Statistical Analysis: ANOVA, Experiments, and Variable Types
Statistical Analysis Definitions and Assumptions
Observational Study: Data is collected without any attempt to manipulate or influence the outcome.
Planned Experiment: Some manipulation is attempted in order to see if the outcome is related to the controlled factor.
Independent Variable: The variable that is manipulated.
Dependent Variable: Variable that is not manipulated but is affected by the independent variable.
Stratification: Units in the sampling frame are first divided into groups.
Simple Treatment:
Read MoreKey Probability Definitions and Rules
Sample Space Definition
A sample space is a collection or a set of possible outcomes of a random experiment. The sample space is represented using the symbol S. The subset of possible outcomes of an experiment is called an event. A sample space may contain a number of outcomes that depend on the experiment. If it contains a finite number of outcomes, then it is known as a discrete or finite sample space.
Probability of an Event
An event in probability can be defined as a set of outcomes of an experiment.
Read MoreEthical Principles, Payroll Deductions, and Accounting Entries
Ethical Principles in Business
Diversity, Integrity, Learning, and Safety are crucial. Unethical behavior includes claiming credit for another’s work, falsifying documents, or obstructing another’s academic tasks to gain an unfair advantage.
It also involves disobeying the rules of ethical research or improperly obtaining access to privileged information and disseminating it. To address ethical issues:
- Identify the Ethical Issues
- Identify the Stakeholders
- Identify Alternative Courses of Action
- Identify
Probability and Statistics: Key Concepts
Sample Space (Ω)
The collection of all possible outcomes of an experiment.
Empty Set (∅)
Indicates that an event E is impossible.
Empirical Probability (EP)
- What is observed.
- Data collection.
- Estimation of some unknown truth.
Theoretical Probability (TP)
What is expected – calculated using mathematical reasoning or computation.
Law of Large Numbers
EP approaches TP as n approaches infinity.
Union of Joint Events (A ∪ B)
A ∪ B: Everything is shaded (“A or B”).
Joint: if they intersect or overlap.
Union of
Read MoreUnderstanding Data Dispersion: Standard Deviation & More
Understanding Data Dispersion
How can we tell if data is dispersed or not?
- There is no clear interpretation of the standard deviation. It depends on the context and our criterion.
- For example, in a sample of screws for technical equipment, where we measure the size of each screw, we expect a dispersion close to zero. Otherwise, it will mean we have to consider lots of screws as defective.
- On the other hand, on a sample of workers in a company and their salaries, we should expect high dispersion in the
Solving First-Order Ordinary Differential Equations
Separable First-Order ODEs
- Separate the variables by putting all terms with “y” on one side of the equation and all terms with “x” on the other side.
- Integrate both sides of the equation with respect to their respective variables.
- Solve for y to find the general solution, adding a constant of integration at the end of the integration step; if an initial condition is given, substitute it to find the particular solution.
Key Steps in Detail
A separable first-order ODE can be written as dy/dx = f(x)g(y)
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