W3: RQ for Associations (Page 22-34) Flashcards
What is the margin of error in confidence intervals.
Are they symmetrical?
Margins of Error
- Lengths from sample estimates to lower bound and to upper bound.
- They can be asymmetrical
What is a two-way contingency table
Two-way contingency table:
Frequency counts of belong jointly to each category of one variable and each category of a second variable
What does a joint cell in a contingency table contain
Frequency count of all participants who belong to both variables a and b
What is the row and column variable on a contingency table called
Marginal Cells.
Note: Marginal Cells will add up to sample size
What can help us understand a two-way table visually
Mosaic Plots
What is a Cramer’s V? Include details such as range and what does it not do?
- Measure of strength of association in contingency table, where at least 1 variable has 3 + categories
- No direction (No intrsinic ordering to 3 or more categories)
- Range: 0 to 1
- Both a sample statistic and population parameter (Though population paramter is unknown, and hence a CI is calculated for the populaton parameter based on the sample statistic)
Does Cramer’s V use words like significant? What are some issues raised in the lecture?
- No use of words like significant
- Because significant has a strict statistical meaning
- No statment that says no association
- Sample data will never tell us the true state of affairs at the population level
- No P-value
- Cramar’s V does not provide, CI is more informative as it contains any information in a p-value
What is an estimator and an estimate
Estimator:
- Function applied to sample statistic to obtain an estimate for a population parameter (Estimate, not a calculation*)
- __Estimate
- Point: Sample statistic value
- CI: Interval estimator
- __Estimate
How many estimators are there for the same population parameter. Why are there different estimators?
- We can have different estimators for the same population parameter and obtain different values
- Point estimate: Different
- Interval estimate: Different
- They have different properties and based on different assumptions
How can estimators of a population parameter vary in 3 properties: What does a 95% unbiased interval estimator do?
Unbias
Captures the true population parameter value 95% of the time on average over the long run
- Biasness does not depend on sample size
How can estimators of a population parameter vary in 3 properties. What does a 95% consistent interval estimator do?
Consistency
- Increasing closer to capturing the true population parameter value 95% of the time on average over the long run as SAMPLE SIZE increase
- Consistency relates to sample size
How can estimators of a population parameter vary in 3 properties. What does a 95% efficient interval estimator do?
Efficiency
Produces a more narrow confidence interval on average over the long run compared to some competing estimator
what is the ideal interval estimator. What sometimes happens
Ideal Interval Estimator:
- Unbiased and very efficient
- Sometimes, a consistency + efficiency is preferred over unbiased + inefficient
What are examples of effect sizes? What is an effect size and how is it estimated? When is it more useful
- Quantitative measure of strength of relationsip between constructed measures.
- Estimated by sample statistics and can be applied to population parameters.
- It is more useful when accompanied by a CI.
- Correlations
- Cramer’s V
- Regression coefficients
- Means
- Mean differences
- Standardised mean differences
- R-Squared
- It is more useful when accompanied by a CI.
When both variables in a contingency table contain 2 categories, what is often used to report effect size
Odds Ratio
