Statistical Methods

AudiAInce applies rigorous statistical methods to ensure research results are reliable and actionable. This article explains the key methods we use.

Confidence Intervals

Every metric in AudiAInce includes a confidence interval showing the range of likely true values.

Interpretation

A 95% confidence interval of 65-75% means:

• Our best estimate is around 70%
• We're 95% confident the true value is between 65-75%
• There's a 5% chance it falls outside this range

Factors Affecting Width

Narrower intervals (more precise) result from:

• Larger sample sizes
• More consistent responses
• Better calibration data

Wider intervals indicate:

• Smaller samples
• High response variance
• Limited base rate data

Statistical Significance

When comparing results (A vs B), we test whether differences are statistically significant.

Significance Levels

| p-value | Interpretation | | -------- | -------------------------------------- | | p < 0.01 | Highly significant (99% confident) | | p < 0.05 | Significant (95% confident) | | p < 0.10 | Marginally significant (90% confident) | | p ≥ 0.10 | Not significant |

Practical Significance

Statistical significance doesn't always mean practical importance:

• A 0.5% difference can be statistically significant with large samples
• Consider effect size alongside p-values
• Business impact matters more than p-values

Sample Size Calculation

We calculate required sample sizes based on:

Key Parameters

| Parameter | Description | | ------------------- | ----------------------------------------- | | Expected Effect | How large a difference you want to detect | | Confidence Level | Desired certainty (typically 95%) | | Population Variance | How much responses vary |

Recommended Samples

| Use Case | Minimum Sample | | ------------------ | -------------- | | Exploratory | 50 | | Standard Survey | 100 | | Segment Analysis | 150 | | Precision Required | 250+ |

Monte Carlo Simulation

For complex analyses, we use Monte Carlo methods:

How It Works

1. Generate thousands of simulated scenarios
2. Apply random variation based on known distributions
3. Analyze outcome distribution
4. Report percentiles as predictions

Applications

• Price optimization (Van Westendorp)
• Market share estimation
• Risk assessment
• Scenario planning

Clustering Analysis

For audience segmentation, we use k-means clustering:

Process

1. Collect response vectors per persona
2. Apply dimensionality reduction
3. Identify natural groupings
4. Validate cluster stability

Output

Each cluster becomes a segment with:

• Size (percentage of sample)
• Centroid characteristics
• Distinctiveness score
• Stability rating

Weighting Methods

Results are weighted to match target populations:

Demographic Weighting

Adjust for over/under-representation of:

• Age groups
• Income levels
• Geographic regions
• Other demographics

Response Quality Weighting

Lower weight for:

• Inconsistent responses
• Extreme outliers
• Pattern responses

Reporting Standards

All results in AudiAInce follow these standards:

1. Show uncertainty - Always display confidence intervals
2. Flag significance - Clearly mark significant differences
3. Explain limitations - Note when data is limited
4. Provide context - Compare to benchmarks when available

Related Articles

• Calibration - Base rate calibration
• Validation - Accuracy verification
• Surveys - Applying statistics in surveys