Harriet Harman's office is in trouble with the statistics watchdog again.

After ticking off the equality minister in June for using a figure which "risks giving a misleading quantification of the gender pay gap", the UK Statistics Authority is more than a little perturbed that a quango based in her office - the Women and Work Commission - went ahead and published the figure again just a few weeks later. The number was quoted across the British media - including the BBC.

The figure in question is 22.6 - the percentage that Ms Harman's department likes to suggest is the difference between the earnings of men and women. But the head of the UK Statistics Authority, Sir Michael Scholar, told the Government Equalities Office on 11 June that the figure should not be used, because to do so "may undermine public trust in official statistics".

Imagine his reaction, therefore, when he went to the GEO website on 29 July and saw what they had published [334Kb PDF] .

There, clear as day on page five, in the foreword written by commission chair Baroness Prosser, is this:

When Sir Michael finished reading the offending paragraph, he had another bone to pick with Ms Harman's department: namely, the figure of 39.9% cited as the pay gap for part-time workers.

In a letter sent to Baroness Prosser at the GEO today, he points out that the document "does not explain what this is a measure of". However, he assumes that this must be another figure his authority red-flagged in June - "39.9 per cent appears to be a measure of the difference between the median hourly earnings of part-time women compared with full-time men".

This is apples and oranges statistics - comparing the pay rates of women who work part-time with men who work full-time in order, cynics might assume, to achieve a really big number.

Back in June, Sir Michael told Harriet Harman that "such a comparison needs particularly careful presentation and justification if it is not to mislead".

Today, he told Baroness Prosser that he was "disappointed that it should have appeared in the Foreword to Shaping the Future without any explanation".

Sir Michael makes the point that the story of part-time pay looks very different if one compares like with like:

"The casual reader would be surprised to learn then that median hourly earnings of women and of men (excluding overtime) are very close, with women's median pay actually being slightly higher than men's (by 3.4 per cent)."

Yes, that's right. If you compare part-time women with part-time men, women get paid slightly more. This fact, needless to say, is not found anywhere in Shaping A Fairer Future.

Reading that offending paragraph again, one could be forgiven for thinking it is an attempt to make matters appear worse than they really are. As Sir Michael puts it in his letter:

"It would be an easy mistake for a casual reader to conclude from the Foreword that if the overall gender pay gap stands at 22.6 per cent and the full-time gender pay gap stands at 12.8 per cent, then the part-time gender pay gap must be considerably greater than 22.6 per cent. Indeed, the Foreword appears to confirm just such a conclusion when it states that 'pay gaps are even greater for part-time workers (39.9 per cent)'."

I am awaiting a response from the Government Equalities Office. In the meantime, this is what they said last time a letter from Sir Michael dropped on the departmental doormat:

"The 23% gender pay gap figure used by the Government Equalities Office includes both full and part-time employees. With women representing over three-quarters of the UK's part-time workforce, we believe this figure gives the fullest picture of the country's gender pay gap."

Update: In a statement this evening, the government said:

"The WWC is an independent body, and the way they chose to measure the gender pay gap in their report is a matter for them. "The 22.6% gender pay gap figure used in the report is also used by the Government and includes both full and part-time employees. "With 41.9% of women working part-time, and women representing over three-quarters of the UK's part-time workforce, we believe this figure gives the fullest picture of the country's gender pay gap. "As Sir Michael's letter makes clear, GEO has discussed this issue with ONS and the National Statistician has agreed to look at the way the gender pay gap is presented in ONS statistical bulletins."