Introduction to Statistics

Statistics: The Science of Organizing Data

Statistics is the science of organizing data to draw conclusions or answer questions.

Descriptive Statistics

Descriptive statistics describe data through numerical summaries and graphs.

Variables

Variables are characteristics of individuals within the population.

Discrete and Continuous Variables

Discrete variables are counted, while continuous variables are measured.

Nominal and Ordinal Variables

Nominal variables are named, while ordinal variables are ranked or ordered.

Interval and Ratio Variables

Interval variables have no meaningful zero and equal intervals between values, while ratio variables have a meaningful zero.

Types of Variables in a Study

The response variable is what is being studied, the explanatory variable is how much a variable affects the response, confounding variables are factors that affect the response but are not separated, and lurking variables are variables that were not considered in the study. Studies only show association.

Types of Studies

Cross-sectional studies involve a group of people at a specific point in time, case-control studies look to the past to find answers, and cohort studies involve a group of people over a long period of time.

Sampling Methods

Random sampling involves using chance to select individuals. Simple random sampling is selecting names from a hat or random chart. Stratified sampling is cheaper than random sampling and involves separating the population into different groups and obtaining a simple random sample from each group. Systematic sampling involves selecting every nth individual from the population. Cluster sampling involves selecting all individuals within randomly selected collections.

Bias in Sampling

Bias occurs when samples are not representative of the population. Sampling bias can result from undercoverage or favoring one part of the population. Non-response bias occurs when individuals may not respond and have a different opinion. Response bias can result from answers not being worded correctly.

Experimental Design

An experiment is a study conducted to determine the effect of one or more explanatory variables on a response. The treatment is the combination of values or factors being tested. The experimental unit is the person being studied. Matched pairs involve comparing before and after data, such as husband and wife.