size -0.315 (Medium)
Group 1 Median=79.00, n=475
Group 2 Median=35.00, n=25
Findings
Recommendations
IN

Key Insights

Interpretation

Purpose

This section synthesizes the Mann-Whitney U test results to determine whether ad exposure differs meaningfully between treatment groups. It validates whether the observed difference in median exposure (79 vs. 35) represents a genuine effect or random variation, directly addressing the core analysis objective.

Key Findings

  • P-value (0.0079): Statistically significant difference detected at α = 0.05 level, indicating the groups’ exposure distributions are unlikely to be identical by chance
  • Effect Size (r = -0.315): Medium practical effect with 95% CI [-0.547, -0.083], confirming the difference is not only statistically significant but also practically meaningful
  • Median Exposure Gap: Ad group median (79) substantially exceeds PSA group median (35), a 126% difference
  • Sample Size Imbalance: Ad group (n=475) vastly outnumbers PSA group (n=25), yet significance persists despite this disparity

Interpretation

The analysis reveals that the ad group received meaningfully higher exposure than the PSA group. The p-value confirms this difference is statistically reliable, while the medium effect size indicates the practical magnitude is substantial. The similar distribution shapes (shape_similar = TRUE) validate the Mann-Whitney U test’s appropriateness for this comparison.

Context

The severe sample size

IN

Key Insights

Interpretation

Purpose

This section synthesizes the Mann-Whitney U test results to determine whether ad exposure differs meaningfully between treatment groups. It validates whether the observed difference in median exposure (79 vs. 35) represents a genuine effect or random variation, directly addressing the core analysis objective.

Key Findings

  • P-value (0.0079): Statistically significant difference detected at α = 0.05 level, indicating the groups’ exposure distributions are unlikely to be identical by chance
  • Effect Size (r = -0.315): Medium practical effect with 95% CI [-0.547, -0.083], confirming the difference is not only statistically significant but also practically meaningful
  • Median Exposure Gap: Ad group median (79) substantially exceeds PSA group median (35), a 126% difference
  • Sample Size Imbalance: Ad group (n=475) vastly outnumbers PSA group (n=25), yet significance persists despite this disparity

Interpretation

The analysis reveals that the ad group received meaningfully higher exposure than the PSA group. The p-value confirms this difference is statistically reliable, while the medium effect size indicates the practical magnitude is substantial. The similar distribution shapes (shape_similar = TRUE) validate the Mann-Whitney U test’s appropriateness for this comparison.

Context

The severe sample size

Job ID: test_analytics__statistical__groups__mann_whitney_20260307_231506
Secret Hash: 36f2d40ab80e