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Understanding Inferential Statistics and Testing
Oct 2, 2024
Lecture on Inferential Statistics and Hypothesis Testing
Recap and Introduction
Continuing from previous discussions on inferential statistics.
Use of Excel for examples and computations in inferential statistics.
The goal is to develop a universal resource covering various topics, some not directly relevant to the course.
Inferential Statistics Overview
Divided into sections:
Introductive guide (comprehensive but should be named 'introduction').
Guide to Inferential Statistics (includes data sets for computations).
Hypothesis Testing
Concept similar to legal argumentation.
Formal Steps of Hypothesis Testing:
State the Null and Alternative Hypothesis
Null Hypothesis (H0): Assumed true, similar to 'innocence' in court.
Alternative Hypothesis (HA): What we propose if H0 is false.
Example: Testing average height or weight.
Choose a Significance Level
Significance level indicates the accuracy of your testing (e.g., 5% significance level implies 95% confidence).
Compute Test Statistic
Used to reach a conclusion based on sample data.
Compare Test Statistic to Critical Value or P-value
Decide whether to reject the Null Hypothesis.
Example: Testing Hypothesis with Apple Weights
Given sample data of apple weights, hypothesis testing determines if the average weight is 150g.
Importance of understanding the process beyond following patterns.
Chi-Squared Test
Used to test relationships between categorical variables.
Example with apples: Testing relationship between apple color (red, green) and sweetness.
Null Hypothesis:
No relationship between color and sweetness.
Alternative Hypothesis:
There is a relationship.
Procedure:
Compare observed values against expected values if no relationship exists.
Use Excel to perform chi-squared test and interpret results.
P-Value and Significance
P-Value:
Probability of observing a result as extreme as the one observed.
Alpha Value:
Threshold for rejecting the null hypothesis, linked to type I error.
Types of Errors in Hypothesis Testing:
Type I Error:
Rejecting a true null hypothesis (similar to innocent found guilty).
Type II Error:
Accepting a false null hypothesis.
Key Concepts Related to Errors
Importance of understanding type I (worse for morality of law) and type II errors (worse for societal impact).
Analogy to legal system errors (innocent vs. guilty verdicts).
Conclusion and Next Steps
Plan to correct and revisit earlier hypothesis testing example.
Emphasis on understanding concepts and formulas.
Reminder of errors and precautions in analysis, similar to legal proceedings.
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