Critical Thinking - Lecture 9 Statistics and Causation
Introduction to Statistics and Causation
The speaker expresses a personal dislike for the module on statistics and causation, noting that it will be made accessible with minimal math involved. The intent is to clear misunderstandings and enhance comprehension of the subject.
Administrative Updates
Surveys for Student Feedback
Two surveys have been introduced for student feedback:
Feedback Survey: Created by the student representative, Jalaya, for discussing any topics or concerns during the semester.
SET Evaluations: General university evaluations to provide feedback on course effectiveness, including remarks about the module and instructor.
Emphasizes that students can express dissatisfaction or commendation regarding the module or instructor during evaluations.
Assignment Feedback
Assignment one marks have been released. Students who believe theirs were marked incorrectly should reach out directly to the instructor.
Common errors identified include:
Standard Form Mistakes: Frequent misunderstanding; although useful, it is not the most critical component of the course.
Argument Evaluation Errors: Particularly important as it will reappear in subsequent assignments and examinations; students are advised to study this area.
Misunderstandings in Assignment Content: Common on question three involving biases and fallacies.
The instructor acknowledges the overall good performance with a B+ average noted, higher than typical.
Upcoming Deadlines and Expectations
Assignment two is due soon; students should review comments and marks promptly after it is returned, as the exam follows shortly thereafter.
Administrative queries about assignments can be directed via Ed Discussion, while content-related queries are best directed to the marker of the assignment.
Understanding Statistics in Causation
Clarification on Content
This module is not an in-depth statistics course focusing on mathematics; it aims to cover conceptual aspects relevant to statistics in relation to reasoning about causation.
The expectation is that students will engage more with concepts rather than mathematical operations.
Sampling in Statistics
Definition: Sampling is the technique used to gather data from a smaller segment of a population to infer conclusions about the entire population.
General Population vs. Sample:
General Population: The complete collection of items or individuals of interest.
Sample: A subset taken from the general population, ideally representative of the larger group.
Importance of representativeness in sampling:
A relevantly similar sample leads to valid analogical reasoning, concluding properties from samples to the general population.
Example illustrating poor sampling:
Sampling frogs on Instagram does not provide accurate reflections of the global frog population due to inherent biases in the sampling method.
Types of Sampling Errors
Procedural Errors: Mistakes during the data collection phase that fail to adhere to established protocols.
Random Sampling Errors: Occur purely by chance; larger sample sizes mitigate this issue.
Systematic Biases: Result from selecting samples in a way that produces skewed results, either intentionally or accidentally.
Example of systematic bias: Asking only certain demographics about opinions on frogs may distort general sentiment.
Avoiding Systematic Bias
Need for randomness in sampling selection:
A true random sample consists of members chosen without bias, yet achieving this is often more challenging than it appears.
Key considerations include ensuring inclusion of diverse populations.
Graphical Misrepresentation of Data
Importance of Proper Graphing
Graphs are often used to visually represent complex statistics; however, they can be abused or misused, leading to incorrect interpretations of the data.
Common pitfalls:
Skewed axes or improperly sized bars.
Omitting relevant data points.
Example of a bad graph:
A graph of average female height that distorts heights through improper scaling of the y-axis.
Importance of Margins of Error:
This outlines the range within which the true population parameter is expected to fall based on sample results.
Introduction to Probability
Probability is the measure of the likelihood that a specific event will occur, often interrelated with causation.
Types of probability relationships:
Independent Events: No impact on each other.
Positive Correlation: Situation where the occurrence of one event increases the likelihood of the others occurring.
Negative Correlation: Where one event’s occurrence decreases the likelihood of the other.
Conceptual Overview
Engaging in non-deductive arguments might blur the lines between probability and causal links; recognizing these distinctions is crucial to avoid erroneous beliefs.
Correlation Interpretation:
While correlation can indicate some form of relationship, it does not confirm causation.
Notable example: Higher ice cream sales correlate with an increase in shark attacks, illustrating a factor (summer) affecting both.
Causation Clarification
Understanding Causation
Causation implies a direct cause-effect relationship between two events.
Correlation does not equate to causation:
Understanding this distinction is critical.
Situations can involve:
Direct cause-effect relationships.
Common causes influencing both events.
Coincidence without any causal factors.
Important example: The correlation between poverty and educational performance highlights complex dynamics, suggesting interconnected but multifaceted causes.
Causal Explanation Construction for Assignments
In the second assignment, students will analyze provided graphs and develop causal explanations following the discussed patterns.
Instructions for Assignment:
Use any of the identified causal connections except for chance explanations; each proposed explanation should adhere to the causal frameworks presented.
Discussion of Psychological Biases
Survivorship Bias
Defined as drawing conclusions based solely on the success of those who 'survived' a selection process while ignoring those who didn't.
Example drawn from World War II regarding plane reinforcement strategies highlights the risk of overlooking those that failed.
Applies to scenarios in various fields (business success, etc.), often leading to distorted views of what contributes to success.
Other Fallacies in Statistics and Causation
Base Rate Fallacy: Misinterpreting data by focusing on the wrong population base.
Correlation Fallacy: Mistaking correlation for causation, exemplified through misleading claims.
Single Cause Fallacy: Assuming that a single factor causes an event despite multiple potential causes.
Overdetermination Fallacy: Assigning a single cause to events where multiple factors may contribute significantly.
Critical Thinking Skills in Analyzing Beliefs
Ruthlessness in Self-Critique
Encourage students to ruthlessly analyze their beliefs for truth and improvement, while remaining mindful of emotional well-being.
Recognize the importance of updating knowledge continuously, especially in rapidly evolving fields.
Closing Remarks
This module serves as a building block for examining critical thinking alongside further philosophical endeavors.
Encouragement for students to apply the concepts learned, particularly in upcoming assignments.
Conclusion
Acknowledgment of student endurance through challenging content.
Invitation to next sessions emphasizing more engaging material related to critical thinking in moral reasoning.
Encouragement to reach out for further clarifications or concerns regarding the material.