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Introduction to Statistics
Module 1
Stanford University
Lecture Notes
Introduction
Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It provides tools and techniques for making decisions and inferences based on numerical data.
Types of Data
Qualitative data: is non-numeric and includes attributes or characteristics such as gender, race, or color. Quantitative data: is numeric and includes measurements or counts such as height, weight, or income.
Scales of Measurement
Nominal scales: are used to classify data into categories or groups, such as colors or types of cars. Ordinal scales: are used to rank or order data, such as rating movies on a scale from one to five. Interval scales: Interval scales have equal intervals between values, but there is no true zero, such as temperature measured in Celsius or Fahrenheit. Ratio scales: Ratio scales have equal intervals and a true zero, such as weight or height.
Populations and Samples
A population is the entire group of individuals, objects, or events that we are interested in studying. A sample is a subset of the population that we collect data from. The goal of statistical analysis is to make inferences about the population based on the sample.
Descriptive Statistics
Descriptive statistics are used to summarize and describe data. Measures of central tendency include the mean, median, and mode, which indicate the typical or central value of the data. Measures of dispersion include the range, variance, and standard deviation, which indicate the spread or variability of the data.
Inferential Statistics
Inferential statistics are used to make predictions or generalizations about the population based on the sample. Probability is the branch of statistics that deals with the likelihood of events occurring. Probability distributions describe the pattern of probabilities for all possible outcomes of a random variable.
Hypothesis Testing
Hypothesis testing is a process of using statistical methods to evaluate whether a hypothesis about a population is supported by the data. The null hypothesis is the assumption that there is no difference or no effect, while the alternative hypothesis is the opposite assumption. The level of significance, or alpha, is the probability of rejecting the null hypothesis when it is true.
