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520
Marriage frequency is measured by marriage rates^{1} or nuptiality rates^{1}, among which the crude marriage rate^{2} gives the ratio either of the total number of marriages to the total population in a given period, or of the number of newlymarried persons (5054) to the total population. The second ratio is, of course, exactly twice the first.
521
The terms male nuptiality^{1} and female nuptiality^{2} are used for the marriage frequency of the different sexes. Sexspecific marriage rates^{3} may be computed with the appropriate population at risk (1342) of each sex as a base. It is usual to distinguish between a first marriage rate^{4} which relates the number of bachelors or spinsters (5153 and 4) marrying to the total number of bachelors or spinsters respectively and a remarriage rate^{5} which relates the number of remarriages to the total number of widowed and divorced persons. Agespecific marriage rates^{6} or agespecific nuptiality rates^{6} are usually computed with the number of marriageable persons in the appropriate sexage group as a base. The average age at marriage^{7} is frequently computed as an indicator of nuptiality.
522
Agespecific nuptiality rates (5216) are often combined in a nuptiality table^{1} which is similar to a life table (4311). The terminology relating to life tables is discussed in paras. 421437. Gross nuptiality tables^{1} trace the history of a cohort (1162) of men or women who reach the minimum age of marriage and are subjected to a set of agospecific nuptiality rates on the assumption that there is no mortality. It is possible to calculate functions analogous to life table functions, as for instance the probabilities of marriage^{2} between birthday x and birthday x + 1, and the numbers remaining single^{3} at various ages. A net nuptiality table^{4} takes death rates as well as marriage rates into account. It is called a double decrement table^{5} or double attrition table^{5} because the population of single persons is subjected to attrition both by death and by marriage. The main functions of the net imptiality table are the single survivors^{6}, persons who remain alive and unmarried at birthday x; the evermarried survivors^{7}, persons alive at birthday x who have been married before that birthday; and the probability of single survival^{8} over a period, generally taken as a year. The expectation of unmarried life^{9} at a given age may be computed according to the gross nuptiality table and the net nuptiality table.
523
A divorce rate^{1} may be calculated in different ways. The crude divorce rate^{2} gives the ratio of the number of divorces to the average population during a given period. The ratio of divorces to the number of married couples is sometimes computed and may be called the crude divorce rate of the married population. Ideally, however, the rate should be the ratio between the divorces taking place in a given period and the number of marriages at risk (1342) of divorce during that period. But there is no accepted terminology. If divorces are tabulated by age of the divorced person or by duration of marriage, agespecific divorce rates^{4} or durationspecific divorce rates^{5} can be computed. Another index of divorce frequency is obtained by computing the number of divorces per new marriage^{6}.
524
Where the requisite basic statistics are available, marriage dissolution rates^{1} may be computed, showing for each sex the probability of the marriage being dissolved by death or divorce according to some combination of age at marriage^{2}, age difference between spouses^{3}, and duration of marriage^{4}. These rates may be combined into marriage dissolution tables^{5} of different kinds.
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