06. Chi-square analysis⚓︎

Module items⚓︎

R Script file⚓︎

Copy the code below ➜ Paste into [[RStudio console]] ➜ Hit Enter

source(url("https://raw.githubusercontent.com/ttezcann/ssric-reg/refs/heads/main/regression/docs/assets/r-scripts/0_packages_data.R")); 
download.file("https://raw.githubusercontent.com/ttezcann/ssric-reg/refs/heads/main/regression/docs/assets/r-scripts/06-chisquare.R", "06-chisquare.R"); 
file.edit("06-chisquare.R")

Lab assignment⚓︎

Chi-square

Sample lab assignment⚓︎

Sample: Chi-square

Learning outcomes⚓︎

1. Learn chi-square analysis
2. Learn how to run chi-square analysis
3. Learn statistical significance

Suggested reading⚓︎

Chi-square basics⚓︎

• The [[chi-square]]test is used to discover if there is a relationship between:
  • Two [[categorical]] variables.
  • The chi-square test can only compare categorical variables.
  • It cannot make comparisons between continuous variables or between categorical and continuous variables.

Functions of variables: Factor variable and outcome variable⚓︎

• A [[variable]]:
  • Depending on the [[functions of the variable]] in the analysis is either:
    • [[Outcome variable]]: the main topic that we investigate. It is the outcome: What is being affected or changed? This is also called the dependent variable.
    • [[Factor variable]]: the variable used to explain or understand the outcome variable (main topic). This is also called the independent variable.
      • A factor variable is assumed to cause a change in the outcome variable.
  • If we consider the "relationship between preferred pet and respondents’ age group" table, we need to ask the following question:
    • In this table, what seems to change what?
      • Someone's preferred pet will not change their age group. However, the opposite could be the case: someone's age group may influence their preferred pet. Therefore:
        • Age group is the [[factor variable]],
        • Preferred pet is the [[outcome variable]].
• We need to identify, logically, which variable plays which role, because the codes we use depend on this distinction.
  • Some variables can function as either a [[factor variable]] or an [[outcome variable]]:
    • For example, we could argue that the level of education increases someone’s income. In this case, education is the factor variable, and income is the outcome variable.
    • In another study, we could argue the opposite: income increases someone’s level of education. In this case, income is the factor variable, and education is the outcome variable.
      • These two research examples are completely different because their factor and outcome variables are defined differently.
  • However, some variables cannot realistically be outcome variables:
    • Nothing can change a person’s age.
    • Similarly, variables such as biological sex (in most survey contexts), place of birth, or past events (e.g., childhood conditions) cannot be outcomes because they are not influenced by other variables in the dataset.
    • These variables can only serve as [[factor variable]]s because they may influence other outcomes:
      • Age → may influence political attitudes, health status, or technology use.
      • Place of birth → may influence language ability or cultural preferences.
      • Biological sex → may influence income, occupation, or health outcomes.

[[Statistical significance]] and p-value⚓︎

• This, and all the analyses in this site, will show the statistical significance, for example, if age group actually influence the preferred pet, meaning if those percentage differences are negligible or not.
• Statistical significance
  • A measure of whether the research findings are meaningful. In other words, if the factor variable causes a change in the outcome variable in a statistically significant way. We will determine this using [[p-value]].
  • A [[p-value]] is a measure of the probability that an observed difference could have occurred just by random chance.
  • The lower the p-value, the greater the statistical significance of the observed difference.
    • All p-values are between 0 and 1;
      • The most reliable studies have p-values very close to 0.
      • A p-value of 0.001 means that there is a 1 in 1000 probability that the results are due to chance and do not reflect a real difference.
      • A p-value of 0.05 means there is a 5 in 100 probability that the results are due to chance.
      • When a p-value is 0.05 or below, the result is considered to be "statistically significant."
        • We refer to statistical significance as p < 0.05.

How to make sure p-value is significant?⚓︎

• [[Is my p-value less than 0.05?]]
  • To determine [[statistical significance]]
    • Use this website: www.whichnumberislarger.com.
      • Put the p-value in the first box, put 0.05 in the second box.
• [[Check asterisks]]

  • To determine [[statistical significance]]

    Check asterisks (*)

    • Our tables and figures will show the statistical significance of the p-values with asterisks.

    • If we see at least one asterisk (*), we will consider that result statistically significant.

      (1) * means p < 0.05
      (2) ** means p < 0.01
      (3) *** means p < 0.001

[[Chi-square]] specifics⚓︎

• When both [[factor variable]] and [[outcome variable]] are [[categorical]], we conduct chi-square.
  • For example, we could wonder if income groups have a statistically significant effect on life satisfaction level:
    • Factor variable: Income groups [(1) Low, (2) Medium, (3)High],
    • Outcome variable: Life satisfaction level [(1)Not satisfied, (2) Moderately satisfied, (3) Satisfied],
      • If the p-value that chi-square test generates is lower than 0.05, we will assume that someone's income group would determine their life satisfaction level.

GSS example 1: Significant p-value (degree and health)⚓︎

Find the variables in Variables in GSS page⚓︎

1. We wonder if respondents' education degree have a statistically significant influence on their perceived personal health quality.
2. We want to make sure that degree and health are categorical variables.
3. We check this information in the Variables in GSS page.

4. Search   Ctrl+F  /  Cmd+F  for the variable names, degree and health. We see that they are categorical variables.

   Variable name	Variable label	Variable type	Question wording and response categories
   degree	Respondents' education degree	Ordinal	Do you have less than high school, high school, associate/junior college, bachelor's, or graduate degree? (0: Less than high school; 1: High school; 2: Associate/junior college; 3: Bachelor's; 4: Graduate)
   health From: Variables in GSS	Perceived personal health quality	Ordinal ✅ RECODE	Would you say that in general your health is Excellent, Very good, Good, Fair, or Poor? (1: Excellent; 2: Very Good; 3: Good; 4: Fair; 5: Poor)

[[Chi-square]] #code⚓︎

• [[Model code]]

  1	sjt.xtab(gss$factor_here, gss$outcome_here, show.row.prc = TRUE)

• [[Working code]]

  1	sjt.xtab(gss$degree, gss$health, show.row.prc = TRUE)

  • Line 1: We will put degree here ➜ factor_here and health here ➜ outcome_here.
    • [[Factor]] varible first, [[outcome]] variable second.
    • Find the working code in this module's R script file. [[Highlighting and running]] this code will create the output below.

[[Chi-square]] #output⚓︎

Perceived personal health quality by respondents' education degree

[[Chi-square]] #interpretation⚓︎

GSS Example 2: Insignificant p-value (sex and happy)⚓︎

Find the variables in Variables in GSS page⚓︎

1. We wonder if respondents' sex have a statistically significant influence on their perceived personal health quality.
2. We want to make sure that sex and happy are categorical variables.
3. We check this information in the Variables in GSS page.

4. Search   Ctrl+F  /  Cmd+F  for the variable names, sex and happy. We see that they are categorical variables.

   Variable name	Variable label	Variable type	Question wording and response categories
   sex	Respondents' sex	Binary	What's your sex? (1: Male; 2: Female)
   happy	Happiness level	Ordinal, RECODE	Would you say that you are very happy, pretty happy, or not too happy? (1: Very happy; 2: Pretty happy; 3: Not too happy)

[[Chi-square]] #code⚓︎

• [[Model code]]

  1	sjt.xtab(gss$factor_here, gss$outcome_here, show.row.prc = TRUE)

• [[Working code]]

  1	sjt.xtab(gss$sex, gss$happy, show.row.prc = TRUE)

  • Line 1: We will put sex here ➜ factor_here and happy here ➜ outcome_here.
    • [[Factor]] varible first, [[outcome]] variable second.
    • Find the working code in this module's R script file. [[Highlighting and running]] this code will create the output below.

[[Chi-square]] #output⚓︎

Happiness level by respondents' sex

[[Chi-square]] #interpretation⚓︎