Study design and data collection
It is a population-based cross-sectional study design based on the 2011 and 2016 EDHS data. The study used data from the 2011 and 2016 EDHS that were collected by the Central Statistical Authority (CSA) of Ethiopia and Opinion Research Corporation Company (ORC) Macro International. It was conducted in all Regional States of Ethiopia namely Tigray, Afar, Amhara, Oromia, Somali, Benishangul Gumuz, Southern Nations Nationalities and Peoples (SNNP), Gambella and Harari, and in Addis Ababa, and Dire Dawa city Administrations (CSA and ICF, 2016) . It is a nationally representative sample survey, aged 15–49 years’ women.
By considering its national representativeness, the sampling method for the 2016 EDHS sample was stratified and selected in two stages . Each region was stratified into urban and rural areas, yielding 21 sampling strata. The survey collected a detailed woman's background characteristics. The survey also collected information from unmarried, married, living with a partner, divorced, and widowed women. However, for this study, the researcher has used only married women’s data. In this study, spouses from all types of marital unions (religious, cultural, and municipality) were included. Based on the valid number of responses for identified variables, the sample size of the study from 2011 to 2016 DHS data was limited to 8369 and 8403 respectively.
Variables and measurement
The study’s dependent variable was women's autonomy in refusing risky sex. This was measured based on women’s response to ‘Reason for not having sex because of husbands have other women’ [24, 25]. Wives who can refuse sex if husbands have other women were considered as ‘autonomous in refusing risky sex’ and wives who cannot refuse sex if husbands have other women were considered as ‘not autonomous in refusing risky sex’. Finally, the dependent variable that dichotomized as ‘‘autonomous in refusing risky sex’, and ‘not autonomous in refusing risky sex’ was coded as “0” and “1” respectively.
The study identified the following independent variables including women’s age, education status, working status, place of residence, household wealth index, religion, and region. The researcher adopted the measurements of the DHS survey for the following four independent variables. However, the measurements of the DHS survey on the following variables including age, education level, and household wealth index were adapted as follows.
The adapted measurements include (1) age of respondents that was open to writing their exact age, but the study that focused on modern contraceptive use measured age of label age of respondents by labeling from aged 15–24, 25–34, and 35–49 . Since there are few women in marriage since the age of 11, this study used 11–24, 25–34, and 35–49 age categories of women. (2) For educational attainment, the DHS used six responses such as no education, incomplete primary, primary, incomplete secondary, secondary, and higher. As studies were done using DHS data on "the effect of maternal health service utilization in early initiation of breastfeeding among Nepalese mothers" . as well as “women empowerment and their reproductive behavior among currently married women in Ethiopia”  have used 'illiterate', 'primary', 'secondary' and 'higher' to measure this variable, for this study, incomplete primary and primary, and incomplete secondary and secondary merged into 'primary' and 'secondary' respectively. (3) Concerning the wealth index, the middle was taken as it is but the categories poorest and poor, and rich and richest were merged into poor and rich respectively. Similarly, other studies [28,29,30,31] have used these variables to measure the wealth index.
Method of data analysis
The data obtained from 2011 to 2016 EDHS were analyzed through SPSS version 22 in three levels. First, the univariate/descriptive statistics were used to summarize the socio-demographic variables of the study participants using frequency and percentages. Second, the bivariate analysis was done using the chi-square test (p < 0.05) to identify the socio-demographic variables that were significantly associated with women's autonomy in refusing risky sex. Finally, analysis of the determinants of women's autonomy in refusing risky sex was carried out using logistic regression. This is because logistic regression is used to examine the relationships between a categorical outcome variable and one or more categorical or continuous predictor variables . Principally, binary logistic regression is applied in cases where the dependent variable is dichotomous . This is because the dependent variable (women autonomy in refusing risky sex) was dichotomized as “not autonomous in refusing risky sex” and “autonomous in refusing risky sex”.
For binary logistic regression analyses, statistical inferences were made based on estimates of the odds ratio (OR) with a 95% confidence level and 5% margin of error or p-value less than 0.05. The study used an unadjusted odds ratio to estimate the gross effect of each independent variable on the outcome variable. The independent variables that had an association of a p-value less than 0.05 with the outcome variable were taken for the multiple or adjusted analysis.
Before reporting the result of the adjusted odds ratio, the overall goodness of fit was assessed via the Hosmer–Lemeshow test. The result of this analysis's P value (0.606) was greater than the level of significance α = 0.05, hence the data fit the model well. Because in the Hosmer–Lemeshow test, an insignificant chi-square indicates a good fit to the data . In addition, the final model of the logistic regression was assessed for its robustness using methods of checking multicollinearity. It could be checked using the following three methods such as correlation matrices, tolerance, and variance of inflation factors (VIF) . There is a problem of multicollinearity if the correlation of any two variables is 0.8 and more [35, 36]. The result of the correlation matrix analysis of this study was less than 0.8, which indicates an absence of the problem of multicollinearity. In this study, therefore, these indict an absence of multicollinearity problem [35, 37]. The study’s tolerance and VIF values were more than 0.1 and less than 10 respectively. These also indicate an absence of a problem of multicollinearity.