Introduction to Statistics

Definition of Statistics

• Mathematical science related to:
  • Collection, presentation, analysis, and interpretation of data.
  • Utilized to solve real-world complex problems and make decisions.
  • Involves statistical principles, functions, and algorithms.

Types of Analysis

Statistical Analysis (Quantitative Analysis)

• Involves collecting, exploring, and presenting large data sets to identify patterns/trends.

Non-Statistical Analysis (Qualitative Analysis)

• Provides generic information (text, sound, images).
• Both analyses offer results, but statistical analysis offers more insights, hence vital for businesses.

Categories of Statistics

Descriptive Statistics

• Organizes data and summarizes main characteristics numerically/graphically.
• Example: Heights of students in a classroom (max, min, avg).

Inferential Statistics

• Generalizes larger data sets using probability theory to draw conclusions.
• Example: Heights of students categorized (tall, medium, small) and small samples studied.

Key Statistical Terms

• Population: Entire group data is collected from.
• Sample: Subset of a population.
• Variable: Characteristic of population members which varies.
  • Quantitative Variable: Differ in quantity (e.g., weight).
  • Qualitative Variable: Differ in quality (e.g., color).
  • Discrete Variable: No value between two values (e.g., number of children).
  • Continuous Variable: Any value between two values (e.g., race time).

Statistical Measures

Frequency

• Number of times a data value occurs.

Central Tendency

• Tendency of data to accumulate in the middle.
• Measures: Mean, Median, Mode.

Spread (Dispersion)

• How varied the data values are.
• Measures: Standard Deviation, Variance, Quartiles.

Position

• Exact location of a data value.
• Measures: Percentiles, Quartiles, Standard Scores.

Statistical Analysis System (SAS)

Procedures for Descriptive Statistics

• PROC PRINT: Prints all variables.
• PROC CONTENTS: Describes dataset structure.
• PROC MEANS: Computes descriptive statistics.
• PROC FREQ: Produces frequency tables.
• PROC UNIVARIATE: Conducts basic statistical analyses.
• PROC GCHART: Produces various charts.
• PROC BOXPLOT: Creates box-and-whisker plots.
• PROC GPLOT: Creates 2D graphs.

Inferential Statistics

Hypothesis Testing

• Technique to determine evidence sufficiency to infer population conditions.
• Example: Wages comparison between men and women.
• Hypotheses:
  • Null Hypothesis (H0): Assumed true unless proven otherwise.
  • Alternative Hypothesis (H1): Assumed true if H0 is false.

Variables

• Categorical (Nominal): Multiple categories, unordered (e.g., gender).
• Ordinal: Ordered but unclear relative distances (e.g., size).
• Interval: Ordered, meaningful differences, no true zero (e.g., temperature).
• Ratio: Ordered, meaningful differences, true zero (e.g., height).

Hypothesis Testing with SAS

• Example demonstrates hypothesis testing with T-test.
• Hypothesis: Mean delivery days = 6.
• Alpha value: Probability of error = 0.05.

Hypothesis Testing Procedures

Parametric Tests

• Depend on specified probability distributions.
  • Tests include: T-test, Anova, Chi-square, Linear Regression.

Non-Parametric Tests

• Do not depend on parameter knowledge.
  • Tests include: Wilcoxon rank sum test, Kruskal-Wallis test.

Advantages and Disadvantages

Parametric Tests

Advantages

• Models population parameters.
• Easier modeling and data analysis.

Disadvantages

• Assumes normal data distribution.

Non-Parametric Tests

Advantages

• Fewer assumptions.
• Works with any data.

Disadvantages

• Less efficient, harder to apply to large samples.

End of Lecture