Probability Rules and Statistical Estimation Methods
Probability Theory Fundamentals
Probability Definition
Probability measures the likelihood that an event will occur.
- The probability of an event A is often denoted as P(A). It can be calculated as: P(A) = m / n
- m = number of favorable outcomes for event A
- n = total number of possible outcomes
- P(A) represents the theoretical probability of event A.
Probability is a basic tool in the study and application of statistical methods. Medicine, for instance, often involves probabilistic reasoning.
Properties of
Read MoreKey Concepts in Statistics: Data Analysis and Probability
Key Concepts in Statistics
Data and Variables
Statistics: A branch of science that deals with collecting, organizing, analyzing, interpreting, summarizing, and presenting data.
Unit/Individual: An object on which we take a measurement or observation (e.g., people, places, things).
Population: The collection of all individuals or units under consideration.
Sample: A subset of the population from which we obtain data.
Variable: Any characteristic or property of an individual.
- Quantitative Data: Numerical
Understanding Key Statistical Concepts and Theorems
Law of Large Numbers
If you take samples of larger and larger size from any population, then the mean (x̄) of the sample tends to get closer and closer to μ (the population mean).
Sampling Distribution
The sampling distribution of the mean approaches a normal distribution as n (the sample size) increases.
Central Limit Theorem
The larger the sample size, the more normal the distribution will be.
Standard Error
The standard error is the standard deviation of the distribution of the sample means. T-distributions
Understanding Probability, Distributions, and Statistical Analysis
Understanding Probability
The probability of a given event may be defined as the numerical value given to the likelihood of the occurrence of that event. It is a number lying between ‘0’ and ‘1’. ‘0’ denotes the event which cannot occur, and ‘1’ denotes the event which is certain to occur. For example, when we toss a coin, we can enumerate all the possible outcomes (head and tail), but we cannot say which one will happen.
Permutations
Permutation means arrangement of objects in a definite
Read MoreEpidemiology: Key Concepts and Measures
Proportion: Numerator is always a subset of the denominator; dimensionless (0 to 1 or 0% to 100%).
Rates: Describe changes in one quantity per unit of time. Unit = 1/time. Range (0-infinity).
Risk
Proportion | Dimensionless (can be expressed as a percent) | Appropriate for fixed populations with minimal losses to follow-up because we assume everyone was followed for a specific period.
- New Cases: Numerator. New, non-existing cases. For diseases that can occur more than once, it is the first occurrence
Statistics Essentials: Stem Plots, Quartiles, Correlation
Stem Plots
To make a stem plot:
- Separate each observation into a stem (all but the final digit) and a leaf (the final digit). Stems may have as many digits as needed, but each leaf contains only a single digit.
- Write the stems in a vertical column with the smallest at the top, and draw a vertical line to the right of this column. Include all stems needed to span the data, even with no leaves.
- Write each leaf in the row to the right of its stem, in increasing order out from the stem.