# Recurring Errors in Studies of Gender Differences in Variability

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## Abstract

**:**

## 1. Variability Ratios and Greater Male Variability

## 2. Variance Ratios and the Variance Ratio Test

**Proposition**

**1.**

**Proof.**

**Example**

**1.**

- (i)
- F is uniformly distributed between 150 and 160, and M is uniform between 139 and 150.
- (ii)
- F is uniformly distributed between 130 and 140, and M is uniform between 140 and 151.
- (iii)
- F is normally distributed with a mean of 150 and a standard deviation of 10, and M is normally distributed with a mean of 140 and a standard deviation of 11.

F | The numerical value of a variance ratio alone, without additional assumptions about the underlying distributions, implies nothing about the tail ratio comparisons. |

## 3. Variability Ratios in Mixtures of Distributions

(C) | If VR $>1$ worldwide for a particular trait in humans, then the corresponding variance ratios for each country should all be greater than 1 and similar in value. |

**Example**

**2.**

**Example**

**3.**

## 4. Correlation and Causation

## 5. Design of Experiments

## 6. Discussion

“The data presented here show that human greater male intrasex variability is not limited to intelligence test scores, and suggest that generally greater intrasex variability among males is a fundamental aspect of the differences between sexes”([6] pp. 220–221).

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**MDPI and ACS Style**

Hill, T.P.; Arden, R.
Recurring Errors in Studies of Gender Differences in Variability. *Stats* **2023**, *6*, 519-525.
https://doi.org/10.3390/stats6020033

**AMA Style**

Hill TP, Arden R.
Recurring Errors in Studies of Gender Differences in Variability. *Stats*. 2023; 6(2):519-525.
https://doi.org/10.3390/stats6020033

**Chicago/Turabian Style**

Hill, Theodore P., and Rosalind Arden.
2023. "Recurring Errors in Studies of Gender Differences in Variability" *Stats* 6, no. 2: 519-525.
https://doi.org/10.3390/stats6020033