If marital status and education are perfectly independent in our population, we may still see some relation in our sample by mere chance. The basic problem is that samples usually differ from populations. However, we can't conclude that this holds for our entire population. Now, marital status and education are related -thus not independent- in our sample. Two categorical variables are independent in some population. The null hypothesis for a chi-square independence test is that So what about the population? Chi-Square Test - Null Hypothesis That is: education “says something” about marital status (and reversely) in our sample. Marital status is clearly associated with education level.The lower someone’s education, the smaller the chance he’s married. If we move from top to bottom (highest to lowest education) in this chart, we see the dark blue bar (never married) increase. This becomes much clearer by visualizing this table as a stacked bar chart, shown below. Our last table shows a relation between marital status and education. More highly educated respondents marry more often If we move towards the lower education levels (leftwards), we see this percentage decrease to 31% for respondents having just middle school. Reversely, note that 64% of PhD respondents are married (second row). If we move rightwards (towards higher education levels), we see this percentage decrease: only 18% of respondents with a PhD degree never married (top right cell). If we inspect the first row, we see that 46% of respondents with middle school never married. Is marital status related to education level and -if so- how? Before reading on, take a careful look at this table and tell me This table shows -for each education level separately- the percentages of respondents that fall into each marital status category. This question is answered more easily from a slightly different table as shown below.
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