Is it possible for paycheck cycles and automatic 401k contributions to impact the stock market?

Have there been any studies done to measure the impact of automatic 401k cycles to determine a measurable impact of stock market performance? Does the market perform better than average on the 15th and 30th of the month, for example?

I suspect not, given everyone's pay schedules are highly variable. Some could be weekly, bi-weekly, monthly, 15th/30th, annual bonuses, quarterly bonuses, monthly bonuses. The timing between pay date and contribution could vary between employer and/or 401k provider. Also, the dollar amount is likely too small.

Was just a thought!