Calculation of the median time spent in postpartum abstinence

As mentioned earlier, the analysts of the Demographic and Health Surveys uses the children’s data file when calculating the median time spent in postpartum abstinence.

The children’s file contains the variable (b3) which aggregates the date of birth of the concerned child (in months since 1900), as well as a variable informing on the index to the birth history (midx). The data for this variable is coded in an anti-chronological order. For a woman who has three children, for example, the first child will have the index code "3", and the youngest child will be coded as "1".

The formula below corresponds to the exact code used in the final reports of the Demographic and Health Surveys and it was kindly provided by Sarah Bradley in the DHS Program User Forum (Sarah B. 2013). The first step to measure the time spent in postpartum abstinence is to calculate the age of the children in months. To do so, we shall take the date of birth of the child (b3) and subtract it to the date of the interview (v008) in months:

Age in months:

age_months= v008-b3

Calculating the age of the children in months is key to determine the pool of women who could be postpartum abstaining. Indeed, the DHS delimitates the postpartum period to three years after the last delivery. So, we shall only include women whose children are less than 36 months old. For women who had multiple last births (variable b0) (twins, triplets, etc.) we shall (as done in the DHS) only include the information for the second child (as if they were twins). For other women, we will keep only information for the last child.

Postpartum abstinence denominator:

age_months<36 & (b0==0 | b0==2)

We then need to calculate the women postpartum abstaining (v406==1) at the time of the survey for their last child (midx==1) and who are not pregnant (v213!=1), among women who had a child in the last three years (age_months<36 & (b0==0 | b0==2)).

Postpartum abstaining women:

postpartum_abstinence= 0 if age_months<36 & (b0==0 | b0==2) recode postpartum_abstinence 0=1 if v406==1 & v213!=1 &

midx==1

After obtaining the length of postpartum abstinence in months regarding the women who had children in the last three years, we can proceed to calculating the median time spent in postpartum abstinence. It is important to state that many statistical programs (such as STATA) calculate medians and other percentiles as integers, meaning that the program will only provide us with the median category, rather than the correct decimal length exactly matching the 50th percentile. So, in order to figure out the exact median length of the postpartum abstinence, we need to calculate the fractional or interpolated value of the median (Bridgette-DHS 2013).

Case of the children file of Benin 2006, as an example:

Table 2. Extract from the relative and cumulative frequencies of the months spent in postpartum abstinence among married women. Children DHS file, Benin (2006).

If we look at the cumulative percentages, we observe that 49.30% of women spent less than nine months in postpartum abstinence and that 53.76% of them spent less than ten months in this practice. The exact number of months corresponding to the median would fall between nine and ten. Tom Pullum from the Demographic and Health Surveys provides a code to calculate the exact median in STATA (Liz-DHS 2014). For the case of the children dataset of Benin 2006, for example, the syntax goes as follows:

input x P 9 49.30 . 50.00 10 53.76

end regress x P predict xhat

replace x=xhat if x==.

list x P, table clean 4.3.4 Bivariate analysis & the chi-square test

We are now equipped to assess the profile of different kinds of sexually inactive women.

Our first dependent variable will therefore be constituted of sexually active women, lifestyle sexually inactive, pregnant and postpartum amenorrheic, postpartum abstaining, and non-cohabitating. This first analysis will allow us to find out to what extent sexually inactive women are not having intercourse because of externally imposed factors; then, to understand the profile of women with a sexual inactive lifestyle, it will be key to find out if sexually inactive women are really more socio-economically advantaged than the others. These results will provide us crucial indicators regarding the strength of the argument of Bell & Bishai (2017), based, to a great extent, on the supposition that sexually inactive women have a more modern profile, just as the other contraceptive females in sub-Saharan Africa.

Secondly, we shall remove all sexual inactivity that is externally imposed, and create our second dependent variable that will allow us also to compare sexually active and

Months spent in postpartum abstinence % Cumulative %

… … …

8 3.59 49.30

9 4.45 53.76

10 4.03 57.78

… … …

sexually inactive women to contraceptive users. Our variable will therefore be composed of four categories: sexually active women (non contracepting), lifestyle sexually inactive females (non contracepting), traditional users and modern users. As shown in the literature above, contraceptive use will be handy to distinguish the kind of sexual activity that is related to reproduction from the one unrelated to childbearing.

This variable will be key to further understand if the profile of women who have a sexual inactivity lifestyle is more similar to the ones of women who fall into the abstinence-sex-child cycle of reproduction, or rather, if they are closer to women who use contraception as a means of fertility regulation. These elements will be key to understand whether sexual inactivity which is not externally imposed could indeed be used as a preferred alternative to modern or traditional contraception.

We shall then examine the relations and data distribution between our remaining independent variables and our two dependent ones. As explained earlier, our first dependent variable will inform on sexual activity and on the different kinds of sexual inactivity (lifestyle inactivity; during pregnancy or postpartum amenorrhea; postpartum abstinence; and non-cohabitation); and our second variable on sexual activity, and the remaining non-exposure to pregnancy modalities (lifestyle sexual inactivity, traditional contraceptive use and modern family planning), but removing the external constraints to marital coitus define above.

A standard tool in social sciences is to use cross-tabulations that display the distribution of cases across levels of at least two categorical variable. However, the mere examining of tables will not allow us to confirm a statistical relationship between the two variables.

For this, the mathematician Karl Pearson developed the chi-square test of statistical significance (X²) in the 1900s (Plackett 1983), which allows to determine whether the variables are associated or statistically independent. If there appears to be an association between the two variables in the sample, it is then likely that this relationship also exists in the population (Michael 2001; University of West England 2018).

The chi-square test includes four central assumptions. First, although random sampling is not required, it is paramount for the sample not to be biased. Second, it is required that the observations within that sample be independent, implying that the sampling of a person A should not affect the selection of person B. Third, high frequencies are recommended for the chi-square test to work. Expected frequencies should be above five in 80% or more of the cells, and expected frequencies should not go below one (Appendix Formulas & Codes: Formula 1). According to McHugh (2013), if the sample size is at least as large as the number of cells multiplied by five, this assumption is likely to be met. Finally, rows and columns categories need to be mutually exclusive (Michael 2001). In our case, variables are mutually exclusive and we possess a very large and unbiased sample.

The chi-square test starts with the null hypothesis (H0), which postulates that there is no association between our two variables. In our case, we will reject the null hypothesis

(H0) if the significance level (p-value) of our chi-square test is lower than 0.05 (Michael 2001). It is important to note that since our sample is so large, chi-squares will rarely some out as non-significative. However, we believe it is still important to include it in case variables not associated with our dependent one do appear.