Did the U.S. add half a million jobs in January or did it lose 2.5 million?

The government said both happened—but investors and policy makers cared about the seasonally adjusted increase of 517,000.

The three-million difference shows how views on the economy are shaped by federal agencies accounting for normal yearly patterns due to factors such as the temperature, holidays, school dates and travel schedules.

Throughout the year, consumers and firms alter their behavior, buying coats in the winter and hot dogs in the summer, and stocking folders for back-to-school season. That changes prices and when hiring and layoffs happen.

Government statistical agencies use complex models developed over decades to account for these patterns to make month-to-month comparisons possible.

That arcane process received more attention recently as some economists questioned if strong seasonally adjusted hiring, price and spending data to start the year accurately reflect what’s going on in the economy.

On Tuesday, Federal Reserve Chair Jerome Powell told Congress that “some of this reversal likely reflects the unseasonably warm weather in January in much of the country.”

Pandemic-caused swings in the economy also have complicated recent seasonal adjustments, and figures at the start of the year can be hard to predict, economists say, because seasonality plays a big role.

To help explain this complex topic, zoom in on a treat enjoyed at ballparks, beaches and backyards: the humble hot dog.

For this hypothetical scenario, say that one hot-dog stand near the stadium typically sells $100 of hot dogs each month, but it varies across the year. Sales pick up in March, with opening day, and peak in July.

To seasonally adjust this data, economists would use figures across several years to judge the pattern.

Then they would create something called a seasonal-adjustment factor. That compares sales in one month to average sales for the year as a whole. In this example, sales average $100 a month, and it is a typical year with April sales up 10% from average. So the seasonal adjustment factor for April, which had $110 in sales, would be 1.1.

Adjusting for seasonality allows people to better understand how a company is doing. If next July’s sales are $160, the seasonally adjusted figure would be $107, showing that the month’s sales reflect additional demand beyond what seasonality alone would have expected.

The same concepts are applied to data for the economy as a whole.

People start more gardening and house projects in the spring, leading to higher sales. People buy many gifts in December.

The real world is a bit more complicated than a hot-dog stand. It takes complex math and assumptions to figure out whether any one change is driven by seasonality, a shift in demand, new products or something else. Many government agencies use a model developed by the U.S. Census Bureau to calculate seasonal patterns.

Here are the seasonal-adjustment factors for two categories of spending.

These seasonal-adjustment factors are then used to adjust sales data at stores and online sellers. This turns the swings of the chart into a steadier line.

Seasonal adjustments matter because they allow people to better understand what is happening with the economy.

Large job losses happen every January as companies let go of holiday workers.

“People shouldn’t be panicking over that,” said John Stewart, an economist at the Labor Department. The question is, “Is that a normal seasonal pattern or not?” he said.

When this seasonal impact is taken into account, the U.S. employment picture improved because the jobs data was strong relative to other Januarys.

Seasonal changes don’t stay the same. Over the years, behavior shifts. To account for this, agencies regularly rerun models.

The pandemic and related lockdowns led to big changes in activity that didn’t follow normal patterns. Statistical agencies made manual changes to separate seasonal fluctuations from pandemic changes. New York Federal Reserve research noticed a similar trend after the 2007-09 recession. “For the subsequent few years, an ‘echo’ of the Great Recession took place as economic data kept exceeding the artificially low expectations for that time of year.”

Every year, in February, the Labor Department releases a new estimate of the seasonality of its consumer-price index. The most recent adjustment for the inflation measure was particularly large. Jonathan Wright, an economics professor at Johns Hopkins University who studies seasonality, estimated that the most recent seasonal adjustments had an impact on the inflation numbers that was nearly double what had been seen in the previous four years.

Those changes resulted in revised readings showing monthly price increases in the first half of the year were less than previously estimated, and price changes later in the year were larger than prior estimates.

“Typically they move barely enough to matter,” Mr. Wright said. “They are actually changing what we think happened in the year of 2022.”