Research Methods in Psychology: Key Concepts
Correlation vs. Causation in Research
Karpinski found, in a correlation study, that students who used Facebook had lower GPAs than those who didn’t (3.0 to 3.5 vs. 3.5 to 4.0) and spent less time studying (1-5 hours vs. 11-15 hours). However, correlation doesn’t equal causation. People who prefer more leisure time are more likely to be drawn to distractions like Facebook. Alternatively, students who use Facebook might also spend more time on other non-studying activities, such as sports or music.
Read MoreMerchant Accounting: Essential Record-Keeping Books
Merchant’s Obligatory Books of Record
Every merchant is obliged to have books of record for their accounting and business correspondence. The books that merchants must have are the following:
- The daily book
- The inventory book
- The letter copier
Composition of the Daily Book
In the daily book will be settled, day by day and according to the order in which they are carried out, all the operations that the merchant does. This includes letters or any other credit papers that they give or receive, and in general,
Read MoreStatistical Methods for Data Reduction and Classification
Linear Regression
Linear Regression: Finds the best line that summarizes the relationship between two variables. (Imagine a bunch of dots and a line representing the relationship).
Dimensionality Reduction
A large number of variables results in a dispersion matrix that is too large to study. Dimensionality reduction reduces the number of variables to a few. Why?
- Simpler Analysis: Fewer features make it easier to find patterns.
- Faster Processing (e.g., Trading).
- Better Visualization: It’s easier to visualize
Essential Geometric Definitions and Theorems
Angles and Lines
- Acute Angle: An angle that measures less than 90º.
- Angles: Formed by two rays that share a common endpoint, provided that the two rays are non-collinear.
- Angle Bisector: A ray that contains the vertex and divides the angle into two congruent angles.
- Complementary Angle: A pair of angles that sum 90º.
- Congruent Angles: Two angles are congruent if and only if they have equal measure.
- Corresponding Angles: Angles that are created at the same location at each intersection where a transversal
Understanding Vector Spaces, Linear Algebra, Eigenvalues, and Quadratic Forms
A.1.7. Vector Subspaces
A subset H of a vector space V is a vector subspace if and only if:
- The zero vector 0 is in H.
- For any vectors v1 and v2 in H, their sum v1 + v2 is also in H.
- For any vector v1 in H and any scalar k, the scalar multiple k*v1 is also in H.
Examples of non-vector subspaces:
- Sets defined by polynomial equations.
- Vectors u = (x, y) where xy + x = 0.
- Logarithmic functions.
Examples of vector subspaces:
- Sets defined by linear equations like Ax + By + Cz = 0.
- Sets defined by linear equations
Understanding Floating-Point Representation and Errors
Floating-Point Representation and Errors
t: precision – a positive integer
β: base (or radix) – an integer ≥ 2 (2, 10, 16)
e: exponent – an integer
(decimal) value d1.d2d3 · · · dt × β -> (d1 + d2/β1 + · · · + dt/βt-1 ) × βe
exponent range emin ≤ e ≤ emax
1 + 2*((B -1)B(t-1) * (emax- emin + 1)) norm
1 + 2 * (Bt * (emax – emin + 1)) denorm
Memory stored in 3 fields: sign (1 bit positive negative), exponent (depends on range), fraction or significant (depends on precision)
1 + EpsM
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