Wal-Mart Stores Inc.’s roughly 3,800 employees in Hawaii started to see a little more money in their paychecks Thursday as part of a national wage increase by the world’s largest retailer.

The company said the increase was part of what it called the “the largest single-day private sector pay increase ever.” However, the amount of additional money being put into most worker pockets locally isn’t very large.

The pay raise, on average, for full-time Hawaii Walmart workers amounted to 13 cents an hour, and pushed the average hourly wage to $15.38 compared with the most recent available comparable figure of $15.25 in May, according to Wal-Mart Stores Inc. spokeswoman Delia Garcia.

A 13-cent increase amounts to $5.20 more a week and $270 a year based on 40 hours of work per week for 52 weeks.

Garcia emphasized that increases were much higher for some workers and that other benefits are included in a two-year worker investment program that includes better training, education opportunities and clearer career paths that Wal-Mart Stores Inc. expects to cost $2.7 billion nationally.

For instance, starting hourly pay for sales associates in Walmart’s wireless merchandise department was raised from $9.90 to $10.50, and department managers that used to earn $13 an hour now earn $15 an hour, according to Garcia.

“That’s more than a 13-cent bump,” she said.

Another factor in Walmart’s wage adjustment is giving employees a one-time payment equal to 2 percent of their annual pay if they were at or above the normal maximum pay for their job.

Garcia also added that the number of workers and types of workers in Hawaii stores has changed since May, which muddies the average hourly pay comparison. The company said it promoted more than 700 workers in Hawaii last year to jobs with higher pay and more responsibility, and that more than 400 local employees moved from part-time to full-time work.

Still, it would reason that if some workers received increases far above 13 cents, then some saw far lower raises.

The increases applied to 10 Walmart stores and two Sam’s Club stores statewide.

Part-time workers at Walmarts in Hawaii earn an average of $11.68 an hour. A pre-raise comparison was not available. Most Hawaii Walmart employees work full time, though Garcia did not have a specific count.

Wal-Mart Stores Inc. is the largest private employer in the United States. The company said its wages are competitive, and that all of its employees in Hawaii earn at least $10 an hour. The state-mandated hourly minimum wage rose in January to $8.50 from $7.75 last year, and is scheduled to move to $9.25 next year and to $10.10 in 2018.

Besides wage increases, Wal-Mart Stores Inc. said Thursday’s paycheck for some Hawaii employees included a share of a roughly $890,000 bonus based on individual store performance during the fourth quarter.

On average, the bonus equates to $234, though all workers may not be eligible, which would make the bonus bigger for some employees.