“Is there a relationship between the locale in which a student attends high school and the likelihood of the student becoming a single parent in the future?”

SPSS

Step 1. I’ll be looking at whether or not there’s a relationship between the locale where a student attended high school (rural, urban, or suburban) and if they ended up becoming a single parent. I grew up in a single parent household and although it was not like this my whole life, when my parents did get divorced I realized how most kids in my school that I was growing up with had both parents but when our school would travel to other areas for sports competitions, I would then realize that there was a greater prevalence of single parents depending on the locale of the school that we visited. My theory is that there is a relationship and that the students who attended high school in a rural and urban locale will be more likely to grow up to be single parents than students who attended high school in a suburban locale.

Step 2. My research question is, “Is there a relationship between the locale in which a student attends high school and the likelihood of the student becoming a single parent in the future?” 

Step 3. Upon visual inspection, it does appear that there is some association between the locale where a student attended high school and the likelihood of them becoming a single parent in the future. In particular, not only were there more suburban students in the sample, but it appears that they were proportionately more likely to not become single parents when they grow up.

Step 4.

1. My null hypothesis is that there is no relationship between the locale where a student attended high school and their likelihood of becoming a single parent. My alternative hypothesis is that there is a relationship between the locale where a student attended high school and their likelihood of becoming a single parent. 

2. The test was conducted at a .05 level of significance.

3. Assumption 1: Each variable met the conditions for a multinomial random variable. Yes, the students in this analysis each were coded with exactly one locale and one yes/no response related to being a single parent and having a child. 

Assumption 2: Every cell in the chi-squared table has an expected count of at least 5 students. Yes, the minimum cell count was 80.

1. Because this was a 2x3 contingency table, there were 2 degrees of freedom, which yields a critical chi-squared value of 5.991 at the .05 significance level. According to the output, p < .001.  

2. Because my 𝜒2-statistic of 1.491 is below the critical value of 5.991, I would fail to reject my null hypothesis. In other words, this is not a statistically significant result. As confirmation of this, I have p < .001, which is well below my .05 level of significance. Because I am failing to reject the null hypothesis, it is possible that I am making a Type II error.

3. Our data suggest that there is no statistical evidence that shows a relationship between the locale in which a student attends high school and the likelihood that the student grew up to be a single parent.

4. Looking at the crosstabs, we see that students who attended high school in an urban locale had a higher chance of becoming a single parent in the future than expected, followed by those who attended high school in a rural locale who also showed a higher chance of becoming a single parent than as expected and slightly fewer students who attended high school in a suburban locale grew up to be single parents. However, the Cramer’s V of 0.011 tells us that the effect size is quite small and of questionable significance.