When would a chi-square test of goodness of fit be used versus a chi-square of independence test?
For a chi-square of independence test, state the variables and give an example of a research question.
What are the steps to computing a chi-square?
Lastly, what needs to be reported for a chi-square test of independence?
Sample solution
Dante Alighieri played a critical role in the literature world through his poem Divine Comedy that was written in the 14th century. The poem contains Inferno, Purgatorio, and Paradiso. The Inferno is a description of the nine circles of torment that are found on the earth. It depicts the realms of the people that have gone against the spiritual values and who, instead, have chosen bestial appetite, violence, or fraud and malice. The nine circles of hell are limbo, lust, gluttony, greed and wrath. Others are heresy, violence, fraud, and treachery. The purpose of this paper is to examine the Dante’s Inferno in the perspective of its portrayal of God’s image and the justification of hell.
In this epic poem, God is portrayed as a super being guilty of multiple weaknesses including being egotistic, unjust, and hypocritical. Dante, in this poem, depicts God as being more human than divine by challenging God’s omnipotence. Additionally, the manner in which Dante describes Hell is in full contradiction to the morals of God as written in the Bible. When god arranges Hell to flatter Himself, He commits egotism, a sin that is common among human beings (Cheney, 2016). The weakness is depicted in Limbo and on the Gate of Hell where, for instance, God sends those who do not worship Him to Hell. This implies that failure to worship Him is a sin.
God is also depicted as lacking justice in His actions thus removing the godly image. The injustice is portrayed by the manner in which the sodomites and opportunists are treated. The opportunists are subjected to banner chasing in their lives after death followed by being stung by insects and maggots. They are known to having done neither good nor bad during their lifetimes and, therefore, justice could have demanded that they be granted a neutral punishment having lived a neutral life. The sodomites are also punished unfairly by God when Brunetto Lattini is condemned to hell despite being a good leader (Babor, T. F., McGovern, T., & Robaina, K. (2017). While he commited sodomy, God chooses to ignore all the other good deeds that Brunetto did.
Finally, God is also portrayed as being hypocritical in His actions, a sin that further diminishes His godliness and makes Him more human. A case in point is when God condemns the sin of egotism and goes ahead to commit it repeatedly. Proverbs 29:23 states that “arrogance will bring your downfall, but if you are humble, you will be respected.” When Slattery condemns Dante’s human state as being weak, doubtful, and limited, he is proving God’s hypocrisy because He is also human (Verdicchio, 2015). The actions of God in Hell as portrayed by Dante are inconsistent with the Biblical literature. Both Dante and God are prone to making mistakes, something common among human beings thus making God more human.
To wrap it up, Dante portrays God is more human since He commits the same sins that humans commit: egotism, hypocrisy, and injustice. Hell is justified as being a destination for victims of the mistakes committed by God. The Hell is presented as being a totally different place as compared to what is written about it in the Bible. As a result, reading through the text gives an image of God who is prone to the very mistakes common to humans thus ripping Him off His lofty status of divine and, instead, making Him a mere human. Whether or not Dante did it intentionally is subject to debate but one thing is clear in the poem: the misconstrued notion of God is revealed to future generations.
References
Babor, T. F., McGovern, T., & Robaina, K. (2017). Dante’s inferno: Seven deadly sins in scientific publishing and how to avoid them. Addiction Science: A Guide for the Perplexed, 267.
Cheney, L. D. G. (2016). Illustrations for Dante’s Inferno: A Comparative Study of Sandro Botticelli, Giovanni Stradano, and Federico Zuccaro. Cultural and Religious Studies, 4(8), 487.
Verdicchio, M. (2015). Irony and Desire in Dante’s” Inferno” 27. Italica, 285-297.
Sample Answer
Sample Answer
Chi-Square Test of Goodness of Fit vs. Chi-Square Test of Independence
The chi-square test is a statistical test used to determine if there is a significant relationship between two categorical variables. However, there are different scenarios in which either the chi-square test of goodness of fit or the chi-square test of independence would be more appropriate.
Chi-Square Test of Goodness of Fit
The chi-square test of goodness of fit is used when we want to determine if an observed frequency distribution differs significantly from an expected frequency distribution. This test is typically employed when we have one categorical variable with multiple categories and we want to compare the observed frequencies in each category with the expected frequencies.
For example, let’s say we have a sample of 200 people and we want to determine if their political affiliations differ significantly from what would be expected based on the general population. In this case, our null hypothesis would be that the observed frequencies of political affiliations are equal to the expected frequencies. The alternative hypothesis would be that there is a significant difference between the observed and expected frequencies.
Chi-Square Test of Independence
On the other hand, the chi-square test of independence is used when we want to determine if there is a relationship between two categorical variables. This test is employed when we have two categorical variables and we want to assess whether changes in one variable are associated with changes in the other variable.
For instance, suppose we are conducting a study on gender and voting preference. We want to investigate if there is a relationship between gender (male/female) and voting preference (Republican/Democrat/Independent). The research question could be: “Is there a significant association between gender and voting preference?”
Steps to Computing a Chi-Square Test
To compute a chi-square test, follow these steps:
- State the null hypothesis (H0) and the alternative hypothesis (Ha).
- Set the significance level (alpha) for the test.
- Collect data and create a contingency table, which displays the observed frequencies for each combination of categories.
- Calculate the expected frequencies for each cell in the contingency table. The expected frequency is calculated by multiplying the row total by the column total and dividing it by the overall sample size.
- Calculate the chi-square test statistic using the formula: X2 = Σ((O-E)2 / E), where O is the observed frequency and E is the expected frequency.
- Determine the degrees of freedom (df) for the test, which is calculated as (r-1)(c-1), where r is the number of rows and c is the number of columns in the contingency table.
- Look up the critical value from the chi-square distribution table using the degrees of freedom and significance level.
- Compare the calculated chi-square test statistic with the critical value. If the calculated value exceeds the critical value, reject the null hypothesis; otherwise, fail to reject the null hypothesis.
- Report the results, including the chi-square test statistic, degrees of freedom, p-value, and conclusion about the null hypothesis.
Reporting for Chi-Square Test of Independence
When reporting the results of a chi-square test of independence, it is important to include the following information:
- The chi-square test statistic value (X2).
- The degrees of freedom (df).
- The p-value associated with the test.
- A conclusion about the null hypothesis, indicating whether it should be rejected or failed to be rejected.
For example, “A chi-square test of independence was conducted to examine the relationship between gender and voting preference. The chi-square test statistic was X2 = 16.32 with 2 degrees of freedom, p < 0.001. Therefore, we reject the null hypothesis and conclude that there is a significant association between gender and voting preference.”
In summary, the chi-square test of goodness of fit is used to compare observed and expected frequencies within a single categorical variable, while the chi-square test of independence is employed to assess the relationship between two categorical variables. The steps for computing a chi-square test involve stating hypotheses, collecting data, calculating the test statistic, determining degrees of freedom, comparing with critical values, and reporting the results.
