Calculates the Positive Predictive Value (PPV) and False Discovery Rate (FDR) for research findings based on study characteristics. This tool helps researchers understand the probability that their significant findings are actually true, considering factors like prior probability, statistical power, and research biases.
Arguments
- percTrue
The pre-study probability that the tested relationships are true. In exploratory research fields, this may be 10\ confirmatory research with strong theoretical basis, it may be higher.
- alpha
The significance level (Type I error rate) used in the studies. Standard value is 0.05, but may be lower for multiple testing situations.
- power
Statistical power of the studies to detect true effects. Well-designed studies typically have 80\ studies have much lower actual power.
- percHack
Percentage of studies with questionable research practices (p-hacking, selective reporting, data dredging). This represents bias in the research process that increases false positive rates.
Value
A results object containing:
results$confusion | a table containing the true/false positives/negatives | ||||
results$ppv | a html | ||||
results$dotPlot | an image |
Tables can be converted to data frames with asDF or as.data.frame. For example:
results$confusion$asDF
as.data.frame(results$confusion)
Examples
# Calculate PPV for a typical medical research scenario
ppv(
percTrue = 10, # 10\% of tested hypotheses are true
alpha = 0.05, # 5\% significance level
power = 0.80, # 80\% power
percHack = 30 # 30\% of studies have some bias
)
#>
#> POSITIVE PREDICTIVE VALUE
#>
#> Percentages
#> ─────────────────────────────────────────────────────────
#> Claimed Finding H-0- True H-a- True Total
#> ─────────────────────────────────────────────────────────
#> Postive 30.15000 8.600000 38.75000
#> Negative 1.400000 59.85000 61.25000
#> Total 90.00000 10.000000 100.0000
#> ─────────────────────────────────────────────────────────
#>
#>
#> <div style='background-color: #f8f9fa; padding: 15px; border-radius:
#> 5px; margin-bottom: 15px;'><h4 style='margin-top: 0;'>📊 Results
#> Summary
#>
#> Positive Predictive Value (PPV): 22.19%
#>
#> <p style='margin-left: 20px; color: #666;'>Out of 38.8 claimed
#> positive findings, 8.6 are expected to be genuinely true.
#>
#> False Discovery Rate (FDR): 77.81%
#>
#> <p style='margin-left: 20px; color: #666;'>Out of 38.8 claimed
#> positive findings, 30.1 are expected to be false discoveries.
#>
#> <div style='background-color: #e8f4f8; padding: 15px; border-radius:
#> 5px; margin-bottom: 15px;'><h4 style='margin-top: 0;'>🎯 Research
#> Interpretation
#>
#> Most claimed findings are likely to be false positives.
#>
#> <p style='color: #d73027; font-weight: bold;'>⚠️ Warning: Under these
#> conditions, most research claims are likely false. Consider improving
#> study design, increasing sample sizes, or adjusting significance
#> thresholds.
#>
#> <div style='background-color: #f0f8ff; padding: 15px; border-radius:
#> 5px; margin-bottom: 15px;'><h4 style='margin-top: 0;'>🔬 Methodology
#> Notes
#>
#> Confusion Matrix Context:
#>
#> <ul style='margin: 5px 0 10px 20px;'>True Positives: Correctly
#> identified true relationshipsFalse Positives: Incorrectly claimed
#> relationships (Type I errors + bias)False Negatives: Missed true
#> relationships (Type II errors)True Negatives: Correctly rejected null
#> hypotheses<p style='font-size: 0.9em; color: #666;'>This analysis
#> simulates 100 research studies to estimate the reliability of claimed
#> findings.
#>
#> <div style='background-color: #fff3cd; padding: 15px; border-radius:
#> 5px;'><h4 style='margin-top: 0;'>📋 Study Parameters Used
#>
#> <ul style='margin: 5px 0;'>Prior probability of true hypotheses:
#> 10%Significance level (α): 0.05Statistical power: 0.8Percentage of
#> p-hacked studies: 30%<p style='margin-top: 15px; padding: 10px;
#> background-color: #fff; border-left: 4px solid #ffc107; font-size:
#> 0.9em;'>Reference: Ioannidis, J. P. (2005). Why most published
#> research findings are false. *PLoS Medicine*, 2(8), e124.
#> Formula: PPV = (Power × R + u × β × R) / (R + α - β × R + u - u × α +
#> u × β × R)
#> where R = prior odds, u = bias factor, β = Type II error rate
