Measurement

Measurement is the assignment of numbers to objects to reflect their possession/non-possession or degree of possession of a particular attribute.

Ratio-level

the assignment of numbers to objects to reflect absolute magnitude the zero level is fixed and has meaning ratio comparisons are permitted

Interval-level

the assignment of numbers to objects to reflect magnitudes in terms of differences between differences zero level is not fixed ratio comparisons are not permitted

Ordinal-level

the assignment of numbers to objects to reflect order differences between differences may not be compared ratio comparisons are not permitted

Nominal-level

the assignment of numbers to objects to serve as labels

Population

definable set of entities that are finite and countable.

Census

the recording of one or more characteristics for every member of a population

Sample

a subset of a population.

Random sample

a subset of a population chosen in such a way that every entity in the population possesses an equal chance of being selected.

Stratified random sample

a subset of a population in which different segments have a predetermined number of elements, the number of elements typically corresponding to the size of that segment in the population. Each element within a particular segment has an equal chance of being selected.

Systematic random sample

a subset of a population selected in the following manner: a starting point is chosen at random, then every xth element is selected. x=N/n. (N=population, n=sample size)

Mean

Average Deviation

Variance

Standard deviation

Skewness

Kurtosis

Steps to determine if X and Y are related

Steps to determine if X and Y are unrelated

Scalar

A number

Vector

A column of numbers

Linear combination

A scalar times a vector plus a scalar times a vector,, plus a scalar times a vector . . . etc..

Linear independence

A set of vectors is said to be linearly independent if no vector in the set can be expressed as a linear combination of others in the set..

How to determine linear independence

Calculate F

Linear model

is a linear combination of a set of predictor vectors .

It is a model in the sense that it is intended to reproduce (or fit)) the values for one variable (we call it the dependent variable)) given the values on one or more other variables (we call them the independent variables)).

Full model vs restricted model

To test our hypotheses, we need to create two models — a full model and a restricted model – and compare them in terms of their fit to a set of data. The restricted model is created by imposing a linear restriction on the weights in the full model. If the linear restriction is true, then the restricted model will fit the data almost as well as the full model. If the linear restriction is not true, then the restricted model will not fit the data as well as the full model.

Error sum of square

The error sum-of-squares is a measure of how well our model “fits” the data.

F Statistic

Steps for a 1 independent variable test

Raw values can be included in a regression model when…

variables can be included in a regression model with their original raw values only if they are measured at the interval or ratio level.

Steps for developing a regression model

Adjusted R-Square

Standard Error of the Estimate

t-statistic

the t-statistic is the ratio of the departure of the estimated value of a parameter from its hypothesized value to its standard error. It is used in hypothesis testing.

p-value

When you perform a hypothesis test in statistics, a p-value helps you determine the significance of your results. … The p-value is a number between 0 and 1 and interpreted in the following way: A small p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, so you reject the null hypothesis.

Correlation coefficient