Basic Statistics Overview

Definition: Summarizes and describes characteristics of a data set.
Key Measures:
- Measures of Central Tendency:
  - Mean: Average of data values.
  - Median: Middle value when data is ordered.
  - Mode: Most frequently occurring value(s).
- Measures of Dispersion:
  - Range: Difference between the highest and lowest values.
  - Variance: Average of the squared differences from the mean.
  - Standard Deviation: Square root of variance, indicating data spread.
- Skewness: Measure of asymmetry of the data distribution.
- Kurtosis: Measure of the "tailedness" of the data distribution.
Data Visualization:
- Histograms: Graphical representation of frequency distribution.
- Box Plots: Visual summary of minimum, first quartile, median, third quartile, and maximum.

Definition: Uses sample data to make inferences about a population.
Key Concepts:
- Population vs. Sample:
  - Population: Entire group being studied.
  - Sample: Subset of the population used for analysis.
- Estimation:
  - Point Estimate: Single value estimate of a population parameter.
  - Confidence Interval: Range of values within which a population parameter is expected to lie, with a specified level of confidence.
- Hypothesis Testing:
  - Null Hypothesis (H0): Statement of no effect or no difference, tested against an alternative hypothesis (H1).
  - p-value: Probability of obtaining results as extreme as observed, under the null hypothesis.
  - Type I Error: Rejecting a true null hypothesis (false positive).
  - Type II Error: Failing to reject a false null hypothesis (false negative).
- Common Tests:
  - t-test: Compares means between two groups.
  - ANOVA: Compares means among three or more groups.
  - Chi-Square Test: Tests relationships between categorical variables.

Purpose:
- Descriptive: Summarizes data.
- Inferential: Makes predictions or generalizations about a population.
Data Type:
- Descriptive: Describes collected data directly.
- Inferential: Involves interpretation beyond the data collected.
Outcome:
- Descriptive: Provides a snapshot of current data.
- Inferential: Tests hypotheses and estimates population parameters.

Summarizes and describes the main characteristics of a data set.
Measures of Central Tendency include:
- Mean: The arithmetic average of all data values.
- Median: The middle value when the data is arranged in ascending order.
- Mode: The most frequently occurring value(s) within a data set.
Measures of Dispersion provide insights into data variability:
- Range: The difference between the highest and lowest data points.
- Variance: The average of the squared differences of each data point from the mean.
- Standard Deviation: The square root of variance, showing how spread out the data is.
Skewness indicates the asymmetry of the data distribution, while Kurtosis measures the "tailedness."
Data Visualization Techniques:
- Histograms: Display frequency distribution graphically.
- Box Plots: Summarize key statistics including minimum, first quartile, median, third quartile, and maximum.

Utilizes sample data to draw conclusions about a larger population.
Key Concepts include:
- Population vs. Sample:
  - Population: The complete group under study.
  - Sample: A subset used to analyze and infer about the population.
- Estimation Techniques:
  - Point Estimate: A single value that estimates a population parameter.
  - Confidence Interval: A range likely to contain the true population parameter, accompanied by a specified confidence level.
- Hypothesis Testing Basics:
  - Null Hypothesis (H0): Assumes no effect or difference; compared against an alternative hypothesis (H1).
  - p-value: Assesses the strength of evidence against the null hypothesis; lower values indicate stronger evidence.
  - Type I Error: Incorrectly rejecting a true null hypothesis (false positive).
  - Type II Error: Failing to reject a false null hypothesis (false negative).
Common Statistical Tests:
- t-test: Assesses differences between means of two groups.
- ANOVA: Evaluates means across three or more groups.
- Chi-Square Test: Examines relationships in categorical data.

Purpose:
- Descriptive statistics summarize and provide insights on available data.
- Inferential statistics aim to generalize findings from a sample to the broader population.
Nature of Data:
- Descriptive focuses on direct summarization of collected data.
- Inferential involves interpretations and predictions beyond current data.
Outcome:
- Descriptive delivers a current data snapshot.
- Inferential tests hypotheses and estimates population parameters for broader application.