Descriptive and Inferential Statistics

Descriptive Statistics

• Measures of Central Tendency:
  • Mean: average value of a dataset
  • Median: middle value of a dataset when arranged in order
  • Mode: most frequently occurring value in a dataset
• Measures of Variability:
  • Range: difference between the largest and smallest values
  • Variance: average of the squared differences from the mean
  • Standard Deviation: square root of the variance

Inferential Statistics

• Hypothesis Testing:
  • Null Hypothesis (H0): a statement of no difference or effect
  • Alternative Hypothesis (H1): a statement of difference or effect
  • Test Statistic: a value calculated from the sample data to determine the probability of the null hypothesis
  • P-Value: the probability of obtaining the test statistic (or a more extreme value) assuming the null hypothesis is true
• Confidence Intervals:
  • A range of values within which the true population parameter is likely to lie
  • Confidence Level: the probability that the interval contains the true parameter (e.g. 95%)

Data Visualization

• Types of Plots:
  • Histogram: a graph of frequency vs. value for a single variable
  • Box Plot: a graph of the five-number summary (min, Q1, median, Q3, max) for a single variable
  • Scatter Plot: a graph of two variables to show relationships
• Types of Charts:
  • Bar Chart: a graph of categorical data with bars representing frequencies or proportions
  • Pie Chart: a circular graph showing proportions of a whole

Probability

• Basic Concepts:
  • Experiment: an action or situation that can produce a set of outcomes
  • Outcome: a specific result of an experiment
  • Event: a set of one or more outcomes of an experiment
• Probability Rules:
  • The probability of an event is a number between 0 and 1
  • The probability of the sample space (all outcomes) is 1
  • The probability of the empty set (no outcomes) is 0
  • The probability of the union of two events is the sum of their individual probabilities minus the probability of their intersection

Regression Analysis

• Simple Linear Regression:
  • A model that predicts a continuous outcome variable (y) based on a single predictor variable (x)
  • Equation: y = β0 + β1x + ε
  • Coefficients: β0 (intercept) and β1 (slope)
• Multiple Linear Regression:
  • A model that predicts a continuous outcome variable (y) based on multiple predictor variables (x1, x2, ...)
  • Equation: y = β0 + β1x1 + β2x2 + … + ε

Descriptive Statistics

• Mean is the average value of a dataset.
• Median is the middle value of a dataset when arranged in order.
• Mode is the most frequently occurring value in a dataset.
• Range is the difference between the largest and smallest values.
• Variance is the average of the squared differences from the mean.
• Standard Deviation is the square root of the variance.

Inferential Statistics

• Null Hypothesis (H0) is a statement of no difference or effect.
• Alternative Hypothesis (H1) is a statement of difference or effect.
• Test Statistic is a value calculated from the sample data to determine the probability of the null hypothesis.
• P-Value is the probability of obtaining the test statistic (or a more extreme value) assuming the null hypothesis is true.
• A Confidence Interval is a range of values within which the true population parameter is likely to lie.
• Confidence Level is the probability that the interval contains the true parameter (e.g. 95%).

Data Visualization

• Histogram is a graph of frequency vs. value for a single variable.
• Box Plot is a graph of the five-number summary (min, Q1, median, Q3, max) for a single variable.
• Scatter Plot is a graph of two variables to show relationships.
• Bar Chart is a graph of categorical data with bars representing frequencies or proportions.
• Pie Chart is a circular graph showing proportions of a whole.

Probability

• Experiment is an action or situation that can produce a set of outcomes.
• Outcome is a specific result of an experiment.
• Event is a set of one or more outcomes of an experiment.
• The probability of an event is a number between 0 and 1.
• The probability of the sample space (all outcomes) is 1.
• The probability of the empty set (no outcomes) is 0.
• The probability of the union of two events is the sum of their individual probabilities minus the probability of their intersection.

Regression Analysis

• Simple Linear Regression is a model that predicts a continuous outcome variable (y) based on a single predictor variable (x).
• The equation for Simple Linear Regression is y = β0 + β1x + ε.
• β0 is the intercept and β1 is the slope in Simple Linear Regression.
• Multiple Linear Regression is a model that predicts a continuous outcome variable (y) based on multiple predictor variables (x1, x2,...).
• The equation for Multiple Linear Regression is y = β0 + β1x1 + β2x2 + … + ε.