6  Epistemic

Required reading

Neal (2020, ch. 1-2), Bickel et al. (1975)

Recommended reading

Jones (2020)

6.1 Pitfalls

This section highlights some common pitfalls when dealing with data. Being aware of these pitfalls helps build best practices to maintain the integrity of analyses and visualizations. More pitfalls and explanations can be found in the excellent book by Jones (2020). I recommend reading this book.

Epistemic errors occur when there are mistakes in our understanding and conceptualization of data. These errors arise from cognitive biases, misunderstandings, and incorrect assumptions about the nature of data and the reality it represents. Recognizing and addressing these errors is crucial for accurate data analysis and effective decision-making.

One significant type of epistemic error is the data-reality gap, which refers to the difference between the data we collect and the reality it is supposed to represent. For example, a survey on customer satisfaction that only includes responses from a self-selected group of highly engaged customers may not accurately reflect the overall customer base. To avoid this specific pitfall, it is essential to ensure that your data collection methods are representative and unbiased, and to validate your data against external benchmarks or additional data sources.

The Data-Reality Gap

The difference between the data we collect and the reality it is supposed to represent.

To avoid epistemic errors, critically assess your assumptions, methodologies, and interpretations. Engage in critical thinking by regularly questioning your assumptions and seeking alternative explanations for your findings. Employ methodological rigor by using standardized and validated methods for data collection and analysis. Engage with peers to review and critique your work, providing a fresh perspective and identifying potential biases. Finally, stay updated with the latest research and best practices in your field to avoid outdated or incorrect methodologies.

Another common epistemic error involves the influence of human biases during data collection and interpretation. Known as the all too human data error, this occurs when personal biases or inaccuracies affect the data. An example would be a researcher’s personal bias influencing the design of a study or the interpretation of its results. To mitigate this, implement rigorous protocols for data collection and analysis, and consider using double-blind studies and peer reviews to minimize bias.

All Too Human Data

Errors introduced by human biases or inaccuracies during data collection and interpretation.

Inconsistent ratings can also lead to epistemic errors. This happens when there is variability in data collection methods, resulting in inconsistent or unreliable data. For example, different evaluators might rate the same product using different criteria or standards. To avoid this issue, standardize data collection processes and provide training for all individuals involved in data collection to ensure consistency.

Inconsistent Ratings

Variability in data collection methods that leads to inconsistent or unreliable data.

Understanding and addressing epistemic errors can significantly improve the reliability and accuracy of your data analyses, leading to better decision-making and more trustworthy insights.

Exercise 6.1  

Figure 6.1: Bananas in various stages of ripeness

Source: Jones (2020, p. 33)

  1. Rate the ripeness level of the bananas pictured by Figure 6.1. Compare your assessment to that of a colleague and discuss any differences in your ratings. What might account for the variance in perception of the bananas’ ripeness between you and your colleague?

  2. Specify how you rated the second and the last bananas on the ripeness scale?

  3. Upon reevaluation, it appears that the second and the last bananas are identical in ripeness. How would you justify your initial decision now? This scenario underscores an important lesson for interpreting polls and surveys: it illustrates how subjective assessments can lead to variance in results. It highlights the necessity of ensuring clarity and consistency in the criteria used for evaluations to minimize subjective discrepancies.

Jones, B. (2020). Avoiding data pitfalls: How to steer clear of common blunders when working with data and presenting analysis and visualizations. John Wiley & Sons.

6.2 Correlation does not imply causation

Correlation refers to a statistical relationship between two variables, where one variable tends to increase or decrease as the other variable also increases or decreases. However, just because two variables are correlated does not necessarily mean that one variable causes the other. This is known as the correlation does not imply causation principle.

For example, across many areas the number of storks is correlated with the birth rate of babies (see Matthews, 2000). However, this does not mean that the presence of storks causes an increase in the birth rate. It is possible that both the number of storks and the number of babies born are influenced by other factors, such as the overall population density or economic conditions in the area.

Matthews, R. (2000). Storks deliver babies (p= 0.008). Teaching Statistics, 22(2), 36–38.

Therefore, it is important to carefully consider all possible explanations (confounders) for a correlation and to use data to disentangle the true cause-and-effect relationship between variables.

Figure 6.2: Correlation does not imply causation1

1 Source: https://youtu.be/DFPm_a-_uJM

Tip 6.1

Watch the video of Brady Neal’s lecture Correlation Does Not Imply Causation and Why. Alternatively, you can read chapter 1.3 of his lecture notes (Neal, 2020) which you find here.

Neal, B. (2020). Introduction to causal inference from a machine learning perspective: Course lecture notes. Accessed January 30, 2023. https://www.bradyneal.com/Introduction_to_Causal_Inference-Dec17_2020-Neal.pdf

6.3 Simpsons Paradox

Figure 6.3: Discrimination2

2 Source: The photography is public domain and stems from the Library of Congress Prints and Photographs Division Washington, see: http://hdl.loc.gov/loc.pnp/pp.print.

Discrimination is bad. Whenever we see it, we should try to find ways to overcome it. De jure segregation mandated the separation of races by law is clearly discriminatory. Other forms of discrimination, however, are often more difficult to spot and as long we don’t have good evidence for discrimination, we should not judge prematurely. That means, we should be sure that we see an act of making unjustified distinctions between individuals based on some categories to which they belong or perceived to belong. For example, if men and women are treated differently without an acceptable reason, we consider it discriminative.

However, as the following example discussed in Bickel et al. (1975) will show, it is often challenging to identify discrimination. In 1973, UC Berkeley was accused of discrimination because it admitted only 35% of female applicants but 44% of male applicants overall. The difference was statistical significant and based on that many people protested claiming justice and equality. However, it turned out that the selection of students was not discriminative against women but against men. Accordingly to Bickel et al. (1975) the different overall admission rates can be largely explained by a “tendency of women to apply to graduate departments that are more difficult for applicants of either sex to enter” (Bickel et al., 1975, p. 403). Figure Figure 6.4 taken from Bickel et al. (1975, p. 403) visualizes this fact. Looking on the decisions within the departments seperately, there is even a “statistically significant bias in favor of women” (Bickel et al., 1975, p. 403).

Figure 6.4: Proportion of applicants that are women plotted against proportion of applicants admitted3

3 Source: Bickel et al. (1975, p. 403)

Bickel, P. J., Hammel, E. A., & O’Connell, J. W. (1975). Sex bias in graduate admissions: Data from Berkeley: Measuring bias is harder than is usually assumed, and the evidence is sometimes contrary to expectation. Science, 187(4175), 398–404.

Here is a summary of Bickel et al. (1975, p. 403):

“Examination of aggregate data on graduate admissions to the University of California, Berkeley, for fall 1973 shows a clear but misleading pattern of bias against female applicants. Examination of the disaggregated data reveals few decision-making units that show statistically significant departures from expected frequencies of female admissions, and about as many units appear to favor women as to favor men. If the data are properly pooled, taking into account the autonomy of departmental decision making, thus correcting for the tendency of women to apply to graduate departments that are more difficult for applicants of either sex to enter, there is a small but statistically significant bias in favor of women. The graduate departments that are easier to enter tend to be those that require more mathematics in the undergraduate preparatory curriculum. The bias in the aggregated data stems not from any pattern of discrimination on the part of admissions committees, which seem quite fair on the whole, but apparently from prior screening at earlier levels of the educational system. Women are shunted by their socialization and education toward fields of graduate study that are generally more crowded, less productive of completed degrees, and less well funded, and that frequently offer poorer professional employment prospects.”

Exercise 6.2 Graduate admissions

Read the first three pages of Bickel et al. (1975), i.e., pages 398-400, and answer the following questions. The article can be found here.

  1. Describe the two assumptions that must be true in order to prove that UC Berkeley discriminates against women or men overall.
  2. Table 1, shows that 277 fewer women and 277 more men were admitted than we would have expected under the two assumptions. Show how this number was calculated.
  3. Table 2 of the paper which you find also in Table 6.1 shows admissions data by sex of applicant for two hypothetical departments. Explain the discrimation that is explained in that example.
Table 6.1: Admissions data by sex of applicant for two hypothetical departments
Applicants Admit (observed) Deny (observed) Admit (expected) Deny (expected) Admit (difference) Deny (difference)
Department of Machismatics
Men 200 200 200 200 0 0
Women 100 100 100 100 0 0
Department of Social Warfare
Men 50 100 50 100 0 0
Women 150 300 150 300 0 0
Totals
Men 250 300 229.2 320.8 20.8 -20.8
Women 250 400 270.8 379.2 -20.8 20.8

Source: Bickel et al. (1975, p. 400)

  1. Explain the analogy with fish that illustrates the danger of pooling data.
  1. Assumption 1 is that in any given discipline male and female applicants do not differ in respect of their intelligence, skill, qualifications, promise, or other attribute deemed legitimately pertinent to their acceptance as students. It is precisely this assumption that makes the study of “sex bias” meaningful, for if we did not hold it any differences in acceptance of applicants by sex could be attributed to differences in their qualifications, promise as scholars, and so on. (…) Assumption 2 is that the sex ratios of applicants to the various fields of graduate study are not importantly associated with any other factors in admission. (Bickel et al., 1975, p. 398)
  2. Expectations were taken based on the overall acceptance rate of about 0.416 and multiplied by the total observed numbers of applicants admitted and rejected. For example: \((3738+4704) \cdot 0.41666 \approx 3460\) and \((3738+4704) \cdot (1-0.41666) \approx 4981\). Taking the difference of these two measures gives the number to be explained.
  3. In the department of machismatics no gender discrimination can be observed as 50% of women and men were accepted. Also, in the department of social warfare no gender discrimination can be spotted as 1/3 of women and men were accepted. However, overall only about 38% (250 of 650) of women have been accepted while about 45% (250 of 550) of men were accepted. The latter can be explained by more female applicants in the department with the higher rejection rate.
  4. The analogy is explained on page 400:

“Picture a fishnet with two different mesh sizes. A school of fish, all of identical size (assumption 1), swim toward the net and seek to pass. The female fish all try to get through the small mesh, while the male fish all try to get through the large mesh. On the other side of the net all the fish are male. Assumption 2 said that the sex of the fish had no relation to the size of the mesh they tried to get through. It is false.”

The UC Berkley case is just one of many examples to illustrate that uniformity of group assignment of individuals is a necessary condition to ensure that pooling of data does not lead to misleading conclusions when using statistics. The phenomenon of obtaining different results depending on whether one considers the data pooled or unpooled is often referred to as the Simpson Paradox.

Exercise 6.3 Simpson’s Paradox

  1. What is Simpson’s Paradox?
    1. A phenomenon in which the direction of a relationship between two variables changes when a third variable is introduced
    2. A phenomenon in which the strength of a relationship between two variables changes when a third variable is introduced
    3. The phenomenon where correlation appears to be present in different groups of data, but disappears or reverses when the groups are combined
  2. What is a potential cause of Simpson’s Paradox?
    1. Differences in the variance of the two variables
    2. Differences in the correlation of the two variables
    3. Confounding variables
    4. Differences in the sample size of the two variables
  1. a), 2. c) and d)