Statistical Tests and Models

Flashcards from lecture notes on statistical tests, distributions, and models.

Mann-Whitney U Test

Non-parametric analogue of the unpaired t-test, used to compare two independent groups when data is not normally distributed.

Tied Ranks in Mann-Whitney U Test

Assign the mean of the potential ranks to tied data.

Null Hypothesis (H0) in Mann-Whitney U Test (Oil Price Example)

The medians of the two groups (January and June oil prices) are equal.

Alternative Hypothesis (H1) in Mann-Whitney U Test (Oil Price Example)

The medians of the two groups (January and June oil prices) are not equal.

Chi-squared distribution properties

If Y1, Y2, and Y3 are independent χ² random variables, then ΣYi is also χ² distributed, with degrees of freedom equal to the sum of the individual degrees of freedom.

Expected Frequencies Assumption for Chi-squared Test

If the expected frequencies assumption for using the χ² test of association fails, Fisher's exact test may be used.

Linear-by-linear procedure

R option to modify the X² statistic for cases where we are dealing with ordinal data in contingency tables.

Generalized Linear Models (GLMs)

Family of distributions considered for generalized linear models: The exponential family.

Linearity in GLMs

The linear predictor must be linear with respect to the coefficients (i.e., Βi).

Poisson Distribution

Typically used to model count data, where we count events over a period of time (e.g., number of calls to a call center).

Log Link Function for Count Data

Used to model count data in GLMs as it avoids obtaining negative counts.

Logistic Regression Dependent Variable Distribution

In logistic regression, the dependent variable must follow a binomial distribution.

Linearity in Logistic Regression

Each continuous independent variable must be linearly related to the logit of the dependent variable.

Odds

P / (1 - P)

Logit(p)

ln(odds)