Full and Free Tutorial about Statistics

Outline of the Video

1. Introduction to Statistics
2. Hypothesis Tests
3. Correlation and Regression Analysis
4. Class Analysis

Part 1: Introduction to Statistics

What is Statistics?

• Definition: Deals with the collection, analysis, and presentation of data.
• Example: Investigating the influence of gender on the preferred newspaper.
• Steps:
  1. Collect data via survey or experiment.
  2. Display the data in a table (variables as columns, responses as rows).
  3. Decide between describing the sample (descriptive statistics) or making population inferences (inferential statistics).

Descriptive Statistics

• Purpose: Describes and summarizes data.
• Key Components:
  1. Measures of Central Tendency: Mean, Median, and Mode.
     • Mean: Sum of all observations divided by the number of observations.
     • Median: Middle value in an ordered data set.
     • Mode: Most frequently occurring value in a data set.
  2. Measures of Dispersion: Variance, Standard Deviation, Range, and Interquartile Range.
     • Standard Deviation: Average distance between each data point and the mean.
     • Range: Difference between maximum and minimum values.
     • Interquartile Range: Middle 50% of the data.
  3. Frequency Tables: Shows how often each distinct value appears in a data set.
  4. Charts: Frequency distribution using bar charts, pie charts, histograms, and box plots.

Inferential Statistics

• Purpose: Draws conclusions about a population using sample data.
• Key Components:
  1. Hypothesis Testing: Method for testing a claim or hypothesis about a population parameter.
     • Null Hypothesis (H0): Assumes no effect or relationship.
     • Alternative Hypothesis (H1): Assumes an effect or relationship exists.
  2. P-Value: Probability of obtaining a sample result, assuming the null hypothesis is true.
  3. Statistical Significance: When P-value < significance level (usually 0.05), reject the null hypothesis.
  4. Type I and Type II Errors:
     • Type I Error: Incorrectly rejecting a true null hypothesis (false positive).
     • Type II Error: Failing to reject a false null hypothesis (false negative).

Part 2: Hypothesis Tests

Common Hypothesis Tests

• T Test: Tests differences between means.
  • One-Sample T Test: Compares sample mean to a known mean.
  • Independent Samples T Test: Compares means between two independent groups.
  • Paired Samples T Test: Compares means from the same group at different times.
• ANOVA: Tests differences among means for three or more groups.
  • One-Way ANOVA: Single independent variable.
  • Two-Way ANOVA: Two independent variables and their interaction effects.
• Non-Parametric Tests: For data not meeting parametric test assumptions.
  • Mann-Whitney U Test: Nonparametric counterpart to the independent T test.
  • Wilcoxon Signed-Rank Test: Nonparametric counterpart to the paired T test.
  • Kruskal-Wallis Test: Nonparametric ANOVA.
  • Friedman Test: Nonparametric test for more than two dependent samples.
• Chi-Square Test: Tests relationships between categorical variables.
  • Assumptions: Expected frequencies > 5.

Part 3: Correlation and Regression Analysis

Correlation Analysis

• Purpose: Measures the relationship between two variables.
• Types:
  1. Pearson Correlation (r): Measures linear relationship between two metric variables.
  2. Spearman Rank Correlation (rs): Measures ordinal relationship or non-linear relationships.
  3. Kendall’s Tau: Another measure of ordinal relationship, useful with many tied ranks.
  4. Point-Biserial Correlation (rpb): Measures relationship between a dichotomous variable and a metric variable.
• Directional Correlation: Positive (both variables move in the same direction) vs. Negative (one variable increases as the other decreases).
• Significance Testing: Determines if the correlation is statistically significant.

Regression Analysis

• Purpose: Predicts a dependent variable based on one or more independent variables.
• Types:
  1. Simple Linear Regression: One independent variable.
     • Model: y = a + bx.
     • Coefficients: Slope (b) and intercept (a).
  2. Multiple Linear Regression: Multiple independent variables.
     • Model: y = a + b1x1 + b2x2 + ... + bnxn.
  3. Logistic Regression: Categorical dependent variable (e.g., yes/no outcomes).
     • Model: Uses logistic function to predict probabilities.

Part 4: Class Analysis

K-Means Clustering

• Purpose: Clusters data into k groups based on similarity.
• Process:
  1. Define the number of clusters (k).
  2. Randomly assign initial cluster centers.
  3. Assign each element to the nearest cluster center.
  4. Update cluster centers based on the mean of the assigned elements.
  5. Repeat steps 3 and 4 until cluster assignments don't change.
• Optimal Clusters: Determined using the elbow method, which plots the reduction in distance versus the number of clusters.