In terms of our self-esteem measure, describe how looking at this measure from a classical test theory perspective would differ from an item-response theory perspective. mplete the following readings:
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.
Let’s break down how a self-esteem measure would be analyzed from the perspectives of Classical Test Theory (CTT) and Item Response Theory (IRT).
Classical Test Theory (CTT) Perspective:
From a CTT perspective, our focus would be primarily on the overall test score as a reflection of an individual’s true self-esteem, acknowledging that this observed score contains some degree of error. The central equation of CTT is:
X=T+E
Where:
- X = Observed score on the self-esteem measure
- T = True score (the individual’s actual level of self-esteem, which we aim to estimate)
- E = Error score (random fluctuations or factors unrelated to true self-esteem that influence the observed score)
Let’s break down how a self-esteem measure would be analyzed from the perspectives of Classical Test Theory (CTT) and Item Response Theory (IRT).
Classical Test Theory (CTT) Perspective:
From a CTT perspective, our focus would be primarily on the overall test score as a reflection of an individual’s true self-esteem, acknowledging that this observed score contains some degree of error. The central equation of CTT is:
X=T+E
Where:
- X = Observed score on the self-esteem measure
- T = True score (the individual’s actual level of self-esteem, which we aim to estimate)
- E = Error score (random fluctuations or factors unrelated to true self-esteem that influence the observed score)
Here’s how we would analyze our self-esteem measure using CTT:
- Reliability: CTT emphasizes the reliability of the entire test. We would want to know how consistently our measure yields similar scores over time (test-retest reliability), how internally consistent the items are within the test (internal consistency reliability, often measured using Cronbach’s alpha), or how much agreement there is between different administrations or raters (parallel forms or inter-rater reliability, if applicable). A high reliability coefficient (e.g., above 0.70 or 0.80, depending on the context) would suggest that a larger proportion of the variance in observed scores is due to true self-esteem rather than error.
- Validity: CTT also addresses the validity of the test – whether it measures what it is intended to measure (self-esteem). We might examine:
- Content Validity: Do the items on the measure adequately represent the domain of self-esteem? This is often a subjective judgment by experts.
- Criterion-Related Validity: Does the test score correlate with other measures that it theoretically should (concurrent validity) or predict future outcomes related to self-esteem (predictive validity)? For example, we might correlate our self-esteem scores with measures of social anxiety or academic performance.
- Construct Validity: Does the test score relate to other constructs in a way that aligns with the theoretical understanding of self-esteem? This often involves examining correlations with related (convergent validity) and unrelated (discriminant validity) constructs.
- Item Analysis (in a limited way): CTT can involve some basic item analysis, such as calculating the item difficulty (the proportion of respondents who endorse the item in a particular direction) and item discrimination (the extent to which an item differentiates between individuals with high and low overall test scores). For example, we might look at the correlation between an individual item score and the total test score. However, CTT item statistics are sample-dependent; they can change depending on the characteristics of the group taking the test.
- Standard Error of Measurement (SEM): CTT provides an estimate of the SEM, which represents the average amount of error in an individual’s observed score. This helps us create a confidence interval around an individual’s score to estimate the range within which their true score likely falls.
Item Response Theory (IRT) Perspective:
IRT offers a more sophisticated approach by focusing on the individual items within the self-esteem measure rather than just the overall test score. IRT models the probability of a specific response to an item as a mathematical function of the individual’s underlying trait level (self-esteem in this case) and certain item characteristics.
Here’s how we would analyze our self-esteem measure using IRT:
- Item Parameters: IRT estimates item parameters that are assumed to be invariant across different groups of respondents (a key advantage over CTT). Common parameters include:
- Difficulty (b parameter): This indicates the level of self-esteem at which an individual has a 50% probability of endorsing the item in a particular direction (e.g., agreeing with a positive self-esteem statement).
- Discrimination (a parameter): This indicates how well the item differentiates between individuals with different levels of self-esteem. A higher discrimination parameter means the probability of endorsing the item changes more rapidly as self-esteem levels change.
- Guessing (c parameter – less common in self-esteem scales): This represents the probability that an individual with very low self-esteem would still endorse the item (more relevant for multiple-choice tests where guessing is possible).
- Person Parameters (Trait Levels): IRT estimates the trait level (self-esteem) of each individual based on their pattern of responses to all the items. This trait level is typically represented on a continuous scale. Unlike CTT, where the score is simply the sum of items, IRT uses the item parameters to derive a more precise estimate of the underlying trait.
- Item Characteristic Curves (ICCs): IRT allows us to visualize the relationship between an individual’s self-esteem level and the probability of endorsing each item through ICCs. These curves provide detailed information about how each item functions across the range of self-esteem.
- Test Information Function (TIF): IRT provides a TIF, which indicates the precision of the self-esteem measure at different levels of the trait. Unlike CTT’s single reliability coefficient, the TIF shows that the test may be more reliable for individuals with certain levels of self-esteem than others.
- Differential Item Functioning (DIF): IRT allows us to examine whether different groups of individuals (e.g., men and women) with the same underlying level of self-esteem respond differently to specific items. This is crucial for identifying potential bias in the measure.
Key Differences:
| Feature | Classical Test Theory (CTT) | Item Response Theory (IRT) |
|---|---|---|
| Focus | Overall test score | Individual items |
| Reliability | Single reliability coefficient for the entire test | Test Information Function (reliability varies across trait levels) |
| Item Statistics | Sample-dependent (difficulty and discrimination vary by group) | Sample-invariant (item parameters are theoretically stable) |
| Trait Estimation | Summed or averaged item scores | More sophisticated modeling based on item parameters |
| Error Estimation | Standard Error of Measurement (single value for the test) | Standard error of estimation (varies across trait levels) |
| Bias Detection | Limited methods (e.g., group comparisons of item means) | Differential Item Functioning (DIF) analysis for individual items |
| Model Complexity | Simpler statistical models | More complex mathematical models |
| Sample Size Needs | Generally requires smaller sample sizes | Typically requires larger sample sizes for stable item parameter estimates |
In summary:
- CTT would provide us with an overall sense of the reliability and validity of our self-esteem measure as a whole, along with some basic information about the difficulty and discrimination of the items within a specific sample.
- IRT would offer a more nuanced understanding of the individual items, their characteristics, and how they function across different levels of self-esteem. It would provide more precise estimates of individual self-esteem levels and allow us to assess the reliability of the measure at different points on the self-esteem continuum. IRT also offers powerful tools for detecting potential bias in individual items that CTT struggles to address effectively.
Ultimately, IRT provides a more detailed and flexible framework for understanding the psychometric properties of our self-esteem measure compared to the more traditional approach of CTT. However, IRT models are more complex and require larger datasets for accurate parameter estimation. The choice of which theory to apply often depends on the research question, the characteristics of the measure, and the available data.
