In cknotz/bst290: An R Package To Complement the BST290 (UiS) Course

library(learnr)
knitr::opts_chunk$set(echo = FALSE)

library(bst290)

ess <- bst290::ess

Introduction {data-progressive=TRUE}

In these de-bugging exercises, you continue the analysis of relationship between gender and political participation, and you will look at one of the most central forms of political participation: voting in a national election.

Unlike in the main tutorial, you will here work with the small practice dataset (ess) that is included in the bst290 package.

Variables {data-progressive=TRUE}

The two variables you will work with are:

1. gndr, the respondent's gender;
2. vote, whether or not the respondent participated in the most recent national election in Norway;

question("Which variable is the *dependent* and which is the *independent* variable?",
         answer("`gndr` is the dependent variable, `vote` is the independent variable",
                message = "Nope, wrong! Think again: Which variable is the one that is affected  --- or *depends* on another?"),
         answer("`gndr` is the independent variable, `vote` is the dependent variable",
                correct = T),
         random_answer_order = T, allow_retry = T)

Analysis {data-progressive=TRUE}

Frequency table

First, let's create a simple cross tabulation of the two variables that shows frequencies. The code chunk below is almost complete, but you still have to add one variable:

table(ess$vote, )

**Hint:** Which variable was the independent variable?

This should not have been too difficult: You just needed to add the independent variable, gndr into the table() call:

table(ess$vote,ess$gndr)

Percentage table

A percentage table showing column percentages is a better way to show the relationship between the two categorical variables. Can you complete the code below --- and make sure that you place the variables in the correct positions!

bst290::krysstabell(dataset = ess,
                    rowvar = ,
                    colvar = )

**Hint:** See also Kellstedt and Whitten (2018, p. 168).

This should also not have been difficult: The dependent variable, vote, goes into the row; the independent variable, gndr, goes into the columns:

bst290::krysstabell(dataset = ess,
                    rowvar = "vote",
                    colvar = "gndr")

Running a $\chi^2$ test

The code below is not quite complete --- can you make it run?

table(ess$vote,ess$gndr)
chisq.test()

**Hint:** See the main tutorial, section 4.2.

As shown in the main tutorial, you first create the cross table, store it, and then use it in the chisq.test() function:

crosstab <- table(ess$vote,ess$gndr)
chisq.test(crosstab)

This would also be correct:

chisq.test(table(ess$vote,ess$gndr))

Here, you would directly use the table() result within the chisq.test() call.

Interpretation {data-progressive=TRUE}

Now to the more interesting part: Making sense of the results!

Is the test significant?

First, can you tell if the test is significant?

chisq.test(table(ess$vote,ess$gndr))

question("Is the test significant at a conventional level of significance?",
         answer("Yes, because we get a super high *p*-value of around .75!",
                message = "That is not a correct reading of *p*-values. Maybe you should go over Kellstedt and Whitten (2018, Chapter 8.3) again?"),
         answer("No, because we get a super high *p*-value of around .75!",
                correct = T),
         random_answer_order = T, allow_retry = T)

The critical $\chi^2$ value

Apparently, the test is not significant. But what would have been the critical $\chi^2$ value for this test and a 0.05 level of significance? (Feel free to use the table shown in Kellstedt and Whitten, Appendix A)

chisq.test(table(ess$vote,ess$gndr))

question("The critical value is:",
         answer("3.841",
                message = "Not quite. This would be true at 1 degree of freedom."),
         answer("5.991",
                correct = T,
                message = "Yes, the critical value at 2 degrees of freedom and a 0.05 level of significance is 5.991."),
         answer("7.378",
                message = "No, that is not it. Make sure you use the correct level of significance."),
         answer("42",
                message = "It may be the answer to life, the universe, and everthing  -- but unfortunately not to this question..."),
         random_answer_order = T, allow_retry = T)

Writing up

Now, finally, how would you formulate your interpretation in a paper or report?

chisq.test(table(ess$vote,ess$gndr))

question("I would write:",
         answer("''The test indicates that the relationship between gender and voting is not statistically significant at conventional levels. We can therefore reject the null hypothesis.''",
                message = "Careful! What is the null hypothesis, and when can we reject it?"),
         answer("''The test indicates that the relationship between gender and voting is statistically significant at conventional levels. We can therefore not reject the null hypothesis''",
                message = "Maybe check again: Is the test really significant?"),
         answer("''The test indicates that the relationship between gender and voting is not statistically significant. We can therefore not reject the null hypothesis''",
         correct = T),
         random_answer_order = T, allow_retry = T)

Wrapping up

And that is it! Hopefully, you feel like you now have a solid understanding of how to conduct a tabular analysis in R and how to interpret the results of a $\chi^2$ test.

cknotz/bst290 documentation built on Nov. 11, 2023, 1 p.m.