The Kaiser Family Foundation and the Episcopal Health Foundation conducted the survey between Oct. 17 and Nov. 20, using cellphones and landlines to obtain responses from 1,635 randomly selected adults in 24 Texas counties hammered by Harvey. The survey’s margin of sampling error is plus or minus 3 percentage points.

Two out of three respondents said they’d personally suffered property damage, lost income or job disruptions. About 4 in 10 hurricane survivors applied for disaster assistance from the Federal Emergency Management Agency or the Small Business Administration.

But only 26 percent said they’d been approved, and 33 percent said they’d been denied. The remainder said their applications were pending or they simply didn’t know the status of their cases. About 4 in 10 of the people who had been denied assistance said they weren’t given a reason. About 6 in 10 said they were not given instructions on how to revise their applications.

Sixty-four percent of black residents said they weren’t getting the help they need, along with 44 percent of Hispanics and 37 percent of whites.

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“A lot of people who were affected say they need more help,” said Liz Hamel, a researcher with Kaiser who worked on the study.

A FEMA spokesperson Monday afternoon said the agency had not yet seen the embargoed study, and pointed to a news release stating that more than $10 billion in federal and state assistance has helped Texans recover from Harvey. That includes $1.4 billion in federal money given to 350,000 homeowners and renters, and $2.6 billion in low-interest loans to businesses. Inspectors examined 580,000 damaged homes, FEMA said, and volunteers “mucked and gutted” 18,000 homes.

Jackie Chandler, spokeswoman for FEMA’s Hurricane Harvey response in Texas, said Monday night that people who are declared ineligible for assistance are always given specific reasons, in a letter, for that determination. “The reason is in their letter. Everybody should know why they are ineligible.”

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There are a number of common reasons for such a decision by FEMA, she said. At the top of the list is that people already have insurance. Or they may have damage that is relatively minor; FEMA does not claim it will make people “whole” after a disaster. Another common reason: More than one person in the household files for disaster assistance.

Chandler said people have the right to appeal the decision. But she acknowledged that the bureaucratic hurdles can be difficult for people who have been through a natural disaster.

“There’s this whole process they have to go through, and I’m sure that can be frustrating and confusing. They call it a catastrophic disaster for a reason,” she said. “Yes, it’s hard to understand it. We go to them to help them through that process.”

The survey points to an enduring challenge for emergency management agencies: People with low levels of income often don’t have a “rainy day” fund. Of the people negatively affected by Harvey, nearly half — 48 percent — reported having no savings at all.

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Nearly 2 in 3 Hispanics (65 percent) reported income losses, as did 46 percent of African Americans and 31 percent of whites.

“The people who were struggling before the storm — people with lower income — they were hit harder and they were having more trouble recovering as well,” Hamel said.