According to Stats NZ's interim calculations, around 10 per cent of New Zealanders didn't fill out their Census forms, resulting in the lowest participation of the past five surveys.
The calculations, released last year, showed that full or partial information for only 90 per cent of individuals was received, compared with 94.5 per cent for the 2013 Census.
The low participation has caused a delay in the release of information collected, which was due to be released in October, then March, now on the date yet to be announced.
Stats NZ will also have to use other sources of information and different imputation approaches to fill in the missing data.
The 2018 Census was the first time Stats NZ used a digital-first approach, which encouraged respondents to complete the census online.
"We know Census 2018 was a shambles with the lowest participation rate ever and over 400,000 people not counted. It now appears there is a major problem with the completion rates for those who did participate," Yang said.
"The Chief Statistician is further damaging the reputation of Statistics NZ by playing games with Parliament by refusing to disclose this number, despite repeated requests," he said in a statement.
MacPherson had told the committee on February 13 that the number was available and would be provided but then declined to provide it, saying it needed more context.
She again declined to provide the number when she appeared before the committee last week.
"The committee has taken the extraordinary step on invoking Standing Orders and requiring an answer," Yang said.
"Parliament is entitled to know the size of the statistical hole from those who did not participate, as well as those who did not complete Census 2018. The refusal to provide this information is inconsistent with the Government's pledge to be the most open and transparent ever."
MacPherson said her announcement at the end of April would outline what would be included in the first release and provide context.
"In light of the select committee's request, I will be providing information on the breakdown of census forms that were full and partial responses.
"Stats NZ is an open and transparent organisation. When we produce information for the public we outline the methodology and limitations of any data produced," she said.
The select committee's annual review of Statistics NZ, released last week, said it had sought from MacPherson information about the proportion of Census forms that were fully completed.
"We believe this is important data around the performance of the Census, and that if a large portion were unanswered it would raise concerns about the quality of the Census output, and also about the value for money in the overall expenditure."
The committee had formally required her to respond with an answer under Standing Order 227 (2). That Standing Order requires a witness to answer a question.
The request can then be referred to Speaker Trevor Mallard who can decide whether to compel the witness to respond.
National MP Nick Smith has said MacPherson has until April 10 before he takes further action.
The Government allocated $113 million to the 2018 Census, compared with $72m for the 2013 Census.
