Statistics Lecture Notes

Introduction to Statistics

• Not a specialized statistics class, but important for research.
• Focus on practical application using a website for data analysis.

Why Use Statistics?

• To interpret collected data.
• Analyze differences between groups (e.g., Group A vs Group B).
• Statistical tests like t-test and ANOVA will be used.
• Also look for relationships between variables (e.g., X and Y).

Statistical Tests

• t-test: When comparing two groups.
• ANOVA: When comparing more than two groups.
• Correlation and Regression: To determine relationships between variables.
• Single Sample t-test: Compare data against a hypothetical value.

Understanding Data

• Population vs Sample: Logistical challenges in measuring entire populations, use samples.
• Data Types:
  • Categories (Buckets): Non-numeric data grouped for analysis.
  • Numeric Data: Can be continuous (plotted on number lines) or ordinal.

Graphical Representation

• Pie Chart: Used for showing percentages.
• Column Graph: Compare averages (e.g., test scores of different groups).
• Histogram: Distribution of scores.
• Box Plot: Shows spread, distribution, and outliers.

Statistical Concepts

• Mean, Median, Mode: Measures of central tendency.
• Range: Difference between highest and lowest value.
• Standard Deviation: Gauges accuracy and precision.

Hypotheses in Statistics

• Null Hypothesis (H0): Assumes no difference or change.
• Alternative Hypothesis (H1): Assumes there is a difference.
• Example: Temperature differences between genders.

Statistical Tests & Decisions

• p-value: Indicates probability that differences are due to chance.
• Alpha Value: Acceptable level of randomness (commonly 0.05 or 5%).
• Interpretation:
  • p < 0.05: Alternative hypothesis likely true, difference real.
  • p > 0.05: Null hypothesis likely true, difference due to chance.

Practical Application

• Use of a website for running statistical tests.
• Interpretation of p-values to determine outcomes of tests.