Chi-Square Test for Independence

 
Chi-Square Test for Independence

The General Social Survey (GSS) gathers data on contemporary American society in order to monitor and explain trends and constants in attitudes, behaviors, and attributes. It allows researchers to examine the structure and functioning of society in general as well as the role played by relevant subgroups and to compare the United States to other nations. The GSS contains a standard core of demographic, behavioral, and attitudinal questions, plus topics of special interest. The variables that I have selected for this assignment come from a special module on gender collected in 2012.

You will conduct the following web-based analysis using the Survey Documentation and Analysis (SDA) software to create contingency tables. For this assignment, you will choose a dependent variable (outcome) from the options listed below. You will generate four tables to explore your outcome with four different independent variables and determine if these associations are statistically significant.[1] For each table, I need to see the following:

The null and research hypotheses, clearly stating the variables that you are testing. No x, no y, no general or vague statements.
The contingency table that you will copy and paste on your assignment.
The value of the chi-square test which will be part of the output generated by the software and that you will copy and paste on your assignment.
Your decision regarding the null hypothesis and how you reached that decision. For the decision, you can either use a chi-square table or the chi-square calculator from the Online Statistics Education textbook.
Once you reject or fail to reject the null in the previous step, briefly describe its meaning for the table you are analyzing.

Bonus points: include a brief description of the results presented in the table. What can you say about the results? Are there any visible differences that are worth mentioning? Any patterns or trends? For example, is there an increase (or decrease) in the percentages as education increases (between men and women/as social class increases/between different racial groups) for your particular outcome?

Your choices for dependent variables are the following. Choose one. Remember that you’re analyzing how the dependent variable of your choice is associated with five different independent variables.

famwkbst: categorical variable on the best way to organize family and work life with a child under school age (six categories)
famwklst: categorical variable on the worst way to organize family and work life with a child under school age (six categories)
paidlvdv: categorical variable on how the paid leave period should be divided between the mother and the father (five categories)
Your independent variables are:
sex: dichotomous variable (male or female).
degree: highest degree obtained by interviewee (less than high school, high school, community college, college, graduate).
class: subjective class identification (lower class, working class, middle class, upper class).
race: self-identification (white, black, other)

To generate the tables and the chi-square statistic:
Go to: http://sda.berkeley.edu/sdaweb/analysis/?dataset=gss16.
Your dependent variable will be your “Row” variable and the independent variable will be your “Column” variable. The tables that you will generate must show only column percentages. Type your variables as they appear on italics. The software is not case sensitive but if you misspell the variable, you will get an error message.

First, enter your dependent variable on “Row”; and the first independent variable on “Column”.
Under “Output Options”: for “Percentaging” check “Column”, uncheck “Weighted N”.
Still in “Output Options”: check “Summary statistics” and uncheck “Color coding” under “Other options.”
Add a title that clearly describes the contents of your table. For example, Table 1. Distribution of [insert here your dependent variable] by [insert here your independent variable], 2012. Do not use mnemonics for the variable name.
Under “Chart options”, select “No Chart” for “Type of chart.”
Finally, click “Run the Table.”
Copy the contingency table and the summary statistics table and paste them on a Word document.

Repeat the same steps (1 through 7) for each one of your independent variables.
To assess statistical significance:

Since the SDA software computes both the statistic and the number of degrees of freedom (in parentheses), use this calculator to compare your alpha (0.05) to the p-value: http://onlinestatbook.com/2/calculators/chi_square_prob.html
Use a chi-square table and a probability of 0.95 to find the critical chi-square. Compare the chi-square you got from the SDA software (this is your chi-square obtained) with the critical value from the table. If your chi-square obtained is larger or equal than your critical chi-square, you can reject the null. https://www.itl.nist.gov/div898/handbook/eda/section3/eda3674.htm

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