concepts and notions for econometrics probability and statistics
TRANSCRIPT
Concepts and Notions for EconometricsProbability and Statistics
Table of contentsProbability: Slide 3
Independence of events: Slide 5
Random variables: Slide 6
Normal Probability: Slide 9
Central Limit Theorem: Slide 21
Hypothesis testing: Slide 27
Mean, median : Slide 36
Variance and standart deviation : Slide 44
Covariance : Slide 47
Z-score : Slide 53
Definition of probability
Conditional probability
Independance of events
Random variables
The Normal Probability Distribution
Properties of the Normal Distribution
The standard Normal Distribution
Point estimate
Sampling distribution
Central Limit Theorem for sample proportions
Central Limit Theorem for sample means
The properties of Central Limit Theorem
Hypothesis testing
Possible Outcomes for a Hypothesis Test
Summary of Hypothesis Tests
Measures of Central Tendancy
Mean or average
By definition of mean
• The most appropriate measure of central tendency will depend on the data. The mode can be used for both qualitative and quantitative data.
• For small data sets (relatively few observations) the mean is influenced by extreme values, but the median is resistant.
• For large data sets (many observations) the mean and median tend to be close to each other.
• The mean is easier to calculate than the median since we do not have to sort the data.
Pros and Cons of the Mean, Median, and Mode
Identifying the Shape of a Distribution
Distribution Shape Mean vs. Median
Symmetric Mean nearly equal to median
Skewed left Mean smaller than the median
Skewed right Mean larger than the median
Variance and standard deviation
Covariance and Correlation
Questions:
What does it mean to say that two variables are associated with one another?
How can we mathematically formalize the concept of association?
Covariance
Correlation (I)
Correlation (II)
Properties of correlation coefficients
Correlation and causation
The Z-score or standard score