To answer your question first: Yes, the study shows that divorce and breakup rates are significantly higher for couples where the housework is equally shared or where the man does most of the work.
Oddthinking already linked to the report in Norwegian, the relevant chapter 9 is on the pages 201-214. You can of course run the text through e.g. Google Translate and get a reasonable translation if you are interested in the details. At the end of the study, there is also a short English summary.
I'll try to give a few more details here.
In the introduction, the report refers to a report "Cooke, L. P. (2006). "Doing" gender in context: Household bargaining and risk of divorce in Germany and the United States. American Journal of Sociology 112(2): 442–472.", in which similar correlations have been examined in Germany and the US. They find the same correlation in Germany, whereas in the US, there is an opposite correlation (work sharing couples are more stable).
The Norwegian report is based on a 2007/2008 survey, where couples (married and living together) were asked how they share the housework (female does most of the work, equally shared or the husband does most of the work), if they are satisfied with their marriage (or more exactly: "Have you thought about a breakup within the last year?") and actual statistic data throughout 2011 of their divorces and breakups.
The correlation between housework sharing and relationship satisfaction is shown in chart 9.1 on page 204. The vertical scale is the percentage of the respondents, which have thought about a breakup within the last year. The horizontal scale is from left to right "the woman does clearly most", "the woman does some more", "the work is equally shared" and "the man does most". Women are represented with the square dots, men with the diamond dots.
It shows that:
- Women are most satisfied if the housework is equally shared. They are clearly less satisfied if either of the partners do most of the work.
- Men are most satisfied if the woman does most of the work. The more work is done by the man, the less satisfied he is.
In the following analysis of the actual divorce rates, the respondents are divided into three groups:
A: the woman does most of the work
B: the work is equally shared
C: the man does most of the work
The divorce rates for these groups are found in table 9.2 (page 207). Group A: 3.1%, group B: 4.6%, group C: 5.4%. The numbers were then corrected for several factors, which have known impact on the breakup risk:
- Age - elder people are less likely to breakup
- Education - breakup rates are lower among well educated people
- Children - couples with children are less likely to breakup
- Married or living together - married couples are less likely to breakup than people "only" living together
- Satisfaction - people generally satisfied with the relationship are less likely to breakup
Against the authors' expectations, these corrections emphasized the difference in breakup risk and did not provide any explanation. After corrections, the breakup risk in group B was 50% higher than in group A and 78% higher in group C than in group A.
The report does not find any definitive explanation for these figures. It assumes that the differences in breakup rates can be explained with the respondents' traditional values and attitudes towards work sharing and divorce/breakups. Couples abiding conservative, traditional values are both more likely to let the woman do most of the housework and less likely to breakup or divorce. Couples living a more alternative life style are probably more likely to have untraditional sharing of housework duties and less likely to eager for a stable relationship.
